Lower antes increase your M, which allows you to go into survival mode on a short stack for a longer period of time without feeling the pressure of going all in. Average big blinds per player in the tournament is what you’d look at to see how much “play” there is in a tournament. The higher the average big blinds per player is, the more streets will be bet, and the more maneuvering will occur post flop. A tournament that boasts a higher bb per player average is one that is clearly more skillful because more intricate decisions will be necessary. Deep stacked poker is just harder, plain and simple. That’s not debatable.

The problem with tournaments with tiny antes is that it allows short stacks to hang around longer without having to make a move. Great for short stacks, but much like the epidemic you see online of “short stacking,” when too many players are hanging around with a short stack, the avg bb per player takes a major hit, and average to above average stacks are forced to tighten up significantly because behind them sits three stacks ranging from 8 to 15 big blinds. The bigger stacks are forced to open less.

The post is much longer than this and contains a number of good arguments, but the comparison to short stackers in cash games really hit home for me. I’m convinced that larger antes weight my likely outcomes in a desirable way: I either bust some short stacks, outplay some people post-flop, and get up a big stack, or I get short, get busted, and play something else. Less time circling the bowl for short stacks is a good thing, and I’m a convert. Thanks, Dan.

Edit: Added link.

I believe that a bet or raise should always have an objective (or objectives), and that you should know your objective(s) before betting. This is crucial both to decide whether to bet at all and to size your bets appropriately. In theory, one ought to be able to write an equation for the value of a bet as a function of some combination of factors on this list.

For example, if I make a pot-sized shove with As Qd on an Qh Ts 5s flop in a heads up pot, I believe the value of that bet would be equal to

Value + Protection + Deception

Some of these can be calculated more precisely than others. For Value, I can make an educated guess about how often he will call with worse hands and what my equity is against that calling range. Likewise I can determine how much equity his folding range has. Deception is much less precise, since we are talking about the extent to which shoving AQ here increases the profitablity of a shove with a hand like AJ in some similar future situation.

Does that make sense? What do you think of the current list? The two new additions are at the end, though I’ve revised some of the definitions as well.

1. Value– To get called or raised by worse hands (I believe this would include betting to induce a raise)

2. Bluff– To fold out better hands

3. Protection– To fold out worse hands that have some equity in the pot

4. Information– To make decisions easier on future streets

5. Deception– To increase the profitability of future bets in similar situations

6. Barreling– To set up a bluff at a later opportunity

7. Isolation– To get the pot heads up with a particular player

8. Position– To drive out players who will have position on you later in the hand

9. Blocking– To prevent an opponent from betting or raising now or on a future street (I believe this would include enabling yourself to take a free card or showdown)

10. Image– To encourage opponents to misunderestimate your skill or playing style in later hands

11. Pot Sweetening- To build the pot and increase the stakes in situations where you anticipate making better decisions than your opponents on future streets

12. Secrecy- To avoid having to show your hand at showdown

I’m not 100% sure about Secrecy. I feel like it’s getting at something similar to Image and may not warrant its own category.

Likewise I’m starting to wonder if Isolation isn’t too similar to position. In both cases you are trying to increase your implied odds on future streets by preventing other players from getting in your way. Does anyone else see what I’m getting at there?

Your comments were great last time, please keep them coming!

We start with the “exploitability”, the idea that there is something about how you play that an opponent could potentially take advantage of. Conversely, “unexploitable” means that there is nothing an opponent could do to take advantage of how you play. Importantly, unexploitably is not always the most profitable way to play. Often, you will do something exploitable in order to exploit something exploitable an opponent is doing.

Suppose that you hold AQ in the big blind in a $1/$2 NLHE game. The action folds to the SB, who open shoves for $20. If you know that this opponent will only shove JJ+ and AK, you can fold your AQ. Though itself exploitable, this fold exploits your opponent’s excessively tight shoving range.

If you were to call with AQ, that would be less profitable than folding but it would also be unexploitable. In other words, there is nothing your opponent could do to take advantage of the fact that you are going to call with AQ, and in the long run you will make money, though not as much money, with a strategy that involves calling AQ. This is because the money you lose on the AQ call is more than made up for by all of the pots you win that your opponent could have picked up if he weren’t playing so tight.

It’s relatively simple to determine an optimal shoving range for the SB and then to determine how much you gain if the SB’s shoving strategy is tighter than optimal. Take it a step back and suppose that it is the player on the Button with just $20 and shoving an overly tight range. Now it should be clear that both the SB and BB benefit by having their blinds stolen less often than would be optimal. The money that the Button loses in missed steals is shared by the players in the blinds. The situation is actually more complex for both, but I want to back up again to accentuate a point.

Put the very tight short stack in the CO. It is still possible, and indeed relatively simple, to determine an optimal shoving range for him. If he shoves more tightly than optimal, we can calculate exactly how much Expected Value he loses as a result. This EV must be shared by the Button, SB, and BB. We already know that the blinds’ benefit primarily by having their live money stolen less often.

