In my latest series for Tournament Poker Edge, I review the key hands and tough decisions that brought me to the final two tables.

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Many poker players are introduced to game theoretical concepts like balance and indifference in the form of a simple example in which one player holds a bluff-catcher and faces a bet from a polarized range. These players tend to understand that there is some sort of theoretically optimal ratio of bluffs to value bets for the betting player, even if they don’t fully appreciate what it is, where it comes from, or why it matters. Likewise, they understand that there exists some optimal calling frequency for the bluff-catching player, though they may not know exactly how to calculate it.

Though not technically wrong, this simple example misrepresents the complexity of the real life situations that arise much more frequently. In fact, most ranges aren’t perfectly polarized, at least not at equilibrium. That is, in the majority of real no-limit hold ‘em situations, there are good game theoretical reasons to bet a variety of types of hands, many of which will not slot into neat categories of “bluff” and “value bet”.

It is in these more complex situations where understanding the game theory behind poker is most valuable. So, while it’s a good starting point to learn the game theory of a simple situation such as the one above, it’s not hard to see why players who understand only this situation fail to see the utility of game theoretical approaches. This article will consider, in broad strokes, the game theory underlying more complex bluffing and bluff-catching scenarios. While it is admittedly not practical (and often not desirable) to memorize and implement perfectly balanced mixed strategies, understanding the basic theory behind these strategies is quite useful for crafting exploitive strategies.

Part One is now live, and the rest should be going up over the course of the next week or so.

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The great thing about this kind of review is that the hand examples come from the smaller stakes tournaments that most members play, which provides plenty of opportunity to talk about what does and doesn’t work against those kinds of opponents.

If you’re not already a member, this is a great time to sign up and get access to this plus dozens of my other videos and hundreds more from other instructors!

Oh and do check out the KL Cleeton interview if you haven’t already, it’s one of my favorites from this year!t

The trickiest problem of all is that you can only collect bounties if you have more chips than your opponents, which means that there must be some disjuncture in chip value. To understand this, consider that everyone else has 7,500 chips and you have 7,499. How much would you pay to be able to add a single chip to your stack? I don’t know to put an exact number on that, but considering that that chip would give you a shot at collecting $500 bounties, it must be a good deal more than $0.1133. Losing a single chip, however, would cost you less than that, because that chip would be nowhere near your last.

Let’s consider another hypothetical. At 50/100, you are in the big blind. You and the player on your right both have exactly the 7,500 starting stack. The action folds to the small blind, who moves all in without looking at his cards. Assuming that you are of exactly average skill in this tournament, what should your calling range be?

Please give it a look and let me know what you think!

Perhaps the biggest thing I’ve learned from them is that their reasons for playing games are quite different from my own. Because I enjoy strategic thinking and find game theory interesting, my favorite games (like poker) involve lots of nuance and meaningful decisions with uncertain outcomes.

Of course, for young children in particular, this kind of thinking is not on their radar at all. Consequently, I’ve suffered through my share of War, Candyland, and other games that involve no meaningful decisions whatsoever (assuming one isn’t trying to take advantage of inevitably marked cards).

Why do children enjoy these games? I believe it is for reasons that they share with many recreational poker players: they enjoy manipulating aesthetically pleasing game pieces (it’s no coincidence that casino chips are brightly colored and have a pleasing size and weight), reveling in the ups and downs that follow from the turn of a card (gambling, essentially, even if there’s nothing of value on the line), and engaging with other people in a friendly and/or competitive pursuit.

Enjoy!

Fortunately, I managed to win the first few pots of the day, first with an open shove to take the blinds, then with an UTG raise which went uncontested, then calling a shove with AT in the BB to beat A9 from the SB for a full double.

After that, I was back in action. As I mentioned, I ended Day 1 with a major regret from the then-largest pot of the tournament, but I can honestly say that from Day 2 I can think of only very small things I wish I’d done differently. A few hands I’m proud of:

Bluff on the Bubble

We’re on the bubble, with 20 players remaining and 18 to be paid. Blinds are 1500/3000, and I raise to 6000 UTG with Tc 8c. The only player at the table to have me covered 3-bets to 12K (he said later this was a misclick and he meant to make it 17K, which I believe), and I call.

Flop (34K) Ks 9h 7h. I check, he bets 15K, I raise to 45K, he calls.

Turn (124K) 4h. I bet 45K, he calls.

River (214K) Qc. I shove about 120K, he folds AK and asks me to show. I oblige.

Better Bet Sizing Through Tells

Still on the bubble. Blinds 1500/3000. The player in the BB has only about 60K to start the hand. An active recreational player with a big stack raises to 7500 from the HJ. I have him covered and raise to 20K. A very tight player in the SB looks at his cards and instantly jams ~65K. I put him on KK at worst and am ready to fold, but then the original raiser calls, so I decide to see a flop.

Edit: I have 66!

Flop (~215K) 884r. Checks through.

Turn 4. Checks through.

River 6. Bingo. Original raiser checks, and I am trying to think about how much he might call just an Ace. In my head, I settle on a small number, 40K.

As I grab chips, he says “Dammit!” and kinda bangs the table. I know that sounds so blatant that it must be an act, but in the moment it really felt like genuine frustration at the fact that he knew I was about to put him in a tough spot. This suggested to me that he would actually consider calling a larger bet, so I bet 75K. After much agonizing, he called with an Ace. The all in player had AA, so I scooped a big one there.

Bluff Catching at the Final Table

Recent podcast guest Chase Bianchi was at the final table of 10 with me (and recent podcast guest Elena Stover finished 12th).

Blinds are 2500/5000. UTG1 limps, Chase limps in MP3, the SB folds, and I check my option with the mighty 42o.

Flop (22,500) Q54r. Checks to Chase, who bets 12,500. I raise to 30K, UTG1 folds, and Chase calls. Lots of good things can happen when I raise. Although I may well have the best hand (I don’t think Chase needs much at all to stab at this), it benefits a lot from protection. It’s even possible that I can push UTG1 off of a better pocket pair and get called when I’m ahead against Chase, if he has a draw or just a random float.

Turn (82,500) 5. I bet 45K. This is actually a pretty nice card for me. Even though it reduces the combos of sets and two-pair that I could have, I still have all of them in my range, whereas Chase has only an ever-dwindling number of 54, 44, and 55, some of which I block (suits are actually relevant here, as I imagine he might limp 54s but not 54o, but I don’t remember them). I don’t know how much Qx or 4x he’s limping, and the turn makes 5x less likely for him.

He calls. I now think his range consists of 76, Qx, pocket pairs, 54, 55, and 44 (at least some of which may check the flop). My plan is to check-call river if the straight draw misses, as I don’t think he has much incentive to jam a better pair for value.

River (172,500) 2. I check, he jams 98K, I call, and he shows 97s, which quite surprising to me. I don’t recall whether he had a backdoor flush draw on the flop, but he definitely did not have a flush draw on the turn, so I guess he just thought he was going to straight up own me. Whoops!

In addition to giving me a comfortable chip lead at the final table, this call had several good effects. It eliminated one of my toughest opponents, and it sufficiently awed most of the table such that they were not inclined to mess around with me.

The Rest

We got down to five-handed with me, a satellite qualifier, a guy named Steve who knew me from Tournament Poker Edge, a likely pro from Michigan, and a guy named Carlos Chadha – more on him in a moment.

The satellite qualifier was absolutely unwilling to put his chips in without a top 5% hand, pot odds be damned. He eventually even folded his SB, leaving himself with just three ante chips. Amazingly, he kept picking up AQ and winning with it to stay alive. Eventually, he busted in 5th place.

The kid from Michigan seemed good-natured at heart, so maybe he was just a bit tilted, because on this particular evening he was acting like a salty circuity grinder. He was the second shortest stack at the table, which meant he was handcuffed by the presence of the satellite qualifier who just wouldn’t die. He was getting frustrated at the guy’s abject refusal to put money in the pot and started just openly commenting on how bad some of his folds were. I was happy to see him go out in 4th.

As I mentioned, Steve knew me from Tournament Poker Edge. Carlos, as it turned out, knew me from Poker Savvy Plus, a pre-Black Friday training site I worked for for several years. He was old school and, now, a high roller. Literally, a super high roller. This $570 was the smallest live tournament he’d ever deigned to play. But he was in the area, and he’d never won a live tournament, and he really wanted to do so.

Much as I hate to admit it, I doubt I was the best player out of the three of us. Carlos had an aura of confidence and deep thought about him, and I never saw him miss a trick. Actually, that’s not quite true. He once called down with an unimproved K2 vs Steve, only to find that Steve was indeed bluffing… with a better King! But I mean, if the biggest “mistake” you’re making is correctly identifying a bluff and calling down with King-high….

A Hero Check

We passed chips back and forth for over three hours. Really the only interesting pot I was involved in began with me raising the button (sorry, I don’t recall the stakes – couldn’t keep notes well while playing short-handed) with Kd Qd. Carlos called in the SB, and Steve called in the BB.

Flop As Td 6c. Checks around.

Turn Jd. Bingo. Carlos checks, Steve bets 75K, I raise to 175K with about 325K behind, Carlos folds, and Steve calls.

River Tc. Certainly not what I wanted to see. I watched Steve like a hawk as the river card came down, and to his credit, he didn’t give anything away as it fell, nor as he checked. Not a lot of people can so casually react to such a significant card with so much on the line, and it was only for that reason that I even considered betting the river. I just couldn’t figure what he could call with, as I think he would have re-raised pre-flop with AK/AQ, A6 and J6 got counterfeited, and from the way he called the turn I didn’t really think he had a bare Ace. I checked and allowed my pride in finding that check to counteract my disappointment in seeing Steve roll AT for a full house.

The End

I eventually busted Steve when he jammed ATs on the button and I woke up with QQ in the SB. That left me heads up with Carlos with nearly even stacks, something like his 1.1M to my 1M. That was only 20 big blinds, so there wasn’t much room to play.

I was hoping I might at least be the more experienced heads up player, but apparently Carlos was an online heads up pro for a while. He certainly seemed to know what he was going on a 20BB stack, which to be honest that part of my game is not particularly tight. I haven’t put much thought into a button limping range, for instance.

It was over quickly, though. Just a few hands in, he limped the button for 50K, and I, now with an 18BB stack, raised to 175K with A7s. He jammed, I called, and he showed me TT. Although I turned a flush draw, I didn’t get there on the river, and Carlos won his first-ever live poker tournament!

Although A7s is a strong hand with just a single opponent and 18BBs, against a weaker player, I might not force the action pre-flop. Against Carlos, though, I didn’t feel like there was any room to pass on thin edges, so I went for the raise-call. Basically it was just a cooler, which in all likelihood was how the match was going to end one way or the other.

We finished play around 12:30, nearly 12 hours after we started, but there’s no rest for the weary. The $1500 Main Event starts today!

I suspect, though, that even if we were to give the Hero a slightly stronger holding, such as QQ, many people would still be reluctant to shove. Why is this?

I believe the overriding cause to be classic loss aversion: at some level; most human brains are more concerned about not-losing than they are about winning. Even when we can expect to win at a favorable, very profitable frequency, our guts may very well tell us to be careful.

Does that sound like you? Did you find the article helpful? Please let me know in the comments!

And don’t miss Carlos Welch’s great piece on How to Develop and Use Reads!

.Next week, Terrence Chan and Adam Schwartz of the 2+2 Pokercast will play DeepStack. I wanted to share some of my thoughts from the match with both them and the Thinking Poker community anyway, so I figure I might as well just collect my thoughts here.

1. Bet Sizes. I haven’t discussed this with the Computer Poker Research Group, but it seems like there are only a few bet sizes that DeepStack considers for its own actions (though, as I understand it, its ability to respond to diverse bet sizes is one of its chief advances over previous NLHE AIs). For instance, into a pot of 1600, it might bet 800, 1600, or 3200, but it would never choose 2291 as a bet size unless that were its exact stack size.

   This strikes me as the best opportunity to exploit DeepStack, though Terrence and Adam are probably more capable than I of determining how exactly to take advantage of that (it wasn’t something I actively tried to do during my match). Considering the range of bet sizes DeepStack does use, I suspect that generally it doesn’t lose much by not considering “weirder” amounts. However, this might be somewhat more problematic with shallow stacks, where never betting less than half pot (if that is even a constraint) might prevent it from having a bet-folding range at all.

2. Threat of a Check-Raise. These were the spots where I felt I had the most difficulty setting aside my “feel” based on how human opponents tend to play and constructing minimally exploitable ranges. There are a lot of spots where (non-elite) human opponents don’t check-raise often. This is for a variety of reasons: lack of “obvious” bluffing candidates, difficulty of checking a strong hand multiple times, etc. As a result, I think I ended up with betting ranges that were sometimes too depolarized (getting raised off of strong draws or very-possibly-best made hands sucks) or simply too wide.

   Example: There was one hand where I turned 84 into a bluff on AJ2Q4, and it check-raised me with 85o!

3. Board Coverage. Nate and I talked a bit about this on stream. This is something you see when working with solvers as well, and is probably related to (2). There are subtle things that DeepStack seems to do when making what might seem like arbitrary choices about candidates for floating or bluffing on early streets. The end result is a less predictable range on future streets.

   For instance, I know that I want to have some Kx in my three-betting range when deep, and I typically choose some combination of KTs – KAs for this purpose. DeepStack almost certainly does a better job of getting the exact frequency right, but even we miraculously had the same amount of Kx in our three-betting ranges, it probably builds its range by three-betting all combinations of Kxs at relatively low frequencies. This means it ends up connecting with boards like Q74 in three-bet pots in ways that I don’t. Likewise its candidates for peeling or bluff-raising flop can seem surprising when the truth is that the choice is arbitrary in a vacuum but there is incentive to reach turns and rivers with a wider variety of holdings than most humans do. Consequently, it’s harder (though still not impossible) to recognize a particular run out as good or bad for DeepStack based on its play on earlier streets.

4. Surprising Play. DeepStack did more than a few things that surprised us. For the most part, we were willing to believe that it “knew” better and could, after the fact, wrap our heads around why it may have done what it did. But it made one play against me that I have a really hard time believing could possibly be correct.

   At 200/400, I opened to 1200 with QTo, and DeepStack jammed 18,250 effective with 85o. When we’re talking about move all in pre-flop, board coverage isn’t going to be a consideration, and although shoving ranges won’t be strictly linear because there will exist hands where calling > shoving > folding, it’s hard to imagine how folding could ever be correct if shoving 85o is +EV here.

   It’s worth adding here that one feature of an equilibrium strategy is that it will not include “advertising” or “balancing” plays, even at a low-frequency, that have a negative expected value. Now admittedly, DeepStack does not claim to have an equilibrium strategy, but the point is that shoving, even at a low frequency, can’t be justified simply by saying it’s a balancing play. It would have to have EV not less than 0 for shoving to be correct at any non-zero frequency.

“You are UTG+1 in a nine-handed $5/$10 game in which all players have $2,000 stacks. The UTG player opens to $40. Consider your action with each of the following hands: AA, AKo, AQs, KQo, JTs, 65s.”

Of course, I go on to help you consider your action, using the theoretical framework from the previous article. Hope you’ll find it useful!

Blinds are 2000/4000/500. Villain is in the BB. He’s a decidedly recreational player and seems VERY level 1/level 2 thinking. That is to, he doesn’t seem to consider his own ranges or what he’s representing. I’ve already seen him get caught in one non-sensical river bluff.

I’d been the most active player at the table, though that wasn’t saying much. Most of my pre-flop raises had been minimum, but in this case I chose a larger size because the BB had a lot of chips and seemed to inclined to defend his BB for that reason. My plan was to raise his BB less aggressively, and to use a larger size when doing so.

I begin the hand with about 120K, Villain covers by a lot (probably one of the chip leaders in the tournament).

Folds to me on the Button with Kd Qs. I raise to 10K. SB folds, BB quickly calls. “You don’t even want to think about folding?” I ask him.

“I thought about it,” he said.

“Did you even look at your cards?”

“Nope. I didn’t think you looked at yours.” This was just banter. I knew he’d looked at his cards, and he knew that I knew.

Flop (26,500 in pot) 7s 7c 4d. Villain very quickly bets 10K. I read this as a very Level 2 sort of play, where he just saw a board that was tough to hit and a player with a wide range and figured he could just bet whatever and I would have to fold if I didn’t have a pair. I think he’s looking for a fold basically always, but that doesn’t rule out his having better hands than mine. This is a shitty line to take with Ace-high, but certainly one that I see from people who are excessively concerned about protection and think too much about whether or not they have a “made hand”.

I called, thinking there was a good chance that I had the best hand. Raising is quite possibly better, though I think there’s a case for letting him put more weak money into the pot before doing so.

Turn (46,500) Ts. Villain bets 15K. I read this as weak, which I still think is correct, but in retrospect it’s weak in a different way. When he bets 1/3 pot, he doesn’t really expect me to fold anything I called the flop with, he just doesn’t want to be raised. This could be a blocking bet from a better hand than mine (Ace-high or small pair) or a set-my-own-price bet with a draw. Either way, I think this should just be a jam. It’s not that much more than a pot-sized raise, and even if it does seem suspect (it’s not really how I’d play many strong hands, though he probably won’t realize that anyway), what’s he going to do, hero it off with A3?

River (76,500) 6s. Villain bets 45K. I’d seen him bluff the river before by grabbing a stack of chips and slamming it down in front of him, one of those strong-means-weak tells that’s so blatant that you wonder whether it isn’t a reverse tell. Combined with the fact that I wasn’t giving his earlier bets much credit, I still didn’t believe him.

The trouble was that I wasn’t sure how many of his bluffs I could beat. Though it would be a terrible bet, I don’t even think it’s impossible that he’s just bluffing with a gutter that rivered a pair because he doesn’t want to check and face a bet (though maybe he’d use more of a blocking sizing for that). But if he got this far with Ace high, I think it’s plausible he fires like this. He sees flop with a LOT of combos of Ax so even if the chance of him playing it this way isn’t high, that still adds up to a fair number of combos.

I decided to jam the river for about 85K total to get him off of all of those “accidental value bets”. He groaned, which was a bad sign, because it meant that he thought he had the best hand when he bet, then reluctantly called with 8s 5s for a flush.

Again, I realize that this seems insane in a vacuum and is in fact legitimately not good, particularly with the last of my chips in a very soft tournament. However, I do think it’s an interesting case of considering all of the options on the table, even if that did lead to a bad decision in this case.

Playing $2/$5 NL. Effective stack $600. Villain is a woman in her mid-20s, has a pro-ey vibe to her. I don’t know that we’ve played together before but I see her around Maryland Live a lot. Don’t remember ever seeing her in bigger games even when they were going at MDL. She always has full buyin+ in front of her, often on phone, chummy with dealers, etc. I haven’t been at table long, don’t know what if anything she thinks of me.

She opens to $20 in HJ, I make it $65 with AA in the CO, folds back to her and she calls without much thought (took less than 10 seconds to consider action, including time while other players folded).

Flop ($130 in pot) Qc 9d 9h. She checks, I bet $65, she calls.

Turn ($260) Kd. She checks, I bet $125, she calls.

River ($510) Ks. She checks. $345 remain in effective stacks.

Y’all prefer checking or shoving?

PS: Apologies to Villain, if she sees this. I’m doing this from memory several days after the fact, so there’s a fair chance I’m messing up some moderately important detail such as a suit and a small chance I’m messing up a really significant detail (it’s happened before).

The first half of my conversation with Matt is available here.

Time for Some Game Theory

It’s probably impossible to find a game theoretically optimal betting strategy for me on the flop, and likewise a calling strategy for Villain, as there are more than two players in the game. The river, however, is a different situation.

It’s quite likely that I’m playing a capped range after checking the turn (which may be sufficient reason not to check). If – and this won’t necessarily be the case, we’ll return to that question – Villain arrives at the river with a mix of nut hands (that beat everything in my range), air (that lose to everything in my range), and hands in between, then this is basically just the AKQ game from Mathematics of Poker, and Villain should probably bet all of his nut hands and all of his bluffs for a size that makes me indifferent between calling and folding with my bluff-catchers.

I hedge a little bit there because even in a straightforward scenario like the one I define above actual poker is a bit more complicated than the AKQ game. Blockers, for instance, can make the actual solutions more complex. Still, this is about as good an approximation as you’ll find for the AKQ game in an actual poker hand.

