Timestamps

0:30 hello
15:21 strat
32:35 bill

Strategy

Local card room. It’s still early in a big blind ante tournament; 3rd level. Starting stacks are 15k. EP just got crippled in a hand and is down to 4k. He shoves. MP shoves for 15k and seems like not an idiot. It folds to Hero who has AKo and a 50k stack. 

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!

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.

As I was on his immediate left and he was trying to play every pot, we clashed a lot throughout the tournament. Early on he folded to my 3- and 4-bets or my c-bets, but eventually he shifted that dynamic by check-raising me twice on pretty dry flops. Both times I suspected that he had nothing but folded anyway as I was near the bottom of my range. If I’d gotten into a pissing contest with him, he may well have won. Instead I tried to keep 3-betting and barreling good ranges, and eventually it paid off.

This may seem like a very straight-forward hand, but I think when people know that they’re up against a very aggressive player who tries to win every pot, they’re tempted to get fancy when they turn the nuts and try to induce bluffs or something. I know I have that temptation, anyway. But that’s rarely the best way to play the nuts, and a line that polarizes your range can easily lead to stubborn call downs from these players.

One final points concerns the sizing. In The Mathematics of Poker, Chen and Ankenman prove that, “When the game is static and one player is clairvoyant, the optimal bet size is to make the pot grow by the same amount on each street, such that on the last street the entire stack has been bet” (p. 241). Although that doesn’t perfectly describe this situation, I think it’s a close enough extrapolation to make this half-pot, half-pot, half-pot sizing ideal:

PokerStars – $300+$20|50/100 Ante 10 NL (6 max) – Holdem – 3 players
Hand converted by PokerTracker 4: http://www.pokertracker.com

BB: 57.62 BB (VPIP: 39.64, PFR: 19.82, 3Bet Preflop: 6.12, Hands: 112)
BTN: 189.12 BB (VPIP: 44.03, PFR: 35.07, 3Bet Preflop: 16.98, Hands: 138)
Hero (SB): 53.26 BB

3 players post ante of 0.1 BB, Hero posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.8 BB) Hero has Ac Jh
BTN raises to 2 BB, Hero raises to 6 BB, fold, BTN calls 4 BB

Flop : (13.3 BB, 2 players) 3c 7c Jc
Hero bets 6.65 BB, BTN calls 6.65 BB

Turn : (26.6 BB, 2 players) 6c
Hero bets 13.62 BB, BTN calls 13.62 BB

River : (53.84 BB, 2 players) 9d
Hero bets 26.89 BB and is all-in, BTN calls 26.89 BB

Hero shows Ac Jh (Flush, Ace High) (Pre 63%, Flop 87%, Turn 98%)
BTN shows 4c 5h (Flush, Jack High) (Pre 37%, Flop 13%, Turn 2%)
Hero wins 107.62 BB

I went on to defeat this player heads up and win my first table, only to flame out early on the second table for a min-cash.

So far I’ve played every WCOOP event, though that streak will end when I skip the NL Draw tournament tomorrow morning. I’ve cashed three of the six events I’ve played and two of the three that I registered on time. Those are streaks I’d like to keep alive!

Early on, I raised 55 on my CO and called a 3-bet from a fishy player in the BB. I made a questionable call on a 932 flop, then turned a 5 to stack his KK.

The table kept getting tougher, with Amnon Fillippi and a few other solid players (but also Dennis Phillips) filling empty seats. A tight-bad player open limped for 300, I made it 1300 with QQ, Jon called, and Amnon shoved 15K from the Button. I reshoved without much thought but ran into AA.

I’d been playing pretty tightly, but at 300/600/75 I opened to 1600 with K9o in MP3. Jon called in the CO, and Amnon called in the BB. Flop came Kh Kd 6d. I bet slightly over half pot, Jon folded, and Amnon called. Turn 8h, he checks, I bet slightly over half pot again, 6400. He tanks and shoves about 20K, I call, he has Jd 5d. River Qd, and he doubles through me and leaves me at 24K.

I work my way up to about 28K when an aggressive younger guy opens to 2100 in the CO (blinds 400/800/100). Dennis Phillips calls on the Button, and I pick up AA in the SB. I make it 6900, kid 4-bets, Dennis folds what he later claimed was JJ, and I more than double up to about 60K.

A few hands later, I open to 2400 with JJ UTG+1. Dennis re-raises to 6500 with about 21K behind. I reluctantly fold.

Overall I had a tough seat at a tough table and what I’d consider below average luck, but I managed to come out of it with 51,400 chips. We started with 872 runners, and there are 510 left, so my stack is almost exactly average, which would be 51,294.

Sorry the Twitter updates were sporadic, my e-mail-to-Twitter thing isn’t working quite right.