Hand Reading

The biggest caveat is that Villain may not get to the river a lot of air. As several commenters point out, there are good reasons why he might prefer to bet hands without showdown value on the flop rather than check and call with them.

However, that’s not enough to decide that he’s weighted towards value here, for at least two reasons:

1. Many of his strongest value hands might prefer to bet or check-raise the flop as well. Frankly, the flop check-call probably eliminates many of the hands that would otherwise be most likely to overbet the river, whether for value or as a bluff, including busted draws, sets, and even strong top pair hands. It’s a weird, uncommon line, which often means it’s likely to be unbalanced. However, if we can’t deduce or predict the imbalance, then game theory still provides a way to avoid playing into his hands.
2. One option for “finding bluffs” on the river is to turn a hand with a small amount of showdown value into a bluff. If Villain played a hand like AXhh or bottom pair this way on the flop, he may well conclude that bluffing the river would be higher EV than checking, even though his showdown value was part of the reason he played the flop the way he did.

Why Call?

If I’m roughly indifferent between calling and folding at equilibrium, why should I ever call with a bluff-catcher? It’s an understandable question, but as I argue in my recent article To Catch a Bluff:

Remember that an opponent bluffing at a game theoretically optimal frequency is, well, theoretical. It’s the assumption that we make in the absence of any better estimate of her bluffing strategy. If it turns out that she has a particularly poor strategy, bluffing with hands that are really too strong to turn into bluffs, then your bluff-catchers that break-even against an optimal bluffing strategy will actually make money. So, calling with those hands is a freeroll, as long as you don’t call with so many of them that you end up incentivizing your opponent to stop bluffing entirely.

There remains the question of whether my particular hand is a “pure” bluff-catcher or a better-than-average bluff-catcher. With only a vague idea of what Villain’s exact bluff or value hands might be, it’s hard to say with certainty which blockers could make my hand better-than-average. I’m inclined to think that having a heart would be bad and that blocking a set of 8s, top two pair, and a turned straight is good, but depending on the composition of his range for arriving at the river, these effects may be small or non-existent.

They Always Have It

My favorite response to this post came in a tweet that, sadly, I’m not unable to find. I mentioned posting a WYP about facing an overbet on the river, and someone responded to the effect of, “I didn’t read the post, but I fold.” This is reminiscent of a hashtag I’m fond of using, sometimes with tongue in cheek: #TheyAlwaysHaveIt.

There are lots of reasons why the average player bluffs at a lower-than-optimal frequency in many situations. One is just a simple fear of losing. Human brains tend to be loss-averse, which means that they tend to over-emphasize the consequences of losing a bluff. Mathematically, if a bluff of 150% of the pot will cause 70% of an opponent’s better hands to fold and will never be bluff-raised, then it will show a profit. However, if some part of your brain cares more about the money you lose when the bluff is called than the money you win when the bluff succeeds, then it may convince you that the bluff isn’t worth attempting.

On top of that, it can be hard to find bluff candidates. It’s usually obvious when you have a hand strong enough to value bet, but it’s not always clear which hands are best for bluffing. That’s especially true in a case like this one, where, as I argued above, bluffing at an optimal frequency may require the Villain to bet hands with some showdown value.

Results

#TheyAlwaysHaveIt logic becomes less applicable the more sophisticated your opponent is. I didn’t have much experience with this opponent, but he seemed more than competent, and I didn’t want to pursue an excessively exploitive strategy against him.

My logic went something like this:

1. The base rate for bluffing in this situation is probably too little rather than too much, so applying Bayes’ Theorem should lead me to fold pure bluff-catchers.
2. This opponent seems better than most, and the above logic is exploitable, so I don’t want to deviate too drastically from a balanced calling strategy.
3. My hand may be better than a pure bluff-catcher because of the blocker effect.
4. I call.

Villain had Ah Jh, which makes perfect sense and, to my chagrin, was not a hand I considered. The call kind of feels like a mistake in retrospect, but that may just be results oriented thinking. Thanks for your input, everyone!

If you didn’t donate during the campaign, please enjoy the video and then donate whatever you feel it was worth to you. Thanks!

Edit: Courtesy of Carlos Welch, here are links to the TV footage of the hands we discuss:

Hand 1
https://youtu.be/Cbwe7cP2jQI?t=2393

Hand 2
https://www.youtube.com/watch?v=K2qhk6Xuq0k

Also please note that there’s a typo in the video for Hand 2. The flop was actually 844 with two diamonds.

Flop ($205) Jc 8h 6h. Checks to me, I bet $100, folds back to good pro in HJ who calls.

Turn ($405) 5d. Both check.

River ($405) 2s. Villain bets $600. Hero?

Post your thoughts and preferred play in the comments, and I’ll do my best to respond and post results as well as my own thoughts at the end of the week.

When you three-bet, you’re gearing up to play a big pot, so you ought to come strapped. That doesn’t have to mean Aces, but it should mean a hand with a reasonable chance of winning the pot if you go to the flop. In most cases, the stronger your hand, the higher the Expected Value (EV) of your three-bet will be.

It does not follow from this that you should therefore three-bet a strictly linear range, starting from Aces and working your way down. The complication is that many hands that will have a high EV when they three-bet will also have a high EV when they call. Your job is to decide, when you have a reasonably good hand, whether it will play better as a three-bet or a call in this particular situation.

How do you decide when to three-bet? Was this article helpful to you?

Jamie and I created this video as part of a year-end fundraising campaign for the Bay Area Urban Debate League. Donations are always welcome!

We created this video as part of a year-end fundraising campaign for the Bay Area Urban Debate League.  To unlock more videos like this one and get a shot at some great prizes, please donate to the campaign now!

I folded, and I don’t think it’s close. The short explanation is #TheyAlwaysHaveIt. Here’s a longer one:

Is This a Bluff-Catcher?

The first question to ask is whether Villain could be raising worse for value. If yes, he’s either making a huge mistake, or you should not fold. Here, I think it’s unlikely that worse raises for value. The only lower flushes possible are 52dd and 42dd, which are unlikely in a raised pot, and in any event would be awfully ambitious raises (the “huge mistake” exception.

Some comments mention straights or overpairs raising. I really don’t see that happening. The mistake here, I imagine, comes from thinking of betting or raising primarily in terms of protection, which is in fact a very secondary consideration here. You can’t “protect” a hand that may well be behind already – the cost/risk of putting in a raise drawing dead far outweighs any protection benefit.

Now you might argue that a recreational player may not think in those terms, but most tend to err on the side of being too passive, especially when it comes to large bets. Not to mention that a player excessively concerned about protecting his hand would probably raise the flop, not the turn.

It’s also worth noting that a player overvaluing weaker hands may also overvalue slightly stronger hands such as Q- or J-high flushes, which is of course bad news for us.

In short, Hero has a bluff-catcher. To decide how to play such a hand, we can start by thinking exploitively about whether this is a spot where Villain is likely to over- or underbluff.

Is Villain Bluffing Enough?

This is quite a difficult spot for Villain to bluff, because (a) he’s raising into a player who is uncapped; and (b) in order to bluff, he needs to get to the turn with a hand that has minimal showdown value and that doesn’t mind re-opening the betting.

That last caveat is important, because, as many comments point out, a bare Ad is a hand without showdown value that sees the turn. If the raise were a shove, enabling Villain to realize the equity of his draw, I would consider that plausible. However, most players will, probably correctly, not raise the Ad here for fear of facing a shove. Again, I think that if he were inclined to raise this kind of hand, he’d be more likely to do it on the flop.

Hero does have blockers to higher flushes, making this perhaps a slightly-better-than-neutral-EV bluff catch against an optimal bluffing strategy. However, there are many reasons to think Villain is in fact underbluffing this spot quite severely.

I was glad to see that nobody really took the bait concerning the straight flush redraw. It, too, could make the hand a slightly-better-than-neutral bluff catcher, but it’s not nearly enough to overcome the situational factors here.

Results

I folded, as did the second player, but the Villain showed Ad Kd anyway. Frankly, I think even this is optimistic on his part (after all, I folded a lower flush). If he’s ahead, he probably has us drawing slim to dead anyway, and he blocks the hand most likely to pay him off (a K-high flush). In his shoes, I would call and probably call the river, though I can actually imagine scenarios where I fold his hand.

In my own shoes, I would not have bet my 9d8d on the river had Villain just called turn, and there’s a good chance I would have folded it to a bet. It really is not that high up in my range, as I can have lots of better flushes as well as most full houses.

Playing $5/$10 No-Limit at Maryland Live, a game that does not participate in the Bad Beat Jackpot and other promotions. I don’t have a lot of experience with either Villain, but there’s a good chance they know who I am (a lot of people at MDL, many of whom I’ve never spoken to, have turned out to be familiar with the podcast, blog, or Twitter account). At the very least, I expect they perceive me as a smart player who won’t take anything off of the table in terms of bluffs, hero calls, thin value, etc.

UTG1 is a pro who plays mostly 5/10, don’t think I’ve ever seen him at 10/25. MP is a recreational player about whom I don’t know much.

I’m going to skip straight to the major decision in the hand, because I don’t think the others are terribly interesting, but feel free to ask in the comments if other actions surprise you.

Hero ($2000) opens to $35 UTG with 9d 8d. UTG1 ($3500) calls. Two players fold, and then MP ($1800) calls. Everyone else folds.

Flop ($120 in pot) 7d 6d 3d. Hero bets $80, both call.

Turn ($360 in pot) 3c. Hero bets $220, UTG1 folds, MP raises to $625, Hero?

Post your thoughts here. I’ll do my best to respond throughout the week, and will post my own thoughts as well as results on Friday.

Playing with a short stack can be a good way to learn: it simplifies your decisions, minimizes the magnitude of your mistakes, and helps you focus on fundamentals like pre-flop hand selection and evaluating flop textures. However, it’s important to keep learning as you start playing in deeper games, because strategies that are at least reasonably effective when shallow often become liabilities.

Check out the article, and please let me know whether it’s helpful to you!

In the meantime, here’s my latest strategy article for 2+2 Magazine, entitled “Why So Much?“:

[T]here are many situations where very large (or small, for that matter) bets don’t have to mean anything in particular. They can easily be made with a balanced range, in a way that does not cost the bettor anything with any individual hand in that range relative to a different bet size he could also employ. Learning to distinguish between situations where large bets can be balanced and situations where they can not is the key to determining whether your opponent is revealing anything with any particular bet.

Please check it out and let me know what you think!

My Day 1A table draw was quite tough, I think, given the field. Not a lot went right for me, and I busted just a few hours in.

Day 1B went much better. My starting table was amazing, I was playing six-handed with five pretty weak players and a stack that was in play from the start of the tournament and whose owner never showed up to claim it. By the end of the day, it was blinded off, contributing probably $500 in equity to me!

Despite getting into a number of good spots, I didn’t come out ahead after the first two hours of play. It was only after two better players showed up at the table that I claimed a few big pots.

I didn’t recognize the player who landed on my immediate left, but he fit the stereotype of a twenty-something grinder. He was kind of reserved and aloof and played as though he thought he everyone else was clueless (which, to be fair, several of the others basically were). This also resulted, however, in him doing some extremely exploitable things against me that cost him two large pots.

In the first, blinds are 100/200, effective stacks 40K, and the BB is the dead stack. UTG is a really obviously amateurish player who fumbles his chips and tries to raise to 300 but has to make it 400 and is blatantly not too strong here. However, I also know that this guy doesn’t like to fold to 3-bets and will even make some wild 4-bets, so I’d rather just call him with my T9dd. Problem is I’ve got this kid on my left who I’m pretty sure is going to 3-bet if I just call. So I figure fine, let him do it, we’ll play poker, and I call. Sure enough the kids makes it 2000, UTG calls, and so do I.

Flop is K32 with one diamond. We check to the kid who bets 3000, UTG folds, and I call. I can’t rep any strong hands yet, as I wouldn’t check-raise if I had a monster, but I still don’t think he has anything, and I’m going to find a bluff somewhere if I don’t pair up.

Turn is a 5, which is great because now I can bet into him, which is what I’d actually want to do with a lot of strong hands to keep from taking a free card with Ax. I bet 4000, and he quickly raises to 12K which is just extremely implausible. I mean, I don’t think he’s playing Kx this way, so either he has two-pair or better (even then I’d expect more of an act) or he’s full of it.

Still, it wasn’t easy to force myself to move in for 35K here. I didn’t relish sticking in 200 BBs with T-high no draw, but I really had a lot of confidence that this was going to work. He tanked for a while, during which I had more trouble than usual keeping a good poker face because I kept thinking about how stupid I was going to feel if he called. He eventually, folded, though, after which I felt like a genius.

A while later, at 300/600, there was now another good player at the table, and he opened to 1500 from UTG2. I just called with JJ in the SB, and kid from before raised to 5500 from the BB. This time I was sure he was strong. He wasn’t going out of his way to pick fights with the two best players at the table, especially when he had the option of just calling and seeing a cheap flop. Still, I wasn’t going to fold Jacks, so I called.

The flop came 983ss. I checked, he bet 7K (half the pot), and I called. The turn was a 5, I checked, and he bet 14K, leaving about 60K behind. There was some chance he was barreling AK, but that seemed unlikely, and he definitely didn’t have worse for value. In all likelihood, Jacks were no good. However, I also didn’t think he would have re-raised any smaller pairs or suited connectors when he could so easily call them, so really he couldn’t have better than one pair, while I had lots of sets, two-pairs, and straights in my range. This actually makes it a pretty bad idea for him to bet the turn, unless he just assumes I’m not capable of bluff raising him, because opening himself up to a bluff raise is a disaster. So, I went for it. Again, he tanked a long time, and this time he folded QQ face up!

I came into Day 2 with about twice the average in chips, but with 40% of the field remaining, we were still a ways from the money. A few hours later, my table broke, and I still had roughly the chips with which I’d started the day.

With blinds of 1500/3000/500, a player in middle position opened to 6500. I raised to 16500 with QQ on the button, and he pretty quickly ripped it in for 140K. I wasn’t thrilled, but I called it off with QQ and lost to AA, busting in about 100th place, with 63 paying. I’m not sure it was a good call – Nate and I discuss it a bit on the upcoming podcast.

In practice, though, it’s easy to end up doing either too much or too little bluffing, especially on the river. It’s easy to say either, “this is a good card, bombs away” with all of your bluffs, or to say, “eh, I don’t think he’s folding,” and check back all of your bluffs.

That’s all well and good if you’re confident in those reads, but against a tough opponent, it shouldn’t be easy to make such sweeping generalizations. When thinking about which hands to give up with, it’s good to choose candidates that block Villain’s folding range, just as you want to block his calling range when you fire that third barrel. Here, I bet a big draw on the flop and turn, but on the river, I give up, because I expect that much of Villain’s range for calling turn and folding river will consist of pair-plus-draw hands, and my own draws make it hard for him to have those.

PokerStars – $203+$12|250/500 Ante 65 NL (6 max) – Holdem – 5 players
Hand converted by PokerTracker 4: http://www.pokertracker.com

BTN: 13.38 BB (VPIP: 31.22, PFR: 6.91, 3Bet Preflop: 1.22, Hands: 189)
SB: 134.56 BB (VPIP: 19.00, PFR: 14.51, 3Bet Preflop: 4.65, Hands: 326)
BB: 78.9 BB (VPIP: 21.95, PFR: 15.66, 3Bet Preflop: 2.41, Hands: 205)
Hero (UTG): 86.55 BB
CO: 11.42 BB (VPIP: 17.09, PFR: 9.26, 3Bet Preflop: 2.17, Hands: 118)

5 players post ante of 0.13 BB, SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 2.15 BB) Hero has As Ts
Hero raises to 2.28 BB, fold, BTN calls 2.28 BB, SB calls 1.78 BB, BB calls 1.28 BB

Flop : (9.77 BB, 4 players) 3s Qc 9s
SB checks, BB checks, Hero bets 4.88 BB, fold, fold, BB calls 4.88 BB

Turn : (19.54 BB, 2 players) Jd
BB checks, Hero bets 11.72 BB, BB calls 11.72 BB

River : (42.98 BB, 2 players) 3c
BB checks, Hero checks

BB shows Kd Qs (Two Pair, Queens and Threes)
(Pre 38%, Flop 56%, Turn 64%)

Hero mucks As Ts (One Pair, Threes)
(Pre 62%, Flop 44%, Turn 36%)

BB wins 42.98 BB

DP1: A6o is a tough hand to play, even when only a single opponent with a random hand remains. Raising denies the BB some equity and reduces the likelihood that you’ll have to play out of position after the flop, but it also sets you up to get blown out by a 3-bet or to play out of position against a stronger range in a raised pot. With antes in the pot, I think you have too much value to fold, but both calling and raising are reasonable options.

DP2: QJo is generally a good enough hand to raise for value into a small blind limp, especially because most people will raise the hands that dominate you and call some dominated hands. I’m not sure why I didn’t raise at the time, and I probably should have.

DP3: A few commenters seem to suggest that Villain can just bet the flop with any two cards because Hero will often “miss”, and against weaker opponents that may be true. However, better players are aware of the relative difficulty of making a pair and will defend appropriately to a flop bet, including by calling with strong unpaired hands and by bluff-raising. That’s not to say that Villain should never bluff, but he should expect only his better bluffing candidates to be profitable. Turning a hand with this much showdown value into a bluff is a mistake, as it is surely a profitable check and call.

You might object that since I called with worse, we can think of Villain’s bet as a value bet. However, overall he will not be ahead of my calling range, and many of my worse hands (though probably not this one) will often bluff him out on future streets anyway.

DP4: This is a clear call. Villain could easily be bluffing, and I ought to beat all of his bluffs plus have reasonable equity even against many of his value bets. Things get a bit dicier if he’s betting his Aces, but even then I suspect that I have enough equity to call.

As for raising, many of the same arguments apply as with Villain’s limp: the hand has too much value to turn into a bluff, at the moment anyway. On runouts that improve my weaker flop calls, I may end up bluffing with this, as it would then be the bottom of my range.

DP5: Villain’s flop bet, along with this turn card, killed any showdown value his hand had, so now it is a bluffing candidate along with the rest of the air he ought to have bet on the flop. However, Villain ought to have other bluffs with better equity available to him and probably ought to give up on this one.

Essentially, he’s got an Ed Miller pyramid problem here. His flop betting range was too wide, and now on the turn he’s going to hold too many weak hands and will have to get rid of them somehow. He can either keep bluffing, which will make my bluff-catches very profitable, of he can just check and fold, which with this hand at least is the better option.

DP6: An easy call. Villain may not be value betting worse, but even so, I have a very solid bluff-catcher. The hand is too strong to raise as a bluff and not strong enough to raise for value.

DP7: Another pyramid problem. Once again, if Villain is getting to the river with too much air and bluffing with all of it, then my bluff catches will be very profitable. This is certainly a board that favors his range, but that doesn’t mean that he’s guaranteed a profitable bluff when he doesn’t have any blockers to my calling range.

DP8: This is a clear call, though not a super-profitable one (unless Villain is bluffing too much, which this one, in retrospect, seems to have been), as I block JT and KQ or other turned two-pairs. Many players won’t go for a third street of value with top pair, at least not for this size, but even against those who do, I expect this to be a profitable call.

PokerWilo asked about my plan for future streets. While it will depend heavily on the runout, I think there’s an underlying assumption to address here, which is that I need to be able to call future barrels. This would be true if we had reason to believe that Villain would always or usually barrel off after betting the flop, and in retrospect it seems like this one might.

However, that’s not information that I had at the time. All I knew is that Villain might keep betting, and he might not. That means that, no matter the turn card, I need to have some bluff-catchers that fold to further bets and some that do not. That way, I punish (or at least do not reward) both players who give up too often and those who barrel too often. On many turn cards, QJ will be in my folding range, but on this one, it’s in my calling range. In a vacuum, there’s nothing wrong with having a range of hands that will call once and fold to further action – in fact, it’s correct.

Thanks for playing, everyone!

The Game: $200 6-max WCOOP Event (Sunday Warm-Up Replacement). Blinds 1600/3200/400. Villain has 145K, Hero has 175K.

Reads/History: Assume each player knows the other to be a successful and experienced tournament player.

Decision Point 1: Villain open-limps As 6d in the small blind.

DP 2: Hero checks Qc Js in the big blind.

Flop (8800 in pot): Kc 8c 3s

DP3: Villain bets 3200.

DP4: Hero calls.

Turn (15200 in pot): Qd.

DP5: Villain bets 7750.

DP6: Hero calls.

River (30700 in pot): 9h

DP 7: Villain bets 22950.

DP8: Hero calls.

Leave a comment about any decision point(s) you find surprising or mistaken, and I’ll share my thoughts later in the week.

One additional note that may be helpful: try to think not just about whether Villain should bluff at all in these spots (he should) or whether Hero should ever call with less than the nuts (he should) but rather whether these specific hands are good for those purposes on each street.

Interestingly, though, Qs Ts is a pure bet for 75% of the pot on the river, so I was off there (it strictly folds to a raise). GTORB shows Villain folding T7 98% of the time on the turn, which probably means it’s strictly a fold and the results just didn’t quite converge, rather than that Villain is truly indifferent between calling and folding.

At the same time, it enables you to play many more hands/hour very without having to multitable.

How much of an edge do you feel like you’re giving away, if any at all, when playing zoom poker, instead of regular cash games? Would you recommend that those trying to build a bankroll stay away from it? 

A: We generally measure win rates in bb/100, or average number of big blinds won for every hundred hands you play. If you’re a professional or trying to play like one, though, then the metric you really care about is your hourly rate, or the average amount of money you can expect to win for every hour you play in a given game. This is why it can make sense to move up in stakes, even though the higher stakes game will be higher: you can afford to have a lower bb/100 if the big blinds you’re winning are worth more.

When you’re playing online, there are other ways of increasing your hourly rate besides playing higher stakes. You can play multiple tables at once, or you can play “fast-fold poker”, such as Zoom Poker, which many sites now offer. These options similarly offer the potential for a higher hourly rate, generally at the expense of your bb/100.

When multi-tabling, it’s easy to see why more tables means a lower win rate: you can’t pay as much attention to any given game, and so you miss out on forming reads and sometimes can’t focus on a single important decision because you have to act on other tables.

Fast-fold games also tend to mean lower win rates, because they appeal to professionals who are eager to maximize their hands (and winnings) per hour. It’s important to note that these games also appeal to recreational players looking for quick action, because they don’t have to wait around watching others play. I think the biggest problem you’ll find in these games is not that there aren’t fish (though maybe that’s changed over time, as losing players find that they lose money more quickly in these games), but that the pro:fish ratio may be less good, and that the best players are better than their counterparts in regular speed games.

That still doesn’t really answer the question of what’s best for you. Hopefully it helps you to frame a bit differently, though. In all likelihood, the comparison you should be making is not “Should I play regular speed or Zoom $.25/$.50?”, but rather “Should I play regular speed $.25/$.50 or Zoom $.10/$.25?” You’ll have to see where you feel more comfortable and where your hourly rate seems to be highest.

Two other considerations: depending on what you mean by “building a bankroll”, you may also care about reducing variance, in which case, out of two games that offer comparable hourly rates, you’d probably prefer the easier game where your win rate is higher. However, you’ll play more hands and get more experience at the Zoom tables. So again, there’s still a subjective decision you’ll have to make!

It’s called Rate Our Play. I’m going to post a hand featuring multiple decisions points for both myself and my opponent(s). Your job will be to comment on any mistakes (or choices that surprised you in a good way) that you think either of us made. I’ll participate in the comments as I can and return later in the week to post my own thoughts about the most controversial points.

The Game: $10/$25 NLHE at Maryland Live, fresh game. Villain has $2500, I cover.

Reads/History: Villain and I played together for an hour or so the previous night, with him on my immediate left. He made a nuisance of himself, repeatedly 3- and 4-betting me and raising my c-bets. He was playing less than $2500 that night; nevertheless, he did seem to be a serious, probably professional, player. I gave up without a fight in something like five such spots and never really played back at him, so although I doubt he thinks I’m a fish, that history may color his view of me.

Decision Point 1: Villain opens to $75 with Tc 7c on the Button.

DP 2: Hero calls Qs Ts in BB.

Flop: ($160 in pot) As Ad Js.

DP3: Hero checks.

DP4: Villain bets $125.

DP5: Hero calls.

Turn: ($410 in pot) 7s.

DP 6: Hero bets $125.

DP 7: Villain calls.

River: ($660 in pot) 4s.

DP 8: Hero checks.

DP 9: Villain bets $525.

DP 10: Hero calls.

Leave a comment about any decision point(s) you find surprising or mistaken, and I’ll share my thoughts later in the week. Feedback on this format for a post is also encouraged!

I’m currently in Maryland visiting family and have been to Maryland Live a few times. It’s been quite busy; even when I arrived around 4 yesterday there was already a long list for 5/10 and 10/25 and no open tables to start a new game. So, I ended up playing 2/5 for a while.

Maryland Live’s poker room has two stories, and I was in a 2/5 game upstairs, which is annoying because when they call you for another game you have to go downstairs to lock up a seat (or try to get a floor’s attention upstairs, but that’s hard to do). This will become relevant in a moment.

There’s also a bit of history that’s relevant to the hand in question. Just a few hands prior, Players A and B had limped and called a raise from me. We all checked an Axx flop. On a turn Q, Player A bet, B called, and I folded. The river went bet-call again, Player A had A8o, and Player B flashed a Q.

The Hand

Player A ($600) is in the BB. UTG1 ($350) limps, Player B ($950) limps in MP, and I ($1200) make it $25 with Kh Ts on the CO. The BB (Player A), and both limpers call.

Flop (~$100) Ac Qh 6h. Everyone checks.

Turn 9c. Player A bets $60, and the other two call. I raise to $260. I am way less capped than anyone else here, as I can plausibly represent sets and AQ, and judging from prior history these guys are capable of showing up with a ton of weak hands after this action. The biggest risk IMO is that UTG1 has an Ace and just goes with it, as I’ve bet basically his entire stack, but his turn call didn’t seem too confident.

Only Player B calls, leaving about a pot-sized bet in the stacks. Although I was (obviously) bluffing when I raised the turn, I now think there’s a good chance I’m ahead and he’s on some sort of draw. Still, I’ll probably jam a lot of rivers if checked to, just to be safe.

River (~$740) 2h. Villain thinks for a while, moving a lot while he does so. He changes posture a few times, leans his head on his hand, etc. Then he bets $375, a bit over half his stack.

As soon as I saw the river, my first thought was that I should call a shove. The Kh is a very significant blocker to his value range, and I’d expect him to have either a flush or a busted draw if he shoves. I suppose there’s an outside chance I get owned by Kc Jc or a pair with a club draw, but even with that risk it seems like a profitable call.

However, I also have a habit of stationing too much, especially against smaller stakes players who tend to be really risk averse in big pots and to bluff at less-than-optimal frequencies. His body language seemed confident, as generally people who are bluffing will try to avoid looking uncertain or drawing attention to themselves.

Results

As I was pondering this, I heard them announce “ABC for 5/10, second call.” I must have missed the first call, which is another annoying thing about playing upstairs: it’s a bit harder to hear announcements. That frazzled me a bit, as I didn’t want to take up too much time and miss my spot in the 5/10, so I just folded. Villain proudly tabled 8c 3c, and I just barely had time to tell him “Nice hand” as I rushed downstairs to lock up my seat.

It’s not actually a big deal, but man, that would have been such a fun hero call to make. At least I got some “blog equity” out of it anyway.

In the meantime, my latest poker strategy article, “They’re More Afraid of You,” is now appearing in 2+2 Magazine. It’s about using fear to your advantage in poker, but with a particular focus on the WSOP Tag Team event that Nate and I played:

no player wants to be the one to lose all of the team’s chips, especially not in a “boneheaded” way. I mean, if you get Aces cracked, your teammates will understand, but if you call off all of your chips hoping to catch a bluff and get shown a set, how do you explain that to the rest of the team?

Enjoy!

I got off to a good start in the $1500 but ran into some annoying spots. At 150/300, the CO, the weakest player at the table, opened to 1000, and I had KJs on the button. Based on the size of his raise, I figured he was strong, which means calling at all here is borderline, but I was trying to get into pots with him, I had position and a reasonable hand, and we were about 80BBs deep, so I hopped in there.

Then the SB, a player who’d mostly been quite passive, suddenly got it into his head to squeeze. Maybe I was just salty, but just the way he looked at us and gathered his chips, I really didn’t think he had anything. He made it 3500, the CO happily shoved, I folded, and the SB quickly folded as well. I have no idea what prompted him to do that,

The very next hand, a tilted player in early position opened to 875, the HJ (the CO from the previous hand) called, and I called QTs on the CO. The flop came KJ6 with one of my suit, the original raiser checked, and the HJ made a big bet, like 80% pot. Obviously I wasn’t getting immediate odds to draw, but I figured my implied odds would be very good if I hit, so I called. Then the original raiser went into the tank, and it was instantly obvious he was strong and looking to check-raise. He drew the process out for over a minute, stacking and restacking chips and trying to act torn about his decision, which only made it more obvious that he was strong. He raised, the HJ instantly folded, and I eyed his stack but had no choice to fold myself, as he was going to have less than a pot-sized bet behind.

A while later, at a different table, at the 250/500 level, I opened to 1100 with K6o in the CO. Not exactly standard, but the BB seemed very amateurish. Only he called.

The flop came Q63 with two clubs, and I held the Kc. He checked, I bet 1100, and he raised to 5000. My plan, after betting so small on the flop, was to call a check-raise, but I wasn’t expecting such a large one. I think I should have just folded right there, but I called.

The turn was another Q, and he jammed for a pot-sized bet. It seemed crazy not to call him when the only hand I was worried about just got less likely, but I took my time and tried to get a read. Based on his body language, he seemed quite comfortable, and I ultimately folded.

Part of me definitely feels like if I’m not calling a shove on that turn then there’s really no point in calling the flop. Then the other part of me argues that what my flop call bought me was the opportunity to make a read-based decision on the turn, and I (hopefully) made the right one.

The very next hand, I had about 28BB, and the action folded to me in the SB with 77. I’ve been experimenting with open limping a lot from the SB, and I think this is a good spot for it. There aren’t hands I want to open jam for this amount, and there are a lot of hands I don’t really want to raise-call or raise-fold for this amount, which means there’s a lot of merit to a limping strategy. With 77 specifically, raising and getting called doesn’t even produce that great of a situation, as most flops will be difficult to play.

My plan was to shove over a raise, but the BB took that play away from me by shipping his stack. Although I wasn’t eager to race for such a large pot, I thought he would rarely jam hands that dominated me but jam some hands I dominated, including smaller pairs and Ax, which makes calling pretty profitable if high-variance. I called and lost a race to T9s.

Gonna play the $1000 Turbo NLHE today.

Winning at poker isn’t about finding a “sure thing”, such as an unbeatable hand or a bluffing spot where you are certain your opponents will fold. It’s about learning to make good wagers under conditions of uncertainty. That means uncertainty not just about the next card to come but also about your opponents and their likely holdings and strategies. The only sure thing in poker is that you’ll never be a long-term winner if you wait around for a sure thing.

As always, please let me know what you think!

Q: I’ve often wondered how best to consider stack size when confronted by 3 or 4 bets. I have a vague sense it is about trying to get value out of my strong hands, narrow ranges and lower my SPR, but I’d be lying if I knew enough to not feel a little lost here.

For example, …
– I have AKs and open 2.2BB
– V 3-bets to 7BB
– I ?…with 20BB effective vs 80BB vs 200BB…?
At 20BB I’m jaming.
At 80BB am I just calling or 4-betting? Wouldn’t a 4-bet be folding out hands I want in, like AQs?
At 200BB do I add some/more 4-bets? If so, can I ever fold to a reasonable 5-bet?
What about holding KK facing a 5-bet with 200BB effective.
What about QQ…the absence of a K blocker and the presence of a Q blocker makes it more likely we are flipping or behind an average 4-bet calling/raising range? If that is true, do we 3-bet/jam 20BB but 3-bet/call 200BB (just as another example of my question).

I realize this is a pretty wide question and assuming no read on V, and may even be stylistic to some extent, but any feedback would be quite welcome.

A: You’re on the right track with your thinking, but you left out a critical detail from your original question: position. The only reason anyone plays any hand other than Aces is that there is money in the pot pre-flop. The fewer people there are still to act behind me, the more hands I can (and therefore should) profitably open raise.

Once someone raises in front of me, I have a new dilemma: there is more money in the pot, but there is also someone who is claiming to have a strong hand. However, I know that, like me, he has some incentive to raise even without the nuts, which is why I probably don’t have to have the nuts to re-raise him.

When you have a hand that you believe to be ahead of the original raiser’s opening range, you have to make a decision: do I call, 3-bet, or even fold? You need to estimate the expected value of each and choose the option with the highest EV. When considering a 3-bet, this basically means answering four questions:

1. How often will my opponent fold, and how much do I have to gain from those folds? Hands like AK and JJ benefit more from fold equity than KK or AA do, even though you may not be raising them “as a bluff” (in other words, you may also expect to be ahead of a calling or even 4-betting range).

2. How often will my opponent call, and what can I expect that call to be worth? This is a function of your equity vs a likely calling range as well as how well your hand will play after the flop (if your 3-bet is not all in).

3. How often will my opponent 4-bet, and how will I fare against a 4-betting range? Especially when a 4-bet isn’t likely, it’s OK to 3-bet a hand for value even though you will fold to a 4-bet.

4. How does the EV of calling compare to the EV of 3-betting (which is determined by the above three questions)?

We don’t need to inquire about the EV of folding, as it’s always 0. So generally, if calling or 3-betting has positive EV, we can rule out folding, though there are tournament situations where cEV and $EV deviate significantly.

Of course in many cases you don’t know exactly how your opponent will respond and so can’t put exact numbers on these things. However, you should recognize that there’s a relationship between them. If you opponent opens from the CO and you have AK on the button, you are probably far enough ahead of his opening range that he will either fold very often or call/4-bet a range that AK is well ahead of. Either way, you win. The one thing that can’t happen is for your opponent to rarely fold and also reliably have AK smoked. It’s hard to get dealt a hand that strong, especially when an A and a K are accounted for, and your opponent has incentive to raise a wide enough range from the CO.

It is possible that your opponent doesn’t properly understand or respond to his incentive to attack the blinds and is a huge nit when it comes to raising the CO. If you knew that, you might prefer not to 3-bet him with AK.

However, if you do unwittingly 3-bet the nit with AK, that doesn’t mean that his nitty strategy is exploiting you. For one thing, the mere fact that he is raising suggests he is not a nit (nits raise less often than other players). But even if he is, you are passively benefiting from many situations where you would have had to fold your button if he’d raised his CO, but because he made overly tight folds from the CO, you got to make a +EV raise on your button. Basically, all those folding mistakes he makes from the CO overwhelm whatever he gains by getting lucky enough to “trap” you when he has AA in the CO and you have AK on the button.

If you’re interested in examining these spots in greater depth and getting a sense of what balanced opening, 3-betting, 4-betting, etc. ranges look like, Hold ‘Em Resources Calculator is a very good tool for the job.

[T]here are other decisions in poker besides call-or-fold. When you check, you put your opponent to a bet-or-check decision. In other words, after you check, your opponent does not (or should not given you are doing your job well) know whether or not you plan to fold to a bet. Thus, when he holds a weak hand, he has a decision: should he attempt to bluff, or he should he check behind and take a free card or surrender the pot? Just as with calling or folding, this is a decision that your opponent may get wrong, and if she does, then you stand to profit.

As always, please check it out and let me know what you think!

A: Your guess is correct. That doesn’t mean that I don’t see a use for such a thing, but it’s a personal decision. Ideally you would be unaffected by short-term losses, but if you believe you will play less well after losing $X, then I can see why you might want to bring no more than $X with you.

There are some opposite considerations as well. I think that people who bring only one or two buy-ins with them are creating unrealistic expectations for themselves and causing themselves to be extra risk-averse (and tilty, after losses), because they know that even a small loss will require quitting.

I try to keep enough in my box at the casino so that even if I’m having a bad night I’m still not close to running out of money. but that does require trusting oneself not to tilt it all off. You can find more on this concept in Tommy Angelo’s article Enough is Not Enough.

I’ll start by saying that although there are some interesting concepts at play here, this specific spot is not really an important one to get right. For one thing, it’s not exactly an everyday occurrence. Perhaps more importantly, everyone seems to be in agreement that Villain is unlikely to put another dollar in the pot no matter what Hero does, so we can expect the Expected Values of all available options to be quite similar.

Value Betting

There’s some game theory here related to whether Villain has any incentive to call the river with a bluff-catcher, whether Hero should be able to value bet an unimproved bluff catcher, whether Villain should ever check quads, etc. But there’s an important exploitive concept at play as well, which James Antill raises quite succiently: “Villain can’t make a calling mistake if we don’t bet.”

In theory there shouldn’t be much value in betting. Villain took a very polarizing line, and any showdown value he had would have been better played as a bluff-catcher than as such a big bluff. So really, he should either have a boat or better, or a hand that couldn’t even consider calling.

Of course, there also shouldn’t be much risk in betting. I’m embarrassed to say the very important question of whether I blocked 64s did not occur to me at the table. I don’t know for certain that the river was the 4d – I made up the suit for this post, wrongly thinking it unimportant. Of course, I did consider that Villain had no real reason to check a big boat or quads on the river. After all, we’re seriously considering not betting a hand that would almost certainly call a shove! Checking could induce a bluff, but what hand that benefits from bluffing could Hero take to the river?

Patrick raises the very good point that, “As played, it’s kind of a weird SPR by the river that makes getting stacks in hard to do without either an over bet or a raise, which…I’m not sure, but I would say it leans away from V having a stack able value hand like 33.” However, even seemingly good opponents make mistakes, and we want to give them the opportunity to do so. Both checking quads and calling the river without a 6 are probably mistakes, but the latter is a much easier mistake to make.

I don’t agree with James Antill that, “If villain takes this line with worse and is going to hero call it then he’s as likely to do it with 1.5x as 0.25x pot.” Our best hope is to offer Villain such good pot odds that he can’t resist calling (or spazzes out and shoves) with a hand that he wasn’t originally thinking of as a bluff-catcher. He certainly ought to be price-sensitive, given how easily Hero can have a 6 and how difficult it is to find a bluffing candidate.

Bluff Shoving

I also didn’t consider the option of shoving to get Villain off of a chop. I don’t think it’s the best way to play the hand, but it is worth considering, to kudos to those of you who thought of it.

Sean is right that if Villain is equally likely to check any given combo of 6x or 44, and he always folds the 6x, then shoving would be best. However, I think it’s far from certain that Villain will fold a 6 to a shove, even if that would be the correct play.

Checking

The one argument in favor checking that hasn’t yet been made is that we get to see Villain’s likely bluff. It’s very rare that I factor the value of seeing the Villain’s cards into my decision, and I can’t claim that I did so in real time either, but it did prove a bit interesting. And in this case, where there’s so little value in betting anyway, the small value of seeing Villain’s cards might actually outweigh it.

Results

I checked back, and Villain showed As 9s. This certainly raises the question of whether he might have called a $400 bet, but is interesting for other reasons as well. For instance, I don’t think it’s the best candidate for either donking or three-betting the flop. In fact, it probably has enough showdown value to check and call a bet.

“Ancient civilizations invented demons, gods, and myths to explain the random forces of nature, such as weather, earthquakes, and volcanoes, which loomed so large in their lives. Often, the heroes of these stories were mortals, like Odysseus or Beowulf, who triumphed over supernatural forces to become masters of their own destiny.

Like our ancestors, we poker players are at the mercy of a powerful force whose machinations seem indifferent and sometimes even cruel: variance. It is both the beauty and the curse of this game that luck has the final say. No matter how well we play, there is no guarantee that we will win a given pot or even a given session. Is it any surprise that we joke about “the poker gods” or make of ourselves a “Hero” when sharing a hand on the Two Plus Two forums?”

I actually wrote this before I started reading Thinking Fast and Slow, though that book offers plenty of support for the idea that our brains are hard-wired to find causal explanations for random, unconnected events. It’s an excellent book in a lot of ways, with plenty of applicability both to poker and to plenty of other aspects of your life. After all, shouldn’t we all have a better understanding of how our brains work?

We’re playing 10/25 NLHE with effective stacks of about $8K. The main Villain, in the SB, is a capable and experienced player, not 100% sure whether he’s a pro but he’s good enough that I think he could be. I imagine that he has a similar opinion of me. The BB is definitely a pro and strong player.

I’m going to go ahead and skip to the river decision, because I’ve already explained my plan for a three-bet.

Hero opens to $75 with Kd 6d on the button. SB and BB both call.

Flop ($220 in pot) 6h 6c 3s. SB bets $100, BB folds, Hero raises to $300, SB raises to $875, Hero calls.

Turn ($1970 in pot) 3d. SB bets $1050, Hero calls.

River ($4070 in pot) 4s. SB checks, there’s about $6000 in the effective stacks, Hero?

Post your preferred play, along with your reasons, here. I’ll respond as I can in the comments and post the next decision point on Saturday.

Assessing Range Advantage

The only information I gave about the SB was that he’s “capable and experienced” and probably has “a similar opinion of me”. This really isn’t enough to make aggressively exploitive assumptions about what his bet “means” (if he’s doing a good job of balancing, it doesn’t mean any single thing) or how he’ll respond to a 3-bet.

Let’s start instead by examining some structural features of the situation, at the time that we see the flop, before there’s any action. I have to agree with Matt that, “I really don’t see him having a wide calling range from the SB. Playing out of position against tough opponents is not very easy, of course, and calling invites a third (also competent) player into the hand, which leads me to believe that he will be heavy on 3betting and folding from this spot.”

This isn’t an exploitive assumption; he’s out of position and closing the action, so he really is constrained. He can’t just decide to call with a bunch of weak hands because that’s his “style”. If he doesn’t have a disproportionate amount of realizable equity, which will usually be the case, his best play is to fold pre-flop. Many of the hands that do have that kind of equity do better by raising pre-flop. If we act too strongly on these assumptions, then we give him incentive to call more weak or strong hands, but still, we should recognize that he’s dealing with some heavy pre-flop constraints.

Likewise, we can recognize that my range can and should be rather wide, again not as a question of style but because with the button and very deep stacks, there are simply a lot of hands where raising is more profitable than folding. And the BB can have a much wider range than the SB, given that he is closing the action and getting a better price.

I suspect that if we were to compare the overall equity of the SB’s range vs. mine, he would be ahead. Even though I have some very strong hands that’s unlikely to call pre-flop, such as AA or K6s, I also hold a lot of weak hands that he’s unlikely to call pre-flop, such as 74s.

On Donking and Raising

This constrains me a bit: I can’t expect to continuation bet profitably with anywhere near 100% of my range, particularly given that there is also a third player in the pot. So, I will check the flop a significantly non-zero amount of the time, and the SB has many hands like pocket pairs and Ax that are likely best but very vulnerable to free cards. These hands have some interest in donking the flop in order to deny me equity.

However, because his range is, not exactly capped, but weaker at the top end than mine, he’s vulnerable to getting raised by a polarized range. So, his donking range should contain some hands that can profitably continue to a raise, either by calling or three-betting (sometimes for value, sometimes as a bluff).

K6 fares well against those ranges. It figures to be ahead of his calling range (and even ahead of his range for calling down multiple streets), and although it may turn into a bluff catcher if Villain three-bets, it will be a very good bluff-catcher in that it blocks some portion of his value range and has equity against it as well. We may not be rooting for a three-bet, but we shouldn’t be lost about what to do when three-bet, either. I think calling down will yield a profit, even if it’s not the part of the game tree where we’d ideally end up. When we’re holding a 6, though, Villain only has two choices: three-bet rarely, or three-bet a bluff-heavy range. Considering that we’re prepared to call to the river, either is fine.

It’s true that the majority of my continuing range will not benefit from raising, and I’ll respond to his bet far more often by calling than by raising. It’s also true that because my calling range will consist mostly of hands that do not want to play large pots, SB will have some incentive to make large, possibly over-, bets on subsequent streets with a polarized range. This gives me some incentive to just call the flop with very strong hands, which in turn reduces his incentive to employ such a strategy.

These situations usually resolve themselves in a mixed strategy: I should call some hands that are prepared to take a lot of heat, and also raise some such hands. MCG and PokerNoob both do a good job of explaining why K6 is a better candidate for raising than calling.

The Bottom Line

K6 is an extremely strong hand here, so close to the top of Hero’s range that it can happily put in four bets for value and profitably, if begrudgingly, call down five bets as a bluff-catcher. Calling makes it tricky to get that fourth bet in. Sometimes Villain will just check-call down, and we’ll get only three bets (though overbetting might be able to compensate for this). Even if he does bet the turn, as Raffi says, “flatting and potentially raising at a later point makes it really hard to rep a bluff.”

It’s also worth pointing out that, unless Hero’s hand improves, it will not be quite as strong on future streets. Each new card that comes, unless it’s a K or a 6, pushes our hand, as well as our value targets, further from the nuts.

Essentially, this is a hand that benefits from frontloading, and I think raising with it is generally best. You may not be accustomed to thinking about your kicker when you have trips, but when you’re this deep, it matters.

Results and the next decision point are coming in the next post.

This is from a 10/25 NLHE game with effective stacks of about $8K. The main Villain, in the SB, is a capable and experienced player, not 100% sure whether he’s a pro but he’s good enough that I think he could be. I imagine that he has a similar opinion of me. The BB is definitely a pro and strong player.

Hero opens to $75 with Kd 6d on the button. I realize that some of you would fold this pre-flop, and while it’s a bit close, I think it’s a good open in most games and I’m certainly going to err on the side of opening the button more aggressively when we are this deep. SB and BB both call.

Flop 6h 6c 3s. SB bets $100, BB folds, Hero?

Post your preferred play, along with your reasons, here. I’ll respond as I can in the comments and post the next decision point on Wednesday.

But I was wondering why not bet it out on the flop instead? Wouldn’t it achieve a similar result? Also, it can even be considered a blocking bet? I havent actually had any real-life cash poker games, mostly online so does this also make any difference?

A: It’s important to note that this is an old video (uploaded to YouTube in 2009, but perhaps created even earlier than that), and my guess is that this is not something Daniel Negreanu would publish today. I want to get that out front because, frankly, I don’t think what he’s saying makes any sense.

At the very least, it relies on some unfounded assumptions about how an opponent will play.  The bottom line is that if your opponent wants to bet 6000 on the turn, you betting 3000 doesn’t stop him from doing that – he’s allowed to raise. So it doesn’t cause you to “take control of the hand” (a meaningless phrase, in my opinion), it merely helps your opponent correctly fold hands that are worse than yours.

Negreanu unintentionally explains why this isn’t a good play when he says that the bet will only be called by better hands. If you check and call a turn bet, you could be up against either a better hand or a bluff, and although the bluffs aren’t drawing dead against you, they are drawing pretty thin. Overall, calling a bet should be +EV for you (and if you think it isn’t, you can just fold). When you bet, though, you either take down a pot you were probably going to win anyway, if your opponent has nothing, or you put in 3000 drawing to two outs, which is much worse for you than putting in money against a range of better hands and bluffs. Basically, you want those bluffs in your opponents’ range if you’re going to put money in anyway.

Contrary to popular belief, there’s not often anything intrinsically desirable about being the aggressor (or “having the lead” or “initiative”) in no-limit hold ’em. There are certain types of hands that, when played aggressively, can outperform their equity. Extremely strong hands benefit from aggression because although their equity might be 100% of the pot, they can win even more than that if a bet is called. Extremely weak hands benefit because they have little equity but may win the entire pot if the opponent folds.

It does not follow from this that hands in the middle, hands which have good equity against a weak range but poor equity against a strong range, benefit from aggression, and I think that’s the misunderstanding we see here. Taking a marginal hand or bluff-catcher and turning it into a bluff does not cause that hand to outperform its equity. Often, it’s just the opposite.

“Poker lingo is full of bluster and bravado. For some, the colorful language and the opportunity to spin dramatic narratives about aggression and courage is an important part of the game’s appeal….

I also suspect, though, that all these macho turns-of-phrase and bellicose metaphors obscure the mathematical side of the game. It often seems to me that players who worry about “defending” their big blind, or getting “bullied”, are more concerned about damage to their ego than to their expected value.”

Of course it’s not just about language; there’s plenty of strategy content as well! Please have a look and let me know what you think. Do you enjoy turning your poker game into a story of bravery and bravado? Do you find these kinds of metaphors particularly helpful or unhelpful?

I primarily review his play at the final three tables of a $10 rebuy tournament, all the way down to heads up. If you need help making or triumphing at a final table – and who doesn’t?! – be sure to take advantage of this FREE video. Or better yet, see how you can have me review one of your hand histories!

In the meantime, please enjoy the next PLO8 strategy video from Nate and myself:

Please contribute here!

Thanks to everyone who’s donated already, you’ve far exceeded what I thought we were likely to raise. As a result, it’s been tough to keep pace with releasing all the free strategy videos I promised. Thankfully Nate came through in a pinch and gave me permission to use some videos we’d previously recorded. So here’s the first of a three-part series in which we have fun reviewing my play in a PLO8 WCOOP event. Enjoy, and happy new year!

// ]]>

The book is available from the Amazon Kindle Store or in EPUB, Kindle, and PDF formats at Nitcast.com.

Blinds are 50/100, Villain has about 20K (starting stack), and I have about 25K. Only six players (including both blinds) have claimed their seats so far. I have black Aces first to act and open to 300.

Villain calls from the SB, and everyone else folds.

Flop (700 in pot) Jc 8c 6h. Villain checks.

Turn (700 in pot) 6d. Villain bets 400. Hero?

River (1500 in pot) 2s. Villain bets 600.

I was a bit surprised by the comments, in that there seemed to be a consensus that a raise for value would be thin/risky and should be small. This surprises me in no small part because a lot of people seemed to be in favor of raising and then betting safe rivers on the previous street. This river is as good as it could be, so I don’t see what’s changed to reduce confidence in Hero’s hand. If anything, Villain’s bet size should only embolden us. In game, I thought it was extremely likely that he had a Jack, and the only question was how much he’d be willing to call.

The best argument I can see for making only a very small raise is that it’s hard for Hero to have bluffs after taking this line. If Villain is really going to fold a Jack to a pot-sized raise, though, that gives Hero plenty of incentive to take hands that were checked for showdown value on the flop, such as nut clubs or 99, and turn them into bluffs. In spots like this, where your previous actions have taken most if not all air out of your range, turning the bottom of your range into a bluff should be “standard”.

That still may not produce a lot of bluff combos, but Hero isn’t going to have a lot of value combos, either. Even Jacks is not a great candidate for a big river raise, as it blocks so many of your value targets.

The other concern was that raising opens Hero up to a raise which, if balanced properly, would reduce his EV to 0. There’s a lot to say about this.

First and most importantly, it isn’t going to happen. Exploitively, it just isn’t a play that’s in the described Villain’s arsenal. I want to emphasize this, because I think it’s very common for people to miss value on the river out of a misguided fear about getting check-raise bluffed or, in this case, three-bet bluffed. I expect a 3-bet here to be extremely rare, and I wouldn’t think twice about folding to one.

Even if Villain were capable of this, it wouldn’t be a reason not to raise. It’s generally correct to have a range that bets/raises for value and folds to a re-raise, as long as it isn’t the entirety of your value range. Villain should still have a calling range against Hero, because three-betting is too expensive to be his only defense against bluffs, and Aces should be ahead of that calling range.

Results

I raised to 3000. Villain called and mucked.

The possibility of a big payoff when the board runs out so nicely is part of what makes checking the flop competitive with betting. The amount of money Villain puts into the pot versus this line should be comparable to the amount he would put in against a bet-bet-bet line, which is the other way I could see myself playing this runout. If it isn’t, then he can be exploited by taking one line with all weak hands and the other with all strong hands.

Bottom line: Villain is quite unlikely to have a hand better than AA. He also has a lot of incentive to pay off a large raise, even if we don’t make exploitive assumptions about him (which would only make me feel better about putting in a big raise).

Blinds are 50/100, Villain has about 20K (starting stack), and I have about 25K. Only six players (including both blinds) have claimed their seats so far. I have black Aces first to act and open to 300.

Villain calls from the SB, and everyone else folds.

Flop (700 in pot) Jc 8c 6h. Villain checks.

Turn (700 in pot) 6d. Villain bets 400. Hero?

I once again suspect that at equilibrium, the Expected Values of raising and calling will be quite similar for all of Hero’s strong hands. This is because these hands have relatively static value versus Villain’s likely betting range. If you have some exploitable read on Villain, you should employ it. In this case, I’d consider his river bluffing tendencies the most important read. Against overly passive opponents, raising now is probably best, and against overly aggressive ones, calling is probably best. Without such a read, though, it can be tough to tease out the best play, because it’s going to be a small difference, with good arguments on each side. Of course that also means that it won’t matter terribly much what you choose, but I nevertheless think that the exercise of finding the best option is both good practice and intrinsically interesting.

Several commenters argued the merits of calling versus raising in a vacuum quite well. It’s striking, though, that none of these arguments is really specific to the exact hand Hero holds. They would apply just as well to any hand Hero wants to play for value. Now, it’s certainly possible that one option might just be strictly better than the other for value, but I think that would imply some exploitability on Villain’s part, and I’d be more comfortable with such a solution if we could pinpoint what precisely it is we’re exploiting and why we feel comfortable with that read.

In cases like these, I find it helpful to imagine that I will call with some strong hands and raise with others. This enables me to rephrase the question, not as “Is calling strictly better than raising?” but rather, “Is there anything about my hand that would make it better than similar hands for calling or raising?”

Consider the arguments in favor of raising. Dave says, “If villain has a semi-bluff, he seems very likely to call a turn raise since hero could be bluffing and his hand could improve.” I agree that against Villain’s draws, raising is probably somewhat better than calling, as it more or less guarantees that we get a second bet into the pot (or fold out a good bit of equity), whereas on the river Villain may or may not bluff when he misses but will certainly put a bet in when he hits. However, the Ac in our hand significantly reduces the likelihood that Villain holds a draw.

Relatedly, Dave worries that “we have to guess at his bluffing frequency on a good number of draw-completing rivers”. That’s not quite true, though. The Ac is a very significant blocker, which means that bluff-catching with that card in your hand will be +EV even against an opponent with an optimal river bluffing frequency. We know the Ac is in our hand, but he doesn’t know that we know that. This means that on club rivers, we have an information advantage that can be exploited. Although these may not be the best river cards in the deck, they are cards on which Hero can in fact expect to put money into the pot with an edge.

Mark points out that, “Hands opponent is betting for value, particularly Jacks may be scared off by a lot of cards, such as possible flushes, straights, or overcards. This makes up a huge portion of the deck.” Here, again, we have significant blockers. Aces are not good cards for getting value from Jx, and the Ac would be especially bad. When we know that the river is less likely than usual to be an Ace, that becomes an argument in favor of calling with this hand and raising some different value hand, such as 7h 6h, which does not block so many scare card rivers.

As Mark points out, hands like 76 are also more desirable for raising than AA “as they block the portion of opponent’s range that are beating both AA and [trips with a bad kicker]”.

If the decision is otherwise close, we can break the tie by considering the relevance of the exact cards we hold. In this case, they argue for a call, which is what I did.

The next decision point is here.

Blinds are 50/100, Villain has about 20K (starting stack), and I have about 25K. Only six players (including both blinds) have claimed their seats so far. I have black Aces first to act and open to 300.

Villain calls from the SB, and everyone else folds.

Flop (700 in pot) Jc 8c 6h. Villain checks.

Turn (700 in pot) 6d. Villain bets 400. Hero?

Post your thoughts and preferred action here. I’ll respond to comments as I’m able and post my own thoughts as well as the next decision point on Friday.

Blinds are 50/100, Villain has about 20K (starting stack), and I have about 25K. Only six players (including both blinds) have claimed their seats so far. I have black Aces first to act and open to 300.

Villain calls from the SB, and everyone else folds.

Flop (700 in pot) Jc 8c 6h. Villain checks. Hero?

Betting the flop is the obvious play, and I don’t think it’s bad per se, but I think it’s worth asking, if you don’t check this hand, what strong hand would you ever check on the flop? Pocket Jacks? Those three combos aren’t really enough to balance your checking range, especially as this isn’t a particularly good spot to bet hands like AK, KQ, or 99.

Many players, even non-elite ones, are rightly reluctant to give you credit for a strong hand after you check the flop. Of course the turn card will have some scrambling effect on hand values, in that an A, K, or Q will turn some of your weaker checking hands into relatively strong hands, but on many turn cards your opponent can bluff, value bet, and call you down with relative abandon.

As several people pointed out, getting check-raised on the flop is also not a pleasant experience. I probably wouldn’t fold, but it drastically reduces your expected value in the hand, as does betting, getting called, and then seeing one of quite a few turn cards.

There are some runouts where you can bet AA three times for value, but they are in the minority. One very common line after betting the flop will be checking back the turn and then bluff-catching on the river. I think people are inclined to think of that as a “win” because they know the river call is profitable, they get to showdown, etc. But really bluff-catching is often a barely better than neutral-EV option.

Unlike with slightly weaker overpair or top pair hands, there’s little protection value in betting. Most hands that could beat AA thanks to a single card are not folding to a flop bet anyway and will put money into the pot on any turn. Commenters mostly focused on what could go wrong as a result of a flop check (what if Villain improves to a flush or straight or two-pair? what if it’s a scare card and you can’t get paid by a Jack?) but ignore what could go right.

Most of those cards will improve or scare some part of your opponent’s range, but they’ll also embolden some other part. So yes, a K is bad if you were up against KJ or QJ, but it’s good if you were up against KQ or KT that was going to check-fold the flop and now will pay off multiple bets.

Granted, concerns about balance should take a back seat against opponents who aren’t going to bluff/bluff-catch/value bet optimally on future streets. However, checking the flop has a hidden benefit versus these opponents as well. Many of them will reveal a lot of information with their sizing and behavior on future streets, if you put them in the driver’s seat. If you bet the flop and your opponent check-calls, you don’t learn a lot from that, as there are lots of different hands that will play that way. Then, as discussed, you’ll end up checking quite a few turn cards as a result.

However, if you check back the flop and force your opponent to bet into you on the turn, he may reveal quite a bit about what he has and how he feels about it, opening up the possibility of raising for value later, making a hero fold, or even the outside chance of turning your hand into a bluff.

I did in fact check the flop. I’ll post the turn momentarily.

I don’t have any history with the Villain, but if he’s a Lucky Chances regular, he may know that I’m a 5/10 regular, that I have the podcast and blog, etc. In the previous (first) orbit, I opened T9s, called a 3-bet, and ended up making a flush against someone else’s Aces. That’s the only pot that Villain has seen me play.

Blinds are 50/100, Villain has about 20K (starting stack), and I have about 25K. Only six players (including both blinds) have claimed their seats so far. I have black Aces first to act and open to 300. In a game like this, I will limp some hands in early position if the table is full, and AA may well fall into that limping range. When we’re six-handed, though, I’m never open limping anything.

Villain calls from the SB, and everyone else folds.

Flop (700 in pot) Jc 8c 6h. Villain checks. Hero?

In the comments section below, please share your preferred action, your reasoning, your general plan for future streets, etc. If you want to bet, be sure to specify the size and the reason for that size.

I’ll do my best to respond to comments and will post again later in the week, probably Wednesday, with my own thoughts and action, as well as the next decision point.

Weighing your options, even if you end up making the play you were going to make anyway, also helps you become a better player. Outside of “soft” skills like patience and equanimity, the ability to consider all options and choose the best one, even when it is not obvious, is the hallmark of a skilled poker player. Doing this more or less well is what makes one player better or worse than another. Practicing it, even in cases where this practice doesn’t have immediate payoff, is still sharpening one of the most important poker skills there is.

It should come as no surprise that my background in debate is a big part of the reason why I find this a helpful way of framing decisions in poker!

The comments from the pre-flop discussion that I found most interesting were from dullgeek and others who struggled with the problem of how to put money in good once there’s an Ace or King on the board. This is a central dilemma in poker: how do you get paid off when your hand is strong but somewhat obvious (that is, it’s easy to see that there’s an Ace on the flop, and anybody without one will be reluctant to put money in). Of course the same problem occurs when there’s a pair on the board, when you river a flush, etc.

I can think of three answers to this dilemma:

1. Cooler your opponent. If Villain holds KQ or KJ here, we should have no trouble getting the money in. I’m tempted to say there’s no real skill involved here, but that’s not entirely true. If you fail to recognize the strength of your hand and give Villain a chance to put his stack in when he’s coolered, then you’ve made a big mistake. For instance, if Hero checks back the turn and does not shove over a bet on most blank rivers, then you aren’t making the most of a spot where you’re on the right side of a cooler. For the most part, though, coolers are like bad beats: you’ll be on both sides of them over time, and they don’t add or subtract from your theoretical bottom line.

2. Opponent makes a bad call. Plenty of them do. Again the skill is simply in giving them the chance to put the money in. Whether they actually pay you off is beyond your control, but there is also a skill in expanding your value range against these opponents and taking maximum advantage of their errors. In this case we don’t have any read about Villain’s payoff tendencies.

3. Play big pots with a balanced range. This has the potential to pay off in two ways. Many opponents – even, perhaps especially, skilled ones – know or have learned that most people don’t bluff enough in certain spots. If you exhibit this same tendency, even opponents who don’t know you may correctly guess this and make tight folds that successfully exploit you. Correcting your bluffing frequency won’t necessarily help you win more from your big hands, but it will enable you to profit from your opponent’s tight folds without exposing yourself to risk of exploitation. If you’re known or suspected to be capable of playing better than the average bear, then your bluffs may actually be less profitable in this spot (though not money-losing, if you’re balanced) but you’ll win more with your strong hands, again provided that you’re willing to bet them.

That third point is an important one: except in spots where Hero is at a significant range disadvantage, his ability to value bet is limited only by his ability to find hands he’d like to bluff with. Many commenters’ assumption seems to be that because Hero will almost always have a pair on this turn (AK and KQ with a backdoor flush draw being among his weakest flop calls), he therefore can’t have many bluffs and can’t expect to get stacks in with AK.

Realize what you’re saying here, though: AK is extremely close to the top of Hero’s range, so if you aren’t playing this for stacks, you must assume that your opponent will very rarely be willing to put stacks in any hand in his range. With that much fold equity, turning your weakest pairs into bluffs starts to seem appealing. How much showdown value does 77 really have here, especially considering that it can still get bluffed out on the river if you check the turn?

I contend that Hero actually has quite a few hands that would like to bet the turn. The weakest, like 77, have near-zero showdown value. Stronger pairs still have something to gain from protection and may even be able to value bet. Is QQ really going to be behind if a half-pot bet goes in on the turn? And of course the strongest, certainly including AK, want to build a pot and set up a river shove.

Exploitively, if Villain’s range consists only of check-calls and check-folds, Hero may well do best by betting his full range for a small amount. Of course so much betting would give Villain incentive to check-raise both for value and as a bluff, and the equilibrium strategy likely entails a mix of betting and checking. Considering what an important hand AK is for Hero’s range and how static the board is, he’s probably indifferent between betting and checking at equilibrium, checking disproportionately often when he holds at least one heart.

Results

PokerStars – $665+$35|350/700 Ante 85 NL – Holdem – 9 players
Hand converted by PokerTracker 4: http://www.pokertracker.com

BB: 32.41 BB (VPIP: 21.28, PFR: 17.39, 3Bet Preflop: 15.79, Hands: 47)
UTG: 63.83 BB (VPIP: 25.09, PFR: 14.14, 3Bet Preflop: 5.60, Hands: 292)
UTG+1: 22.54 BB (VPIP: 19.23, PFR: 14.56, 3Bet Preflop: 14.29, Hands: 104)
MP: 56.87 BB (VPIP: 25.45, PFR: 22.22, 3Bet Preflop: 13.33, Hands: 56)
MP+1: 26.86 BB (VPIP: 19.21, PFR: 14.29, 3Bet Preflop: 5.26, Hands: 152)
MP+2: 82.3 BB (VPIP: 17.82, PFR: 14.14, 3Bet Preflop: 4.44, Hands: 101)
CO: 25.66 BB (VPIP: 21.43, PFR: 16.06, 3Bet Preflop: 13.33, Hands: 196)
Hero (BTN): 38.02 BB
SB: 25.48 BB (VPIP: 35.58, PFR: 28.62, 3Bet Preflop: 12.80, Hands: 348)

9 players post ante of 0.12 BB, SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 2.59 BB) Hero has Kd Ah
UTG raises to 2 BB, fold, fold, fold, fold, fold, Hero calls 2 BB, fold, fold

Flop : (6.59 BB, 2 players) 5c 4s 5h
UTG bets 3 BB, Hero calls 3 BB

Turn : (12.59 BB, 2 players) Kh
UTG checks, Hero bets 6.3 BB, UTG calls 6.3 BB

River : (25.18 BB, 2 players) 6h
UTG checks, Hero bets 26.6 BB and is all-in, UTG calls 26.6 BB

Hero shows Kd Ah (Two Pair, Kings and Fives)
(Pre 44%, Flop 26%, Turn 95%)

UTG shows Td Th (Two Pair, Tens and Fives)
(Pre 56%, Flop 74%, Turn 5%)

Hero wins 78.38 BB

This river is not quite a blank, but because the important decision about just how big of a pot to try to play is made on the turn, I didn’t think it was worth having a separate discussion about whether to shove the river. If you aren’t going to shove, you might as well check the turn.

This board is static enough that betting the geometric growth of the pot (in other words, the same fraction of the pot on the turn and river) may well be the equilibrium strategy. However, I decided that what I really wanted to do here was bet my full range on the turn, on the assumption that Villain has a more-or-less pure bluff-catching range after his turn check, and then check back the river with hands like JJ or TT that bet for protection/thin value on the turn. Thus, my river range will be much more polarized and therefore make a larger bet than my turn range.

I don’t know what exactly to say about Villain’s call. It’s the sort of hand that should be indifferent at equilibrium. It’s possible that he flipped a coin before calling, and it’s possible that he would have called me with his entire turn range. Against the latter sort of player, you cost yourself a lot by not getting stacks in here.

Either way, the lesson is that you have to give your opponent a chance to pay you off when you have the top of your range. Before you decide that you can’t play for stacks, consider the implications of that assumption for your bluffing strategy. Many players end up missing profitable bluffs because they never ask, “What should my bluffing range look like here?” This mistake can also cause you to miss profitable value bets.

In a recent $5/$10/$20 session, I made quite a few of what might be considered “moves” or “fancy plays”. I called turn and river bets with Ace-high. I floated the flop with bottom pair and bluff-raised the turn. I turned a set into a bluff on the river. I four-bet someone with a 5 in my hand and was prepared to six-bet shove, had my opponent raised back.

Although I got the result I wanted in all but one of these spots, I’m not bragging. These plays were not the result of any “sick reads”. I was not especially in the zone that night, nor was I suffering from Fancy Play Syndrome. In fact, these plays are all part of what I consider ABC poker – the way I play when I don’t have a laser-sharp read on my opponent’s hand or what he’s going to do with it.

It seems to be a common belief that big bluffs and heroic calls require reads or other special justification, such as having a certain image or being stuck. Game theory suggests otherwise.

This is from the $700 NLHE 1R1A WCOOP event. Blinds are 350/700/85. It’s well after the rebuy period but not particularly close to the bubble. Table is on the tough side, featuring many regs/pros, most notably Eugene Katchalov on my immediate left.

UTG is a regular tournament player. I have him at 25/14 over 300 hands, with a 64% continuation bet.

PokerStars – $665+$35|350/700 Ante 85 NL – Holdem – 9 players
Hand converted by PokerTracker 4: http://www.pokertracker.com

BB: 32.41 BB (VPIP: 21.28, PFR: 17.39, 3Bet Preflop: 15.79, Hands: 47)
UTG: 63.83 BB (VPIP: 25.09, PFR: 14.14, 3Bet Preflop: 5.60, Hands: 292)
UTG+1: 22.54 BB (VPIP: 19.23, PFR: 14.56, 3Bet Preflop: 14.29, Hands: 104)
MP: 56.87 BB (VPIP: 25.45, PFR: 22.22, 3Bet Preflop: 13.33, Hands: 56)
MP+1: 26.86 BB (VPIP: 19.21, PFR: 14.29, 3Bet Preflop: 5.26, Hands: 152)
MP+2: 82.3 BB (VPIP: 17.82, PFR: 14.14, 3Bet Preflop: 4.44, Hands: 101)
CO: 25.66 BB (VPIP: 21.43, PFR: 16.06, 3Bet Preflop: 13.33, Hands: 196)
Hero (BTN): 38.02 BB
SB: 25.48 BB (VPIP: 35.58, PFR: 28.62, 3Bet Preflop: 12.80, Hands: 348)

9 players post ante of 0.12 BB, SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 2.59 BB) Hero has Kd Ah
UTG raises to 2 BB, fold, fold, fold, fold, fold, Hero calls 2 BB, fold, fold. For discussion of the pre-flop action, see this post.

Flop : (6.59 BB, 2 players) 5c 4s 5h
UTG bets 3 BB, Hero calls 3 BB. For discussion of the flop action, see this post.

Turn : (12.59 BB, 2 players) Kh
UTG checks, Hero ?

Post your preferred play here, and I’ll participate in the comments as I’m able and post results on Monday. Be sure to consider your entire range as well as future action when deciding how to proceed!

It seems like everyone recognizes that this hand is too strong to fold. Several commenters assigned ranges to Villain that gave Hero 41% – 47% equity. Even recognizing that Villain may check some hands like AQ that contribute significantly to Hero’s equity, there is nonetheless a lot of value in continuing with this hand.

This is a flop that does little to change pre-flop equities. The player with the range advantage pre-flop carries that advantage forward to this flop. There’s a bit of a shift – pairs go up in value and unpaired hands go down – but the fact that remains that Villain should have more nutted hands in the form of big pocket pairs than the Hero.

Despite the lack of draws, this is also a dynamic flop, because big cards on the turn and/or river have the potential to dramatically change the value of certain hands for better or worse. This means that, at least on certain run outs, Hero’s position will have a lot of value.

These two facts taken together suggest that Hero has little to gain by raising the flop. The stacks are shallow enough that the hands at the top of his range don’t need to raise to get full value. Small pairs have some interest in protection, but raising for this purpose alone also means frequently putting in two bets against a range that crushes them and perhaps even opening themselves up to the occasional bluff. Hero will be able to make better bluffing, value betting, and checking decisions on later streets and probably does best by calling with his entire continuing range and waiting to see how Villain reacts to the turn.

The presence of hands like AK in Hero’s range should help Hero’s pocket pairs get to showdown, as Villain will not be able to barrel indiscriminately on Ace or King turns. Likewise, the presence of pocket pairs helps Hero’s AK get to showdown when ahead, as Villain cannot indiscriminately barrel blank turns.

Turning your hand into a bluff may increase your odds of winning the pot, but that doesn’t make it the highest expected-value option. This wasn’t the ideal flop for AK, nor was an under-the-gun raise the ideal pre-flop action, but learning to make the best of non-ideal situations is an important poker skills, and here that means calling and playing poker on future streets.

The turn card and action will follow in a separate post.

In this instance, I chose to call, so I’ll outline the case for that, though again this was well covered in the comments section already:

1. Avoid facing a 4-bet that will put Hero in a tough spot (I would shove, but wouldn’t be happy about it)/avoid playing a large pre-flop pot in a tournament without an appreciable edge.

2. Keep dominated hands in Villain’s range.

3. Create some deception about Hero’s hand. Not that flatting AK here is a shocking play, but I think most tournament players 3-bet it most of the time, so there’s some deception value. Also because much of Hero’s flatting range will consist of pocket pairs, Villain will have incentive to get bluffy on A- or K- high boards.

4. Induce a squeeze.

The next decision point is in this post.

UTG is a regular tournament player. I have him at 25/14 over 300 hands, with a 64% continuation bet.

Seat 1: Referee-20- (22689 in chips)
Seat 2: torkolort1 (44682 in chips)
Seat 3: sonmonedas (15776 in chips)
Seat 4: chilenocl (39807 in chips)
Seat 5: Tankanza (18804 in chips)
Seat 6: tRaMp$d0PrAy (57609 in chips)
Seat 7: carpediem200 (17964 in chips)
Seat 8: foucault82 (26611 in chips)
Seat 9: E. Katchalov (17833 in chips)

E. Katchalov: posts small blind 350
Referee-20-: posts big blind 700

Dealt to foucault82 [Kd Ah]
torkolort1: raises 700 to 1400
sonmonedas: folds
chilenocl: folds
Tankanza: folds
tRaMp$d0PrAy: folds
carpediem200: folds

Hero?

This is a relatively common pre-flop spot, but that makes it important to get right. We can safely rule out folding, but what are your thoughts on calling vs raising? Whichever line you choose to take, what other hands would you play the same way?

I’ll post my own thoughts, along with the next decision point, some time in the next few days (depending on how the discussion is coming along and how the WCOOP Main Event goes for me).

Flop ($118 in pot after rake) 7h 6d 3s. Action checks to Hero. Hero checks. HJ and Button check. For discussion of the flop action, see this post.

Turn ($118 in pot) 7h 6d 3s 3d. Action checks to Hero. Hero bets $80. HJ and Button fold. SB calls. For discussion of the turn action, see this post.

River ($278 in pot) 5c. SB checks. Hero?

Post your thoughts and reasoning here, and I’ll post my own thoughts and results when WCOOP permits. Remember, if you bet, be sure to discuss sizing and your plan if raised.

Hero is UTG+2 with a $2500 stack, and most of the table covers. Action folds to Hero, who opens to $30 with 8s 7s. The hijack, button, and SB call.  For discussion of the preflop action, see this post.

Flop ($118 in pot after rake) 7h 6d 3s. Action checks to Hero. Hero checks. Button checks. For discussion of the flop action, see this post.

Turn ($118 in pot) 7h 6d 3s 3d. Action checks to Hero. Now what?

If you know your opponents are seeing the flop with wide ranges, and then you watch everyone pass up multiple opportunities to put money into the pot, your first thought should not be “Better be careful, what if someone has a monster?!”
Remember how eager everyone was to bet our 8s 7s on the flop? For the same reasons, it’s safe to assume that most bigger pairs, 7s with better kickers, etc. will have bet by now. The logical conclusion here is that our Villains are more or less capped at marginal hands weaker than Hero’s.

Moreover, Hero has plenty of viable bluffing candidates, from turned flush draws to weak, unpaired overs like Jack- or Queen-high. Thus, Hero can start betting big with a polarized range to put pressure on those weak bluff-catchers, and believe it or not, 76 is strong enough to go into the “nut pole”.

It’s not impossible for someone to have a huge hand, which is why we’re not going to make some massive overbet of the pot. Facing a large but reasonably sized bet, though, your opponents will be forced either to pay off with many hands weaker than 87 or fold often to your bluffs. Either way, you win.
If you think you can guess which they’ll do, great. Go ahead and exploit that. Bet your 87 and not your bluffs or vice versa. Checking both for fear that your opponents will somehow call you down frequently and also be ahead of 87 is simply wrong.

It’s not relevant that 87 is a less nutty hand than, say, A3. Whether you are ahead 60% or 90% or 100% when called, you’d still prefer to make the largest bet that you can.

Results and next discussion point coming in the next post.

Flop ($118 in pot after rake) 7h 6d 3s. Action checks to Hero. Hero checks. Button checks. For discussion of the flop action, see this post.

Turn ($118 in pot) 7h 6d 3s 3d. Action checks to Hero. What’s your play and why?

We’ll discuss it in the comments, and I’ll post my thoughts and action later this week (I fly to Montreal tomorrow, so I may not post until Friday).

Hero is UTG+2 with a $2500 stack, and most of the table covers. Action folds to Hero, who opens to $30 with 8s 7s. The hijack, button, and SB call.  For discussion of the preflop action, see this post.

Flop ($118 in pot after rake) 7h 6d 3s. Action checks to Hero. Now what?

Bet, Check, or Both

Most commenters prefer betting, and I agree that that play has obvious appeal. Hero’s hand has a fair chance of being best, but it’s vulnerable and will be difficult to play on later streets.

The value in betting comes primarily from protection. No one seems to think that better hands will fold to a bet, nor does anyone think Hero will have positive expected value when called. There are worse hands that can call, but most have decent to good equity and may successfully bluff on later streets, and there are certainly better hands out there as well. Hero is relatively live against overpairs, not so much against better top pairs, two-pair, sets, or straights.

One quite interesting thing I’ve learned from working with GTO Range Builder is that, at least in heads up pots, very few hands in either player’s range are played with pure strategies at equilibrium. Sometimes there are hands so weak that they categorically prefer folding or hands so strong that they categorically prefer betting, but most hands in the pre-flop raiser’s range are played with a mix of betting and checking. There are good reasons why Hero is incentivized to have top pair and backdoor draws in his checking range.

There are caveats here. There likely is not an optimal equilbrium in a multiway pot, and concerns about hand protection are magnified (then again, concerns about value-cutting oneself are magnified as well). Nevertheless, betting seems thin enough to me that I think checking is worth considering as well. It should certainly have positive expected value, and I don’t think it would take much to be competitive with betting.

In my experience, most players are way too concerned about making sure they win the pot. Protection is a real consideration here, but it’s not the only consideration. The fact that your hand is vulnerable is not, in and of itself, sufficient reason to bet. There are worse things in poker, especially in a deep stacked cash game, than getting drawn out on.

So What?

OK, so checking might be just as good as betting. It’s probably not a lot better, if it’s better at all. If Hero really is indifferent between betting and checking, what’s wrong with just always betting?

Will Tipton addresses this question in Expert Heads Up NLHE, where he determines that the optimal strategy in many heads up spots involves continuation betting at a much lower frequency that what is commonly seen even in matches between two very good players. His conclusion is that, because Hero is indifferent between betting and checking so many hands at equilibrium, he does not lose money in spots where he bets at a very high frequency. He does, however, open himself up to exploitation when he checks a very narrow and defined range in these same spots. The weakness manifests itself not in the betting range but in the checking range.

Basically, if your opponents expect you to always bet a certain type of hand, that gives you a lot of incentive to check it. There may be some bad turn spots for you, but there should also be some very good ones. If, for instance, a 7 turns and no one expects Hero to have a 7, the implied odds can be quite high.

My suspicion is that many of you almost never check this spot with top pair or better, which makes your checks quite easy to play against and means you may well be leaving money on the table by not taking advantage of profitable situations that arise after checking.

If you accept that you should have a checking range, 8s 7s seems like a logical hand to include. It benefits less from protection than does 88 or 99, and it probably fares less well when called than does A7 (assuming 7x is in people’s ranges, but I think at least for some players hands like T7s and 97s should be out there). There are not as many bad turns as it may seem: 9s and below are all safe-to-good (with the exception of a 6), and spades are all fine as well.

Sizing

More important than the frequency with which you bet is the size of your bet. The bigger you bet, the more polarized you should be. I think it’s quite likely that betting 3/4 pot or more with 7s 6s is -EV, at least relative to checking. A smaller bet can more easily accommodate a merged range that includes hands like 7s 6s that mostly benefit from protection. Hero’s range advantage along with the multiway pot means that even facing a half-pot bet, there really isn’t room for people to get too tricky by floating/raising with bare overcards or something like that.

If you’re going to bet a merged range here, it’s not a disaster, but you absolutely should not be near-potting it. Unfortunately, many people seem to have the opposite idea that betting for protection requires betting big, because you want folds. In fact, the hands you are targeting for folds will probably fold to a small bet anyway, and you should also want to avoid putting in a lot of money against a range you’re behind.

Results and next decision point coming in the next post…

Flop ($118 in pot after rake) 7h 6d 3s. Action checks to Hero. What’s your play and why? Try to think about how you would play various parts of your range on this flop. What would your betting and checking ranges look like? If you bet, what are you hoping will happen? If you check, what are you hoping will happen?

We’ll discuss it in the comments, and I’ll post my thoughts and action tomorrow.

As I expected, a lot of the comments hinted at the right answer without quite nailing it on the nose. That’s good, as it will give us a chance to address some common misconceptions. Here’s a representative example: “when you raise pre flop, you don’t raise a hand, you raise a range of hands. You want your range to be balanced, so you have to put big hands and hands with potential. Even when 87s is behind pre and post flop, it’s your whole range that matters.”

This seems to imply that opening 87s is -EV, but we should do it anyway. This should never be the case. The route to optimal play is to make the most +EV decision at every opportunity. Folding has 0EV, so if raising is -EV, then folding is better. Contrary to popular belief (a belief that I myself espoused until not too long ago), you shouldn’t make plays “for the sake of balance”. At equilibrium, the EV you gain from, for instance, giving your opponent more incentive to pay off your strong hands because he knows you also raise weak ones, can’t be so great that it overwhelms whatever you lose by playing weak hands. If it were, your opponent could just revert to not paying off your strong hands, let you get the occasional bluff through, and unilaterally increase his own EV.

What this hints at, however, is that the general composition of your range may actually make it profitable to play other sorts of hands. This is what people have in mind when they talk about “implied odds”, although I find that term misleading because it conjures up images of “slot machine poker”: making big hands and then getting paid off. In fact, as we saw in the hypothetical above, hands can outperform their hot-and-cold equity not only by getting paid big on certain boards but also by bluffing on boards that are good for other parts of your range.

There’s a small universe of hands so strong that they can be opened and, even with six or seven people left to act, be a favorite either to win the blinds or be called by worse. Your opponents simply won’t be dealt better hands than, say, QQ or AK often enough to both defend the blinds vigorously and consistently be ahead. So, you certainly will open hands like that from early position. Just for the sake of argument, let’s say that range is {AQo+, AJs+, TT+}

Now let’s think about how that range will play on two different boards: 654r and AT5r. On the 654 flop, the danger is apparent: this range never makes a stronger hand than one pair, which gives opponents the opportunity to make both bluffs and thin value bets with impunity. Having 87s will not necessarily “protect” you from this strategy. It will, however, give you the opportunity to win a big pot on this flop. This is why I say that it’s not about making a -EV raise with 87s in order to protect some other part of your range, but rather about the composition of your range making it profitable for you to include some different types of hands.

The danger on AT5r is less apparent. Many people are perfectly happy to see a flop like this with AQ and then with the pot and perhaps even another bet before eventually taking it down with a turn or river bet. I even see people who want to bet hands like KK on this flop to “represent the Ace” because the board so strongly favors the pre-flop raiser.

The reason you may have trouble winning big pots with objectively strong hands like AQ or AK is that your opponents correctly perceive you are rarely bluffing on a board like this, because it is so good for your range. If the weakest hand in your range is JJ, well, I guess you might as well turn it into a bluff, but that isn’t going to be terribly profitable. You may not realize it, but a very tight range is missing out on profitable bluffing opportunities for lack of hands that strongly prefer bluffing to checking on a board like this. Playing 87s may not cause you get more action with your strong hands, but it will enable you to profit from your opponent’s folds. This, too, deserves to be called “implied odds”, though it usually isn’t.

More useful terminology has recently entered the poker lexicon. Videos from Ben Sulsky, Sean Lefort, and others use a variable, r, to represent the percentage of its equity that a particular hand can realize after postflop play. This is often used in analysis of blind defense, to determine exactly how little of its equity a hand can realize while still being a profitable call.

In this case, however, we are looking at a hand that will have r > 100%. This is because 87s can win several times the pot on boards where it has near-100% equity and also have a reasonable chance of winning the pot on boards where it has near-0% equity. Thus, even though its hot-and-cold equity is poor relative to other hands in your opening range, the overall composition of that range gives your opponents incentive to play in certain ways against you, which makes it possible for a few weaker hands in your range to outperform their equity.

You have to be careful not to take this too far. If your opponents are so loose and poor at hand reading that you can play a very tight range pre-flop and still happily put your stack in with AQ on AT5r, then 87s will probably not have the implied bluffing outs discussed here, and you may be better off not playing it in early position, especially if your opponents are also very loose pre-flop (and such opponents almost always are). Likewise if you are going to pass on the profitable opportunities that playing this hand presents because you are averse to bluffing. I don’t think you’ll show a profit playing this hand if your only goal is to make two-pair or better and then hope to win a big pot.

There’s room to include only a few such hands in your range – if you go overboard, then you risk exploitation, quite possibly unintentional, by loose opponents, or by passive opponents who don’t attack you on 654r. The stronger suited connectors are the best candidates for this. Their raw equity is higher than that of lower suited connectors or suited gappers, and their ability to realize equity is better than that of off-suit broadway hands like ATo, which tend to be strong or weak on the same sorts of boards that are already good or bad for the majority of your range.

As one commenter pointed out, PokerSnowie does in fact advise folding this UTG at a six-handed table with 100BB stacks. That seems excessive to me, but with sufficiently skilled and aggressive opponents (getting 3-bet when you’re holding 87s sucks), I could see this being correct. In practice, it’s a hand I play 100% UTG in, say, a $1/$2 ZOOM game with a $200 stack. At 250BBs, I think the case for playing it only gets stronger, and it’s stronger still with typical live opponents whose three-bet ranges are, shall we say, sub-optimal.

Pre-Flop

I’m increasingly convinced that this is a fold after all. A very rough estimate is that I have about 15% equity against the Villains’ ranges and need to realize about 80% of that to make money on the call. The fact that I got a well-above-average flop and still can’t find an especially profitable option is telling, as is the fact, pointed out by many, that even if my hand improves the implied odds are not that great.

Results

I’ll start with the results, because my own play is one of the lines I want to consider and dismiss. I raised to $600, Villain 1 called, and Villain 2 folded. The turn was an off-suit J, and we both checked. The river was an offsuit 9, and while I considered shoving, I decided not to do so for exploitive reasons. Villain 1 checked behind and won with QQ.

Bomb the Flop?

While my in-game thought process was admittedly sloppy, I don’t think that, “Someone clearly has top pair or better and they’ve see you bluff before, so don’t ever raise without a set” is the best way to approach the problem either. We’re quite deep, and even for the looser UTG1 player, putting in eleven times the pot with one pair when five people saw the flop is not going to be an automatic decision. If I’m going to raise sets/two pair here, then I should have a bluffing range as well.

It doesn’t necessarily follow that this hand belongs in that range, though. As Jeff G. astutely points out, “Given that hero is calling with 7h2h preflop, I think it’s a safe assumption that hero has every combo of set(9 combos), suited two pair(7), and flush draw(55!! minus any combos we 3bet pre, if any) in his range. So we definitely want to have a check/raise range in this spot however we can easily go overboard if we’re not selective in which draws to use to balance our value hands.”

He argues for using nut flush draws for this purpose, and I think that’s partially right. As deep as we are, nut draws are disproportionately valuable, and the Ace will frequently be live. However, it does block some of the weaker hands in UTG’s range, such as AK and AQ, that he might c-bet even for this sizing into this many people. Getting a fold from him on the flop is one of the best case scenarios, so blocking his most obvious folding hands isn’t great.

You also don’t want your bluffing range to be too dependent on a single card (the Ah, in this case), because a blocker-conscious opponent can use that information to his advantage. In other words, some players are actually savvy enough to call down more often with black Aces than with red Aces because the red Aces block some likely bluffing hands. So, I think there’s a case for raising at least some non-nut draws.

Other good candidates will be gutshots, both with and without flush draws. You have to be especially careful not to go overboard with the bare gutshots, but it’s important to look ahead to the scenario where Hero check-raises and a heart peals off. Many of you correctly anticipate that it will be hard to get paid with a low flush in this scenario, and the corollary to that is that you want to give yourself some bluffs in that scenario, as Matt argues in his very good comment. If your flop raising range is only flush draws and two-pair or better, then what’s your bluffing range on the Qh turn?

The bottom line is that although this is a good spot to raise some big draws, the fact that none of my outs are nutted makes this an unideal candidate for inviting such a large pot, and I have better bluffing candidates. So I want to at least rule out the play that I made, which was raising to $600, as a good option.

Fold the Flop?

Matt also says, “I don’t think folding right away is an option. Running some equities, I think we can expect to have in the neighborhood of 28% equity against both ranges; so although we should expect both Vs to be quite strong I think we most likely have enough immediate equity to continue.”

Chris C, however, argues that, “if we’re calling then we’re calling to improve to the best hand (since I don’t think bluffing is likely to be profitable here). But the strong ranges of the villains (each of which contains sets and lots of better flush draws, all of which leave us in terrible shape) means that we often *can’t* catch up to the better hand, and that we can never be confident about it even when we do. If we end up playing a big pot then we likely lose, and if we hit but then try and keep the pot as small as possible – well, that doesn’t seem too good either.”

I’m on Matt’s side, and I think Chris is conflating some disparate scenarios. Even if Hero has difficulty putting in stacks or even two big bets as a favorite on favorable turns, he should very profitably be able to put in one. That is, if a heart turns, check-calling one bet should be profitable, and calling a second might be a more-or-less neutral-EV proposition (which also means I won’t often face the second – it’s not common that 7h 2h is behind on a heart turn). If the turn is a heart and there is no bet, I can confidently value bet the river.

The prospects are even more favorable on 7 and 2 turns. I can confidently call at least one and often two bets on these turns, can bet the river if the turn checks around, etc. Because of the good immediate odds I’m getting, I don’t need hefty implied odds when I improve. I just need to have the best hand most of the time, which I will. In that case, either I won’t often end up playing a big pot, or I’ll often be ahead when I play a big pot. It can’t be the case that I’ll routinely face multiple big bets after improving my hand and also not be able to call those bets profitably – it just isn’t that easy to be ahead of 72 on a J622 board.

I think there’s a strong case for calling, but there’s one other interesting line that one of you hinted at but no one suggested (nor did it occur to me at the time).

Small Raise?

A big part of the reason why I don’t like bombing the flop is that it sets up an easy and obvious strategy for an opponent holding an overpair or a Jack, which is to call the raise, fold if a heart comes, and call down otherwise. I was somewhat lucky that the turn was a scary enough card for my opponent that he gave me a free river, because I don’t think I could have profitably bet or check-called any turn that didn’t improve my hand. That’s in part because, given how low the SPR was at that point, most players facing a turn bet from a draw-heavy range will correctly shove rather than call if they continue to a bet.

Raising a small amount on the flop in order to deter a turn raise and give me room for a meaningful river shove is an interesting idea, though. Also, as James points out, “Both players calling your raise doesn’t change your equity in the hand (let’s say it’s 40% in the 3-way pot) vs you just calling.” I don’t think this was the point he was getting at, but in fact raising and getting called in two spots is better for me than just calling – I am 40% to win and getting 2:1 on my money. This is the kind of spot that an experienced limit player would probably recognize more quickly, because it’s common to raise hands with less than 50% equity in multiway pots in those games, but it comes up far less often in NLHE. Here, though, if I can’t fold out both players, my next preference is to fold neither. The result I got, and the one I think I’ll commonly get, was the worst.

Leo suggests raising “to something like $420…. The plan is to barrel off here on bricks, targeting overpairs, top pairs, and better flush draws that have paired up.” That would have been an interesting option, and I wish I’d considered it. Maybe next time!

Thanks again everyone.

Villain 2 is loose, especially in small pots. He’s definitely too stubborn post-flop, but that doesn’t mean he shovels three hundred blinds into the pot every time he makes top pair.

Both players have seen me show down some big bluffs, but both have also expressed regret about hands where they’ve stacked off to me as well.

Villain 1 opens $35 UTG, Villain 2 calls UTG1, there are two more calls, and I call 7h 2h in the BB. Just to pre-empt some questions, this isn’t a trivial pre-flop call, and it’s fine to fold here if you aren’t particularly confident in your post-flop game, but it’s a call I’m comfortable making.

Flop ($168 in pot) Jh 6h 2s. I check, Villain 1 bets $135, Villain 2 calls, the other two players fold, and the action is on me.

What’s your play and why? Leave your thoughts and preferred play here, and I’ll do my best to respond throughout the week and post results on Thursday. If you don’t fold, be sure to consider your play on future streets as well, especially if your hand does not improve.

Though popular, the strategy of checking and calling with a hand that can’t win unless it improves, in the hopes of getting paid off big when you do improve, is a poor one. Practitioners of this strategy tend to underestimate the value of betting and raising with draws and overestimate the amount they can win when they improve. The problem is that your opponents can see when a flush or straight draw gets there, which makes them unlikely to put money into the pot with lesser holdings.

All of that said, I did recently encounter a situation where I deliberately played a draw passively even though I believed I had a good chance of winning the pot immediately with a bluff. The point of this article is most emphatically not to encourage you to play draws passively in general, but rather to emphasize just how much the stars had to align to make this strategy the best.

Enjoy!

Q: Hero raises from late position with Q9s and is called by the button. The flop is Q72r. Being out of position with a one-pair hand, shouldn’t I frontload my value? Sure, top pair is a good hand now, but the board will get scary later, and it will get harder to get paid off. I can see check-calling hands like JJ, but Q9 seems good enough to value bet. Basically you’re saying its important to put hands like top pair  (sets/2pair for balance) in our check/call range so that we can strengthen our check/call range as we will be folding too much to 2-3 barrels. Basically it allows us to get to showdown for cheaper with our marginal hand if we’re capable of taking the same line with our monsters/marginal hands? If Villain knows we’re capable of check/calling with monsters, they won’t bluff as much.

A: It’s not just that it protects some other part of your range. The point is that if you have a lot of hands that can’t stand up to multiple barrels after you check, your opponent has a lot of incentive to bluff into your checks. Thus, checking and calling with Q9 may be at least as profitable, if not moreso, than betting it.

With a stronger Q, this is less true, because when you check KQ you may miss value from QT or QJ. Because you have so many stronger hands in your betting range, though, Villain doesn’t have a lot of incentive to call you down with lots of hands weaker than Q9. Thus, betting Q9 for value across multiple streets isn’t going to be super-profitable.

In truth, because this is presumably one of the weakest Qx you could have, you shouldn’t really have a lot in the way of implied odds regardless of how you play it. In other words, your EV on this flop probably isn’t much greater than your equity, regardless of the line you take.

For more discussion of range construction, be sure to check out this week’s strategy segment on the podcast!

Folding is an Opportunity, Not a Cost

Props to those of you who mentioned the relevant toy game from Mathematics of Poker. That was the first thing I thought of when playing this hand, and it was the impetus for my posting it.

For those who aren’t familiar, Chen and Ankenman demonstrate that when you have a big draw against a made hand, it can actually be correct for you to move all-in on the flop, knowing you are behind and have no fold equity, rather than give your opponent the opportunity to blow you off of your equity on blank turns.

The critical difference between that toy game and this hand is that in the toy game, we assume that the made hand knows his opponent is drawing and can play perfectly on the turn. In other words, not only can he force the draw out on blank turns, but he can also correctly check and fold on turns that sharply improve his opponent’s equity. No commenters suggested that Villain might check and fold a 6 or a heart on the turn with any hand that would have called a flop shove, and rightfully so.

There was, however, a lot of talk about how Hero will “have to” fold some turns, as though it were a cost or penalty of some sort. You should see this as an opportunity! In our example, checking back means that Hero will get to benefit from additional information about the hand he’s likely to hold at showdown. Because Villain is not in a position to make similar use of this information, this is an opportunity for the Hero.

The turn card is going to be what it’s going to be. It’s already sitting there on top of the deck, waiting to be dealt. Essentially, you are given the opportunity to peak at that card before you decide whether you want to get all in. Why wouldn’t you do that? Sure, it will be disappointing to see the Ac, but if you are going to see it either way, wouldn’t you prefer to know that it’s coming so that you can avoid putting $300 out there?

Put another way, assume that Villain never folds to a flop shove and will always shove any turn. In this case, shoving flop and calling a shove on any turn are functionally equivalent. The only question is whether Hero can make use of the additional information that the turn brings in order to avoid committing his stack on particularly bad runouts.

Fold Equity

All of that operates under the assumption that Villain never folds the flop. This was my expectation when playing the hand, though I do think that Gavrik makes a very good point (which also has some connection to a discussion in Mathematics of Poker):

Let’s see what happens if we base our play on trying to guess if we have any fold equity or not.

1) We assume we have ~10% fold equity. We are wrong and in reality we have 0% fold equity. We shove, get called and flip for it. We have lost a tiny amount of equity by being wrong.

2) We assume we have 0% fold equity. We are wrong and in reality villain would have folded ~10% of his range. We check back the flop and from there all sorts of bad things can happen – villain can “bluff shove” all the hands he would have folded on the flop, villain can hit a pair on the turn and shove for value, in addition, if villain shoves on a brick turn we are not really getting the right price to call. Seems like a recipe for disaster.

So, a lot depends on how confident you are that you have no fold equity. I was pretty damn confident.

Villain simply has to be strong based on the pre-flop action. If someone re-raises him pre-flop, he’ll be getting well over 2:1 to call. He just can’t make this play with any hand that isn’t ready to get all-in pre-flop, which means he’s functionally jamming $500 into a pot of $150 and an early position raise from a somewhat nitty player. Except that he’s not jamming, he’s deliberately offering his opponents good odds, which if anything only strengthens his range. Also, as Diane points out, the fact that Villain is in the big blind makes an “air squeeze” even less likely, as he could just call $40 more and see a flop.

Some commenters are suggesting that Villain might have KQ or KJ, but I just don’t see that based on the pre-flop action. Even if he did, I think there’s a fair chance he’s shove the flop as opposed to checking and folding. Just as Villain shouldn’t have any hands that will fold pre-flop, I also don’t think he should have any hands that will check-fold this flop. That means that when he does check, it has to be a trap.

I agree with Chris C. that many Villains will just shove AK on the flop, but I actually think it’s a pretty good hand for inducing, as he can’t really expect better to fold. It doesn’t matter, though. Whether or not Villain’s range includes JJ or AQ doesn’t change Hero’s play as long as Villain isn’t folding (and is planning to jam over a small bet, which I also expect to be the case).

The strength of Villain’s pre-flop range is certainly an argument for folding my hand. Against a range of only overpairs, I should fold. With AK in the mix, I have a call. With only a chance of AK being in there, I should probably fold. However, if Villain is going to make mistakes like this on the flop, my call is a little more appealing.

Turn Plan

Hero will need about 30% equity to call a turn shove. Although I think his ranges are too wide, I want to give props to Sean F. for using Pro Poker Tools to graph Hero’s equity across all turns. Here are graphs of Hero’s equity vs AA and vs KK+,AK.

Even against Aces, Hero can call almost 40% of turn cards. That would be any 7, and 8, any 6, and any heart, 18 cards total, 37.5% of the deck. The tricky thing is that Villain has all combinations of AK in his range, Hero should actually call more than twice as many turns, probably folding only on non-heart Aces and Kings. Putting only suited combinations of AK into Villain’s range again makes Hero call only on turns that clearly improve his hand, which was my plan (like Chris C., I’m skeptical that Villain would play AK this way, and don’t want to assign more than a small chance to that).

It’s worth noting that we might even get a check on some bad turns. Both AA and KK might want to check the Ac, for instance, and KK might choose to check Kc. I think shoving would still be a mistake for Hero, but occasionally getting to see a free river when way behind is a pretty nice perk.

Results

I checked. The turn was the 7c, Villain shoved, and I called and caught an 8 on the river to beat his KK. He was not pleased.

This is level 2 (150 – 300) and I ran the starting stack of 15k up to 28k. A player from middle position had 1 limper ahead of him and opened to 750. He just got to the table and has not played an orbit yet. This was his first hand. One person called and I called from the button holding 7h8d. The blinds call and so does the original limper. 6 players to the flop! Seeing 4+ people take the flop was the norm so far at this table. (BTW I’ve discussed this with a couple friends and they both said that it’s likely that 78off is not profitable even with stacks this deep and even knowing the table dynamic… Is this a situation that I should be passing up on often because I don’t often do it this early?)

The flop comes J 10 3 rainbow. Checks over to the original raiser and he bets 800. Folds to me on the button and I look to my left and the two people in the blinds have no interest in this pot. I know that this is a weak attempt at a cbet and he’s not comfortable at all with his hand displaying classic signs of weakness. The strongest he could be a hand like A10 or an under pair to the board or he whiffed with something like AQ and KQ also crossed my mind. I just tried to rip the pot away from him so I raised to 2200 and it folds back to him. He painfully calls and it’s heads up. The turn is a 7 so I’m paired up! No back door flush draws came in. He checks and I cut out 3500 (should I be betting more to get this guy off his hand?). The river comes a 9. His mood quickly changed and he bets out 3500 making sure that he used the exact same chips I used. I want to fold. KQ came but I convinced myself he could easily be doing this with 10 9 or J 9 and I figured that the pot was too big to fold with the worst straight so I did end up calling and he indeed turned over the KQ.

Any critique would be highly appreciated!

A: First off, pre-flop can’t be too bad, as you have a remotely playable hand plus the button with reasonably deep stacks and a lot of people in the pot, but I agree that it’s probably a fold.

UTG1 opens to $60 off of a $3000 stack. I call with 8h 7h on the button (I cover him). The BB squeezes to $160 with $300 behind. UTG1 folds, and I call.

Flop ($399 in pot) 5h 4h 2c. Villain checks. Hero?

Post your thoughts, questions, and preferred play here. I’ll respond to comments throughout the week and post my own thoughts along with results on Friday.

If you choose to check the flop, please consider your play facing a bet (probably a shove) on blank turns.

[E]ven though position is important, and the stacks are deep enough to make 74s less ghastly than if we were 100BBs or shallower, there just aren’t enough reasons to play it. Furthermore, our image is bluffy, and that’s going to make it hard to barrel through this hand if we flop a draw/some equity and miss on the river and have to make a large bet because we either flatted a 4x pre (or 3-bet to even more) and raised or floated the flop and fired the turn. With a stubborn/bluffy image, I’d rather have a hand that wants the call it’s going to get (because our opponents are keen to look us up) instead of one that wants a fold. Sure, the flip side is with deep stacks if we make a well-concealed monster we’ll get paid off huge, but how often will that happen compared to the regrettable number of times we are forced to play into our own image and bluff?

This wouldn’t be much of a thread if Hero did fold, so I imagine there’s going to be a flat here and a float to take advantage of villain’s c-betting tendencies and predictable play from out of position.

This is me keeping my WYP range balanced. Sometimes – often, actually – you’re just supposed to fold, and I don’t want this feature to send the message that some fancy play is called for every time you pick up a remotely decent looking hand. There’s no further action here, Hero folds pre-flop. Still, there were several comments worth discussing, so let’s get to it.

The Players in the Blinds

Tracy Marrow says, “The description leads me to believe that the blinds will come along if I call, which makes indicates much better odds for our call,” and a few others echoed this argument as well.

I gave HJ a range of all broadways, all pairs, and a few suited connectors and other hands. I gave the blinds pretty loose ranges and subtracted QQ+,AK as likely 3-betting hands (which of course hurts our equity even more than if they call with those hands, though it won’t be reflected in the number shown here). Assuming they call, there will be perhaps $155 in the pot after rake, of which Hero will have contributed a little over 25%. Yet Hero will have just 16.5% equity.

If the blinds fold, Hero will be heads up with $90 in the pot, 44% of which was his. He’ll have 32% equity.

In the former case, Hero is 8.5% shy of the equity he needs to avoid losing equity on the pre-flop call, and in the latter case he is 12% shy. So he does slightly better when the blinds call, but not much. Many players overestimate this effect, but the truth is that although you get better odds in multiway pots, you also need better odds, because it’s harder to win multiway pots.

Implied Odds

Of course there is some post-flop advantage to having position on each of these players, but to some extent their favorite mistakes risk cancelling each other out. Matt Glassman says, “The description of villain immediately had me thinking “Call, float flop, take it on the turn” will happen often enough to make getting involved more profitable than folding.” He’s right that this would be the preferred strategy against the pre-flop raiser, and if we could guarantee we’d be heads up with him, this just might be profitable enough to outperform folding – I’ll come back to this argument.

However, throwing a loose player or two into the mix complicates matters. Villain will probably continuation bet less, which immediately makes floating less profitable, never mind that floating now requires hitting a parlay where neither Villain nor one of the blinds flopped much of a hand. Admittedly, less continuation betting will mean more opportunities to check behind and realize some equity on the turn, but in most cases Hero’s hand will be so weak that even a free turn card won’t be of much value. Basically we’d be calling hoping to flop a weak pair or draw with which we’d still either end up playing passively or making some pretty thin bluffs into multiple players.

The whole “make a big hand and get paid” idea isn’t as easy as it sounds when you have 74s and a 250BB stack. Two small pair is not necessarily going to be a favorite when that much money goes into the pot, nor is trips with a weak kicker. There are a few ways to make two-card straights, and those should be solid money makers, but a flush may not be. If three or four people see the flop, and then a flush card comes on the turn, even loose players know to be wary. I’m not saying you won’t win the pot often, just that you can’t count on winning huge pots terribly often.

Floating In a Heads Up Pot

Even if the two loose players in the blinds fold, Hero still isn’t in a great spot to float with no equity. If Villain c-bets $60 close to 100% on the flop and then checks close to 100% on the turn, Hero will have the opportunity to bet perhaps $100. Let’s break it down:

10% chance Villain bets turn. He always has big hands, and Hero always folds, netting -$100.

30% chance Villain checks turn and calls a bet. Hero’s net is -$200 (perhaps he recoups a bit of this with slightly +EV river barreling).

60% chance Villain checks and folds. Hero nets $110.

.10 * -$100 + .3 * -$200 + .6 * $110 = -$4.

This is an important lesson: even if you know someone will overfold on a later street, you aren’t guaranteed a profit by calling to that point with any two cards just hoping you’ll get the opportunity to exploit it. Sometimes the price you have to pay to find out whether you’ll get a profitable any-two-cards bluff is too high.

Now, if we give Hero some equity in the pot, that can easily swing this to a profitable float. But that will happen only about 1/3 of the time, and even then it won’t be a super-profitable spot, so even the “best case scenario” of seeing the flop heads up with the raiser is not an especially good one.

Three Betting

I like Eddie’s question on this subject: ” If you are 3-betting this hand, what percentage of hands will you then be 3-betting overall?” Many players do respond very badly to three-bets, and if this guy folds way too much pre-flop or on the flop, this might well be a profitable AATC (almost any two cards) spot. I didn’t give you that information, though, and it certainly shouldn’t be profitable to three-bet such weak hands against a player with a relatively strong opening range. In other words, if Villain isn’t making a big mistake in a three-bet pot, then Hero is.

In my opinion, fold > three-bet > call.

Some of my blog comments highlight this point starkly. When the Hero in the hypothetical hand example holds a strong hand and is trying to get value from something marginal, some commenters will argue for a small bet, on the grounds that marginal hands need to be offered good odds in order to call. Others will argue for a large bet, on the grounds that it will look like a bluff.

In a real life situation, you might actually have sufficient evidence to make a good guess about how your opponent will interpret or respond to a specific bet size, and in that case, you certainly should play accordingly. My hypotheticals don’t always offer that kind of evidence, though, which makes clear that many people are just blindly guessing about how their opponents will respond. Even in real life situations, blindly guessing is not the most profitable strategy.

…

Your AK wants a call, your bluffs want a fold, but what does your range want?

I also realized that I never told you about my last article, which is now a month old. It’s called Making Money With A GTO Strategy, and it, too, is a response to some common objections to a game theoretical approach:

One of the most significant misunderstandings, and the one that I want to address in this article, is that game theoretically optimal (GTO) play is merely breakeven poker, which after accounting for the rake would actually yield a negative expected value for such a strategy. Although it’s true that two players employing equilibrium strategies would simply push money and back and forth until it was all raked away, such strategies can and do profit from opponents who employ unbalanced strategies.

Enjoy! And of course, I’d be eager to hear what you think of them.

The game is $5/$10 with $2500 effective stacks. Hero is widely perceived as tough but a bit too stubborn/bluffy.

HJ is a straight-forward, experienced recreational type. He’s TAG-ish with his pre-flop hand selection, continuation bets too much, and rarely barrels the turn with either a made hand or a bluff. Unless he has a huge hand, he usually c-bets the flop, check-calls or check-folds the turn depending on whether he has anything, and then check-decides on the river . If the turn checks through, he’s capable of both bluffing and value betting rivers.

The blinds are also recreational players, though more loose and passive than HJ. Their standards for calling pre-flop and on the flop are pretty low, but they tighten up a bit as the bets get bigger.

HJ opens for $40. Hero is on the Button with 7d 4d. What’s your play and why? Posts your suggestions in the comments section below. I’ll do my best to respond throughout the week, and I’ll post my own thoughts along with results on Friday.

But my question is more generally as I seem to have problems with these little pairs when my stack is between 20-25bb. When I am between 15-19bb I like to put these hands into my 3bet allin range of hands. But with 20-25bb that might be to much and I might be to far behind against the range of hands with which my opponent calls me? Could you give me any advice on this problem?

A: I’ll do my best to add to your analysis, but I think you’ve already identified why these are tricky spots and what might be the better play. The thing I’ll say off the top, which you hinted at yourself, is that just because shoving is profitable doesn’t mean it’s the best play. You’re getting great odds on a call, which means that calling will be significantly +EV. If you have doubts about whether shoving is profitable at all, then it’s better to make the obviously +EV call.

A couple of other things to consider. First, small pairs perform best against wide calling ranges. You need to get a lot of coinflips against overcards to make up for the times you are dominated by bigger sets. So even if a HJ opener and a button opener would each call your shove with the same frequency, you’re much better off against the button opener because he will have a wider opening range and thus a wider calling range (or, if they have similar calling ranges, then he’ll fold more frequently, which is probably even better for you).

Second, there’s some chance there’s a sizing tell here. It would be nice to know whether Villain was consistently opening for 16K. It seems to me he may have chosen that size specifically to induce a shove from you, as he easily could have opened to 14K and made it much less likely that you would jam.

I think there are two reasons why many tournament players shy away from calling in these spots:
1. You lose the pot more often. You lose less, of course, than when your shove is called, but you do lose more frequently.
2. You have to make some tough decisions on later streets.

(2) isn’t necessarily a bad thing, because each decision is an opportunity to outplay your opponent, but it does require some comfort in playing postflop. I think that improving your postflop skills and better understanding how to play this bluffcatching/clawing back equity game that you’ll end up playing when you call out of the BB, is about the best way you can improve your results in this and similar circumstances.

Ruud says, “Generally I find Villain has the goods when he bombs the river like this.”

Pepito agrees, “unless he contemptuously views you as a bad, nitty player, what adept villain expects Kx to fold given that particular run out and action? river looks like soul-owning thin value from AK and/or KQ, or fat value from 2P, straights, and flushes.”

Mike argues exactly the opposite: “if he’s a good player, he will know he can try to rep something strong considering both a flush draw and straight draw got there.”

I think this is as telling a demonstration as you’re going to get of the value of guessing at the meaning of Villain’s bet. A “good player” shouldn’t be so easy to pigeonhole as definitely bluffing or definitely value betting, just as he shouldn’t feel confident about whether or not I’m going to call a river bet, so let’s dig a little deeper.

The Knowns (or Strongly Suspecteds)

1. Villain is raising exploitably many hands pre-flop and consequently will see the flop with an overly wide range. That means he’ll see the flop with a lot of weak hands. As long as we don’t fold exploitably often, he can’t show a profit by bluffing with them, so one way or the other our strongest hands will win the pot on any given run out – either Villain gives up frequently and lets us win at showdown, which also benefits some of our more medium-strength hands that aren’t going to call multiple barrels, or he bluffs frequently, meaning that we win the pot less often when we have the best hand but win larger pots with our bluff-catching range.

2. This is a particularly bad river for our hand and a good one for many of the draws Villain could have.

The Unknowns

1. Villain’s value betting strategy. Would he bet AK or AA for value here? If so, would he use this sizing? Multiple bet sizes, particularly on the river, is not necessarily an exploitable strategy, so let’s not rule out the possibility that this bet is more polarized than a $250 would be, but less polarized than a shove would be.

2. Villain’s turn barreling strategy. Does he bluff only/primarily draws? Because his range is more polarized than mine, he has room to make a larger bet with a range that includes more bluffs, and I think his sizing is likely a mistake on the turn, one that forces him either to give up with a lot of his weak hands or offer me appealing odds to call against a bluff-heavy range.

3. Villain’s river bluffing strategy. There are three options here: (a) He does his best to bet in a balanced way, though the number of bluffs available to him may be limited because of his turn sizing and the exact river card that came; (b) He bluffs too much, which requires him to also have bluffed too much on the turn; (c) A large bet means he is weighted towards value hands, which is a common tendency among non-elite players.

Against strategy (c), we do best by folding. Against (b), we’d prefer to call, and against (a) we’re either close to indifferent or prefer folding, depending on whether his turn bluffing strategy enables him to bluff the river adequately. The fact that we prefer folding in a lot of these hypotheticals does seem to argue for a fold, as does the fact that calling against (b) is probably less good than calling against (c) is bad, because (c) contains few if any bluffs, whereas (b) contains all value hands in addition to a lot of bluffs.

There’s another factor to consider, though. Given that Villain bet the turn and river, it’s somewhat more likely that he is playing overly bluffy strategy (b). In other words, because strategy (b) bets more often than the other strategies do (it’s easier to have air than a strong hand, not to mention that (b) bets both), if we thought that all three strategies were equally likely before we saw any action, seeing two bets should incline us towards calling.

Although Villain seems uncommonly good, there are still more players in the 5/10 NLHE pool who play strategy (c) than those who play (b). Bayes’ Theorem cuts us both ways.

Reading Hero’s Range

Although my pre-flop range is somewhat narrow and well-defined as “too good to fold but not a good candidate for three-betting”, the small bets on the flop and turn mean that I haven’t folded too much of it. Pocket pairs, Kx, AJ, AT, sets, and perhaps some 6x and 7x (though I probably three-bet those pre) all call the flop. The AJ and AT get bluff-raised or ditched on the turn, and sets raise, which means that the pocket pairs and Kx both go to the river. I probably don’t make any flushes or straights on the river.

To make Villain indifferent to bluffing, I’d need to call about half the time. The chance of Villain playing AK or KK this way makes KJ a slightly better bluff-catcher than the pocket pairs, though they really aren’t very different.

I’d much rather have the Js for bluff-catching than the Ks. Some of Villain’s Ks Xs might actually check the turn, so I think the blocking value of Ks is not what it seems.

It’s also possible that this river is so good for Villain’s range that I can’t profitably bluff-catch at all, at least not against this sizing. If his large bet prevents him from balancing with sufficient bluffs, I can exploit him by folding all of my bluff-catchers, which is probably what I should have done. In game, I didn’t appreciate the significance of the small turn bet in terms of potentially limiting Villain’s ability to bluff, especially on this river.

Results

I called. Villain had 98o for a rivered straight, which suggests his pre-flop range was even weaker than I expected.

Seeing that hand makes me like my river call even less, though it also makes me dislike folding pre-flop even more than I already did.

Props to Bryan Gour for considering a raise. I did think about that in game, and I agree that the Ks blocker is perfect for it, but I don’t know that I’d ever raise her for value, so I chose not to do it as a bluff either.

Told Ya So

“This is why I would have raised pre-flop…” To be honest, I was expecting more comments like Zachinacubicle’s than I got.

I’ve already talked about three-betting vs calling pre-flop, and while I’ll admit that as Villain’s pre-flop range gets wider, three-betting gets more appealing, I still prefer calling even knowing that Villain may be raising half the deck. After all, KJo is only a very small favorite against that range, and will not play well out of position. The only reason to three-bet this would be if you expect Villain to fold exploitably often, and that doesn’t seem to be his bag.

It’s important to recognize that this was a really bad river, perhaps the worst in the deck, and Hero still ended up with a close decision. Not all run outs will be this bad, and considering that even a bet on this worst case scenario river produced a close-to-break-even spot for the Hero suggests that this hand is really not so hard to play out of position.

If you are in the “Bah, I don’t care about game theory, people are so easy to exploit!” camp, that’s a fine attitude when it comes to calling or folding the river, at least if you think you have a handle on how Villain can be exploited. But if you’re folding pre-flop because you fear post-flop decisions, then learning to defend your equity by checking and calling in an unexploitable way is valuable for you. Calling and then bluff-catching in a balanced way is simply more profitable than folding pre-flop (and than three-betting pre-flop, unless Villain folds too often).

Contrary to Greg’s assertion, you don’t have to “guess” at Villain’s bluffing frequency. You simply have to call often enough that his bluffing frequency doesn’t matter.

Brian has a slightly different criticism of the call: “You play a limited number of hands live and recreational players make enormous mistakes with deep stacks. Setting up dynamics with almost zero EV vs the best players is a waste of your most precious resource – time playing against the recreational players.”

There’s something to this, but I think the argument cuts both ways. By passing on a profitable call here, you are giving your chief nemesis an opportunity to play against the recreational player, and in fact a very profitable opportunity to exploit that player. Not to mention that calling does still give you a chance to see a flop against that player. This is actually a concept that Nate and I discuss in our WSOP Premium Podcasts.

Edit: I meant to add that it’s quite easy to construct scenarios in three-bet pots that will make you wish you called, much as this particular scenario might make you wish you three-bet. Example: you three-bet pre-flop and get this flop. You either bet and get called, or check and call. On the turn you check and call. You’re in at least as bad of a spot now as I was in this hand, and you’ve put a good deal more money into the pot even before you contemplate calling a river bet.

UTG is a typical splashy recreational player, with lots of limping and calling pre-flop followed by lots of checking and folding post-flop. He has about $800 in his stack.

HJ is the best of the competition by a long shot. He definitely knows how to take advantage of different types of players by isolating, barreling, floating, squeezing, etc., and he’s definitely made some plays like these against me in good spots. I don’t have enough experience with him to say whether he’s actually balancing against me or whether he’s playing more of a Level 2, “This guy opens a lot so I’m just going to three-bet him with any two” sort of strategy. He’s definitely unbalanced, in a good way, against the less tough competition. I’m playing about $2500, and he covers.

UTG limps for $10. Three players fold, then HJ raises to $40. Hero calls from the BB with Ks Jd. UTG calls.

Flop Kc 7s 6d ($118 in pot). Hero checks, UTG checks, HJ bets $65, Hero calls, UTG folds.

Turn 2s ($248 in pot). Hero checks, HJ bets $125, Hero calls.

River Ts ($498 in pot). Hero checks, HJ bets $400, Hero?

I think the flop and turn play is pretty uncontroversial, but if you have questions, I’m happy to address them.

Post your thoughts and preferred action on the river, and I’ll post my own thoughts as well as the results towards the end of next week.

I’m actually a bit dismayed by how many people are hurrying to label this player a fish and assume he’s going to be some huge mark after the flop. In fact, the way I described him was a splashy, “with lots of limping and calling pre-flop followed by lots of checking and folding post-flop.” There’s not tremendous value in dragging him into the pot. In fact, I’d probably rather he folded to the raise, as he’ll be getting 3:1 and closing the action with presumably a very playable hand. Short stacked or no, I’m not going to be looking to my stack in against him whenever I flop top pair.

Reverse Implied Odds?

Pretty much every commenter expressed some discomfort with playing KJo from out of position, and rightfully so. This is a hand I’d usually fold from the BB against a player in this position. My strong suspicion, however, is that he is raising more hands than his position warrants, and this presents an opportunity to exploit him by playing some additional hands myself.

The mere fact that KJ could be behind when it flops top pair does not make it a “reverse implied odds hand,” as Notam calls it. It’s true that it will rarely be more than a bluff-catcher, but top pair with a good kicker is generally a very good bluff-catcher. Calling bets is not generally going to be a money-losing proposition when we flop top pair, despite the presence of dominating hands in Villain’s range, because we know (or are comfotable assuming, anyway) that he will see the flop with an overly wide range. Thus, he will have only two options: rarely bet when a K or J flops, enabling us to get loads of cheap showdowns and only rarely pay off value bets, or bluff a lot at these boards, which means we’ll actually have positive implied odds on such boards. In the event that the board runs out in a way that calling is no longer profitable, we can always fold. There is never a point when we’ll be compelled to make a -EV call.

Let’s not forget that KJ probably dominates some hands in Villain’s range as well. He surely raises QJs, JTs, and KTs in this spot, and possibly some of their offsuit cousins as well.

Three-Betting vs Calling

Cromi007 says, “I like an absurd raise here, something like 200-240+.” There’s a reason why that size is absurd. Although a huge raise will indeed win the pot quite frequently, it needs to win the pot quite frequently, because it risks several times what is in the pot. Even if we take it down 75% of the time, we’ll be in such bad shape when we don’t get folds that it will likely overwhelm that fold equity. Three wins of $60 accompanied by a loss of $200 is not an appealing proposition.

Stuart says, “I don’t mind 3betting small ($90) to take control of the hand and maybe even set up a big 5-bet to win the hand pre.” This raise has the opposite problem. Instead of offering our opponent a lot of trivial folds, it offers him a lot of trivial calls. Three-betting does not magically put you in control of the hand. You’ll still be out of position, there will still be lots of money behind, and unless you have some reason to think Villain will fold excessively much either to the 3-bet or the c-bet (my description of him suggests neither), then there’s no reason to expect this to be a profitable play.

All of the information we’re responding to here is public. In other words, Villain probably realizes that UTG is going to give up too much, and will expect us to realize that as well, and will recognize that we don’t have to have a monster to 3-bet him (or 5-bet him, for that matter). It’s not enough to say, “He’s got a wide range, let’s raise in a really unbalanced way!” There’s plenty of room for him to punish that sort of imbalance, and everything we know about him suggests he’s capable of it.

What’s lacking from all of the comments advocating a three-bet is a justification for why this hand in particular is good for a three-bet. The fact that these arguments could just as well apply to 72o are a strong hint that what they’re proposing is an unbalanced play.

The fact is that KJo will not play well in a 3-bet pot. We don’t want to flop a marginal hand in a 3-bet pot, because in a 3-bet pot we want to be bluffing and value betting. KJo will not often make a good bluffing hand, and it will even more rarely make a good value betting hand. It’s going to flop mostly bluff-catchers, and that means that we want to keep Villain’s range as wide as possible and the pot as small as possible.

All of that said, I don’t think folding is terrible here by any means, especially if you aren’t confident in your post-flop ability. I think, however, that simply calling now and then playing a balanced post-flop strategy will show a profit, which should be a lesson to all those who say, “I don’t need game theory in the games I play.” Playing a bluff-catcher out of position against a wide range is one of the times that I find it most handy to be able to fall back on what I’ve learned about unexploitable play.

Results

I called, and UTG called. As you might have guessed, there’s another decision in this hand, which I’ll present momentarily in a separate post.

Thanks again to everyone who participated!

UTG is a typical splashy recreational player, with lots of limping and calling pre-flop followed by lots of checking and folding post-flop. He has about $800 in his stack.

HJ is the best of the competition by a long shot. He definitely knows how to take advantage of different types of players by isolating, barreling, floating, squeezing, etc., and he’s definitely made some plays like these against me in good spots. I don’t have enough experience with him to say whether he’s actually balancing against me or whether he’s playing more of a Level 2, “This guy opens a lot so I’m just going to three-bet him with any two” sort of strategy. He’s definitely unbalanced, in a good way, against the less tough competition. I’m playing about $2500, and he covers.

UTG limps for $10. Three players fold, then HJ raises to $40. Action folds to Hero in the BB with KJo.

What’s your play and why? Comment below with your thoughts and preferred play, and I’ll be back on Friday with my own thoughts and action.

If you were to draw a picture of the prototypical recreational player, you might well end up with a picture of this guy. He’s a slightly doughy white guy, late 30s or early 40s, wearing sporty clothes and expensive wrap-around sunglasses on his forehead. We played together the night before at $5/$10, and I got the impression that he thought I was a bit of a bully.

The flop comes Qh Qc 8h. I bet $80, and he raises to $180 pretty quickly. It’s very difficult for me to believe he has a hand here. I mean, maybe a small pair or a flush draw or something, but I could definitely see him doing this as just a straight Level Two “I don’t think you have anything so I’m raising” sort of thing. I contemplate three-betting the flop but, given my backdoors, decide to call instead. I can check-shove turns that improve me, and I can bluff some rivers if he checks back (though I may not need to).

The turn is the 3d. I check, and he bets $320, which solidifies my conviction that he’s just trying to push me out of the pot. The trouble is that I have K-high, no draw, and only about $150 to shove over his bet. I shove anyway.

He groans and asks the dealer, “How much more?”

“Not much more,” she says as she reaches for my chips.

What the fuck!? It’s a little tricky to keep a poker face through her unsolicited and inappropriate commentary. Thankfully he finds the fold button anyway.

I’m sorely tempted to show my hand. It’s the rare case where showing something so wild really can influence the dynamic of the whole table. Ultimately I didn’t do it, though, because I could also feel the desire to brag (which I guess I’m giving into anyway by making this blog post) motivating me.

The reason I find it interesting is that it reminds me of an important conclusion from Mathematics of Poker that I’d forgotten about entirely until I reread that book. In “Playing Accurately, Part I: Cards Exposed Situations”, Chen and Ankenman demonstrate that there are situations where a player with an obvious (exposed, in their hypothetical) draw actually does better by raising all-in on the flop, knowing he’ll put the rest of his money in from behind (though with sufficient pot odds) rather than calling and giving his opponent the opportunity to bet him out on a blank turn or check-fold when the draw comes in.

Of course there are any number of reasons why that may not be applicable to this hand. It presumes an opponent who will correctly bet the turn when ahead and correctly check-fold when behind. If, as Eddie argues, Villain can be expected to run a big bluff on cards that complete Hero’s draw, then there is more room to outplay him on future streets.

On Calling

I think many commenters are overestimating how easy it will be to outplay Villain on a blank turn, though. Shoving over a turn bet works only if Villain has a lot of air in his range, as he probably isn’t bet-folding a Q or a 9 or a better draw. Calling in hopes of getting there on the river probably requires decent implied odds to be better than getting it in on the flop even if Villain never folds.

I’m not at all sure what would be the best play if Villain checked a blank. I suppose I would opt for a smallish bet of perhaps 1/3 pot, but getting check-shoved is such a disaster that I don’t feel too great about that plan.

I don’t think the best play is particularly clear if the turn is a J or a T, either. Some people seem to want to call down on blank rivers, and I can see why, but Pepito also makes a good point that “villains of these sorts tend to thin hero calling rather than triple barreling with air (particularly in a 3b pot where hero has called a check raise and a second barrel).”

On Shoving

Pepito also asserts that, “shoveling 4.5K into 1.2K pot against a callbox seems terrible– particularly with position.” Having already explained why I don’t see a lot of ways to capitalize on my position, I’ll now address the “callbox” argument.

The tricky thing here is that this hand actually blurs the line between a value bet and a bluff. On the hand, it certainly feels icky to stick in a lot of money with Jack-high against a player who’s shown a willingness to call down extremely light. But what, really, can his looseness do to hurt us?

No one is check-raise-folding the hands that have us in truly bad shape, which would be nut flush draws, two pairs, and sets. I wouldn’t really expect Qx to take this line either – people might check-raise-call it, or they might not check-raise it, but I don’t see it getting check-raise-folded.

So what can Villain’s looseness add to his calling range, and how can that hurt us? All he can do is start calling with really weak hands, and Hero is a pretty big favorite against those, as Sean F. points out. Hero has 63.5% equity against 9d 8d and 76% against 8s 7s.

There’s a lot of talk about not wanting to put your stack in “on a flip”, but that’s a misleading way of framing the situation. What you really need to consider is not just the end result – how much equity do you have when the money goes in – but rather how can your actions manipulate the situation to give you more or less EV.

Regardless of your flop action, there are a lot of scenarios where you end up playing big pots against the top of his range. Against the bottom of his range, you’re a solid favorite, and raising the flop can only lead to good things. Villain can either forfeit a significant amount of equity by folding, or he can put his money in from behind and lose the ability to play well on future streets (he might continue bluffing a spade with air, but will he bet/stack off with 98?).

A lot of the value in calling comes from inducing bluffs. Maybe we get to shove over a bet on a blank turn, and maybe we induce some big bluffs when we hit.

Results

Raising less than all in still leaves open the possibility of inducing a bluff. If Villain check-raises the flop with more than just pairs and draws, then there’s a real chance he’ll four-bet-fold some of that air. He’s shown a propensity for this sort of play in wide range situations before.

That last point was the deciding factor for me. I three-bet the flop $1300, Villain made it $3100, I shoved, and he did some thinking (about what, I’m not sure – whatever it was presumably should have happened before he four-bet) and then called with what turned out to be Ad Kd. That was an outcome I hadn’t anticipated, but again I’m a 65% favorite in the case where Villain decides to make a really loose call, which means that getting it in on the flop is better for me than shoving over the check-raise and having Villain fold (though I would have preferred a fold to the five-bet).

The board ran out blank, and Villain collected a massive pot with Ace-high while the table collectively gawked. I warned you this was a bad beat post!

One example, he bet-called 99 vs a huge check-shove on Qh Th 5d and won vs Ah Kh. Exploitively, it may be a correct call because that player probably does have a draw there all the time, but winning in spots like that has definitely emboldened him.

His strategy probably OK against the weaker regs, but I’ve been punishing him for it. That’s not to say I’ve never backed down when he floated or raised me in spots where I suspected he was unbalanced, but but we’ve tangled a fair bit in spots where we both had wide ranges and the money has on balance flown to me.

Hero is in the straddle with about $4800. Action folds to Villain in SB, who opens for $60. BB folds, Hero makes it $160 with Js Ts, Villain calls.

Flop ($323 in pot) Qs 9s 6d. Villain checks, Hero bets $200, Villain raises to $500, Hero?

Please comment below with your thoughts and preferred action. If you want to do anything other than shove, you should also consider your plan should you see the following turn cards:

1) 3s

2) 3h

3) Td

I’ll respond to comments throughout the week and post my own thoughts as well as results on Friday.

Should Villain Check the Nuts?

Matt says, “I am highly, *highly* disinclined to believe that V checks the Ad on the river here (not to say that it would right or wrong to do so). I find that a lot of people at roughly a live 2/5 skill level have a really hard time checking from out of position on the river with their very strong hands and risking the possibility of having the river check through.”

I agree with this as an empirical observation about live 2/5 players. But should Villain check the nuts? My guess is no, but that a successful shoving strategy with the nuts will also require turning some pretty good pairs into bluffs, which is another thing that 2/5 players are notoriously bad at.

In the AKQ game with a fixed bet size, we know that it’s correct for the OOP player to bet all of his nut hands plus some bluffs for balance, and then to check-call enough of his medium-strength hands to make his opponent indifferent to bluffing. When multiple bet sizes are allowed, it’s better for OOP to make a “blocking bet” with all nut hands, some medium strength hands, and some bluffs, leaving at least enough medium strength hands in his range to call a shove with optimal frequency after checking. That would seem to imply that OOP should bet all of his nuts.

The catch is that OOP will have trouble finding bluffs to balance that bet. If I were Hero here, I’d feel pretty comfortable folding the Kd to a shove, because Villain would have to be turning hands as good as top pair into bluffs (which isn’t actually so unreasonable, because it’s hard to imagine that ever winning at showdown – Hero can probably bluff all worse hands when checked to).

Betting the nuts is not an and of itself a mistake, but failing to balance it with bluffs is.

Hero’s Betting Strategy

Perhaps the more important question is, even if we can conclude that Villain would not check the nuts, what influence should that have on Hero’s strategy? If we knew for certain that Villain did not have the nuts, then we could value bet the second nuts with confidence. On the face of it, it would seem that the unexploitable play would be just to shove all Kd and Ad combinations plus bluffs for balance.

However, Hero might well have a difficult time filling his bluffing range. I argued that Hero’s turn check was, essentially, an exploitive play. I thought it was a very good spot to barrel generally, but I didn’t want to bet-fold such a good draw, so I chose to check. The only other draw to which this logic would apply would be the bare Ad. That means that probably the only air in my range on a diamond river are three combos of QTs.

It’s hard even to find pairs to turn into bluffs. Most pairs weaker than a K I would either have checked on the flop or bluffed on the turn, or they would have a diamond, making me content to check back the river. I also think a set is too strong to bluff on the river.

That leaves Kx with no diamond as the next leading candidate for bluffing, and even that may have some significant showdown value.

Basically, the decision not to take a very good bluffing spot on the turn, combined with a card that nails the weakest part of your turn checking range, leaves you with an overly strong range on this river. This forces you to bet small against a smart player, to avoid giving him a trivial fold.

I’m thinking there are maybe 11 combinations of AdX in my range (3x AQ, 3x AJ, 3x AT, 2x AK) and only three bluffs. The unexploitable play would be to bet about a quarter of the pot with those hands and check everything else.

Many 2/5 players, quite possible including this one, will not be such savvy hand readers and may well misinterpret the turn check as weakness. Exploitively, I could see betting somewhat larger, perhaps more like half pot, with both nuts and bluffs. Whether or not to include the Kd in that range comes down to how confident you are that Villain wouldn’t check the nuts.

“[T]his looks like a textbook example of a “leveling war”, with each player trying to anticipate and stay one step ahead of his opponent’s exploitive strategy. Clearly, Tonking got the upper hand in this case.

That’s not to say that Newhouse was completely misguided to think that a bluff could succeed at an extremely high frequency. It was the final table of poker’s most prestigious tournament, both players had a lot at stake, and he’d already made clear that he did not want to finish in ninth place for a second year in a row. Then again, Tonking may have known and taken all of those factors into consideration.

The point I want to make is that Newhouse did not have to enter into this war at all. When you are genuinely unsure of how your opponent will respond, there are alternatives to taking your best guess. There is more to poker than good reads and “heart”. The fundamental mathematics of the game limit how much you can get away with, at least against a skilled opponent, even when you have the right read and the nerve to act on it.”

I also have an article called “Keep ‘Em Guessing” appearing on Poker News:

“The best guide I’ve found to judging my own play is my opponents’ reactions. If they seem consistently confused about whether to bet or how to respond to my bets, then I’m probably doing something right.”

Hope you enjoy them, please let me know what you think!

You’re at a 9-handed $2/$5 NLHE table with $600 effective stacks. UTG is very loose, especially pre-flop, and the whole table is salivating over him. UTG+2 is tight-aggressive bordering on nitty.

UTG limps for $5. UTG+2 raises to $20, and the action folds to Hero in the CO with Qs Ts. Hero raises to $50, UTG waffles a bit and then calls, and UTG+2 quickly puts in another $30.

Flop ($151 in pot after rake) Ks 8d 6d. UTG and UTG +2 both check without much hesitation. Hero bets $75, UTG folds, and UTG +2 calls.

Turn ($301 in pot) Jd. UTG2 checks, Hero checks.

River ($301 in pot) 2d. UTG2 checks, $475 remain in the effective stacks. Hero?

Post your thoughts and preferred action here, and I’ll be back with results and my own thoughts on Friday.

Pre-flop and on the flop, I argued that Hero had the opportunity, thanks to a bet sizing tell, to get more credit than he deserved on a 3-bet/c-bet and consequently could make these plays with a wide range. Essentially picking up on that tell (if it was in fact a tell) bought Hero some extra fold equity pre-flop and on the flop. Now, though, that fold equity may well be used up, and Soner asks a good question: “I am still having a hard time imagining what a tight aggressive and borderline nitty player would raise UTG2 preflop, call a three bet and call a flop continuation bet on a Ks 8d 6d board. This play doesn’t seem tight aggressive at all to me unless he flopped a monster and knows you will three barrel. Also, you mentioned other players will give hero more credit than he deserves. If that is the case, and UTG2 thinks you have a very strong hand what is he calling you with?”

That’s not to say Villain will never fold the turn. There’s a good chance medium pocket pairs like TT are still in range (if they aren’t in the category of hands he’d raise larger) as well as possibly 98s or 87s, and all of these probably fold if they don’t have flush draws. Maybe he’d even fold KJ or KT without a diamond.

Plus, Hero has plenty of flushes in his range that he’d like to bet. All of that argues for having a bluffing range on the turn. The key question, though, is not whether Hero should ever bluff the turn, but whether this particular hand belongs in his betting range or his checking range?

Bryan Gour’s comment raises a lot of good points, but this one in particular is worth noticing: “I expect the top of his range to be check calling and check raising, and all of his 99/TT/QQ with a diamond to have a pretty low calling frequency.” I would go even further and say that, with stacks being what they are, there’s a good chance that Villain’s calling range will be quite narrow, maybe only pairs with flush draws and the occasional slowplayed nuts, and that he’ll usually raise or fold.

The fact that betting so rarely results in Hero seeing the river card suggests that a draw with substantial equity vs Villain’s folding range might not be the best bluffing candidate, because Hero won’t get to realize that equity. Betting a more polarized range of flushes and hands with little to no equity is probably the better strategy.

You’re at a 9-handed $2/$5 NLHE table with $600 effective stacks. UTG is very loose, especially pre-flop, and the whole table is salivating over him. UTG+2 is tight-aggressive bordering on nitty.

UTG limps for $5. UTG+2 raises to $20, and the action folds to Hero in the CO with Qs Ts. Hero raises to $50, UTG waffles a bit and then calls, and UTG+2 quickly puts in another $30.

Flop ($151 in pot after rake) Ks 8d 6d. UTG and UTG +2 both check without much hesitation. Hero bets $75, UTG folds, and UTG +2 calls.

Turn ($301 in pot) Jd. UTG2 checks, $475 remain in the effective stacks. Hero?

Leave a comment below with your thoughts and preferred action. I’ll do my best to respond to comments over the next few days and will post the next decision point on Monday.

Pre-Flop Ranges

Don’t get too bogged down in trying to assign exact ranges to each opponent. It’s mostly guesswork, and I don’t think precision will greatly influence the correct play in most situations anyway. Do recognize, though, that the absence of a four-bet greatly reduces the likelihood of either of these players holding KK, AA, or AK. I’m less comfortable making assumptions about what AQ, QQ, or anything weaker would do, but I’m not too worried about running into an overpair here.

UTG’s range is surely wider than it should be (then again, who knows what a range for limping UTG and then cold calling a 3-bet “should” look like), but it may be stronger than you think. Even loose players usually have some standards for cold calling 3-bets.

I doubt UTG2 has much of a folding range considering the odds he’s getting once the action is back on him.

Hero’s range probably looks stronger than it is, because this was an exploitive three-bet. If it weren’t for the reads and sizing tell Hero acted on, he wouldn’t be three-betting this wide, and presumably the other players don’t recognize those features of the situation and so will give Hero more credit than he deserves. So although Hero may in fact have the most air-heavy range of the three, I still want to play the hand aggressively.

Bet Sizing and Barreling

We’re only on the flop, but with an SPR of less than four, we have to think about whether and how to put stacks into play. There are a lot of arguments for planning to fire multiple barrels at this pot. As I argued above, both Villains likely have a lot of medium strength hands but very few hands they’ll be comfortable playing for stacks. Their ranges consist mostly of good but not great bluff-catchers, and they’re likely to overestimate Hero’s strength. That along with Hero’s backdoor draws all argues for barreling a lot of runouts.

There was a lot of agreement about betting the flop, but not much consensus on sizing. Commenters advocated anywhere from $80 to $140, and a lot of people seemed to be just throwing out a number without a lot of justification for it.

This is why it’s so important to think ahead and think about your entire range. You need to decide whether you’re going to try to bet flop and shove turn with your strongest hands, or whether you’d rather break the betting over three streets. Then you need to construct a bluffing range that at least balances those bets, though in this case I’d want to be weighted towards bluffs anyway.

This is a relatively static flop. A few specific turns will do a lot to improve formerly weak hands, but most of the time the strongest hands on the flop will still be among the strongest hands on the river. That argues for more, smaller bets.

In Mathematics of Poker, Chen and Ankenman demonstrate that in a completely static game with no raising, the optimal strategy is to bet the same fraction of the pot on each street such that your last bet is all-in. Those conditions don’t quite hold here, but they are close enough to make this strategy worth following in my opinion.

I set up a spreadsheet to help me solve this, and it turns that if force ourselves to bet in increments of $5, the closest we can get is to bet $75 on the flop. This assumes we bet and get a single caller, which is a far more likely outcome than getting two calls. If the latter happens, we’ll just cross the bridge when we come to it.

Counter-Arguments

My suspicion is that some people will be uncomfortable with this sizing because it seems small and thus could be perceived as weak. But how, really, can our opponents respond to that? They can either check-raise bluff or they can call light.

We can protect against the possibility of excessive check-raise bluffing simply by having appropriate calling and re-bluffing ranges. It’s not a reason to bluff less often or with a larger size, just a reason to defend more after betting.

As for calling light, I agree that quite possibly neither player will fold a pair or a draw to the flop bet. It’s true that a larger size will get you more folds, but then again it needs to get more folds, because it risks more.

It’s not obvious to me that getting called by 99 on the flop is such a bad thing. Not only does Hero have pretty decent equity against that hand, but it’s a hand that’s not likely to go to the felt unimproved, so as long as aggressive barreling is in the works, Hero may actually prefer for 99 to call rather than fold.