The Button, however, does not have any money in the pot, yet he too benefits from an overly tight CO. If we can calculate how much the blinds gain from the CO’s mistake, then the difference between what the CO loses relative to an optimal shoving strategy and how much the blinds collectively gain will be the value of the button.

I suppose it would be the value of the Button assuming the other players all play optimally, such that it would change if the Button were more or less skillful than the blinds. Still, it seems like this could be a strategy for someone more mathematically inclined than myself to approximate the value of position.

Am I on to something or just tired?

Edit: I was just tired. After sleeping on this, I realized that the BB’s EV is intrinsically dependent on that of the Button. In other words, the deeper the stacks are and the better Button plays, the more the Button is worth and the less the BB is worse. I was hoping to come at the Button backwards, treating the SB’s and BB’s EVs as roughly solvable quantities and using those to approximate the Button’s EV as a variable. But we can’t actually find the BB’s EV without knowing the Button’s EV, since most of the latter comes at the expense of the former. And the same problem exists for the SB.

He sounded like he’d had a rough week and was pretty tilted, started telling me I was terrible and trying to get me to play him heads up. As much as I complain about how nobody at 5/10 will play me, the truth is that I am also pretty nitty about only playing heads up against people I think I hae an edge on. I don’t have a ton of experience with this particular player, but he sits waiting for action at 25/50 and seems solid enough, so it’s a good bet that he’s better than I am.

Long story short, he offered me a 5% return on losses to play him. When I declined, he offered 7%. Now, there were some reasons I didn’t want to play him anyway. We didn’t get into terms, but he discussed it with another player, and wanted to play at least 3 tables of 25/50 for at least 1 hour. Although I will take shots when the games are good, I don’t actually have enough money on stars to play those stakes habitually. Plus, in order to focus, I’d probably have to quit most or all of the other games I was playing, some of which were reasonably good.

I’m curious, though, what a 7% return on losses is really worth. Obviously it’s worth nothing if I’m up on the session. If we were equally likely to finish up, then it would be worth a 3.5% edge. But if he is a bit better than I am, then he’s presumably somewhat more likely to finish up on the session, so maybe it’s worth something like 4%?

I guess it could even affect my strategy, as the ideal one for me would produce distribution of outcomes with a few big wins and many small losses. Perhaps it would be correct to play a few more speculative hands, chase a few more draws, etc.

I’m very curious what you math-types think (ie looking to hear from you here, brue). If opportunity cost and online bankroll weren’t issues, how much of an edge would this guy need to make his offer profitable? How, if at all, should my play change as a result of this arrangement?

This is a tantalizing post with some really interesting ideas that need more meat. Can you say more? In my experience, trying to blow someone off an Ax hand is just too disruptive to my bankroll. Many players are just too stubborn and will chk-call all three streets. I finally learned that my best counter-strategy is to simply bet the hell out of my hand when I can beat Ax. Turning 2nd pair into a bluff in the hopes of blowing someone off Ax? I dunno, I need to hear more.

It’s a good question. This concept isn’t just a neat way to bluff. The point is that when you have position and a good sense of your opponent’s range, you have a generous edge because of your ability to make better decisions on the river. You want to have a big pot and also enough money behind for a big river bet, ideally with nothing left over in the effective stacks, to maximize that edge. Then, it’s just a matter of actually making that river decision.

Against this opponent, I’m confident that in a 4-bet pot, a bluff in that spot would be very profitable. Against a looser opponent who will not fold Ax, then you will value shove more hands and bluff less.

Before I could even get around to posting that, I found myself in another heads up match against the same opponent where several exemplary hands arose. Here’s one where I employ the same line for value with AA:

Full Tilt Poker, $5/$10 NL Hold’em Cash Game, 2 Players
LeggoPoker.com – Hand History Converter

Hero (SB): $2,937.50
BB: $2,044.50

Pre-Flop: A A dealt to Hero (SB)
Hero raises to $30, BB raises to $120, Hero raises to $270, BB calls $150

Flop: ($540) 3 T 9 (2 Players)
BB checks, Hero bets $222, BB calls $222

Turn: ($984) 9 (2 Players)
BB checks, Hero bets $444, BB folds

Results: $984 Pot ($0.50 Rake)
Hero mucked A A and WON $983.50 (+$491.50 NET)

And an example of how one might defend against such a line:

Full Tilt Poker, $5/$10 NL Hold’em Cash Game, 2 Players
LeggoPoker.com – Hand History Converter

SB: $3,578
Hero (BB): $3,958.50

Pre-Flop: J J dealt to Hero (BB)
SB raises to $30, Hero raises to $111, SB raises to $265, Hero calls $154

Flop: ($530) 5 5 9 (2 Players)
Hero checks, SB bets $285, Hero calls $285

Turn: ($1,100) J (2 Players)
Hero checks, SB bets $865, Hero calls $865

River: ($2,830) T (2 Players)
Hero checks, SB bets $2,163 and is All-In, Hero calls $2,163

Results: $7,156 Pot ($0.50 Rake)
SB showed 3 5 (three of a kind, Fives) and LOST (-$3,578 NET)
Hero showed J J (a full house, Jacks full of Fives) and WON $7,155.50 (+$3,577.50 NET)

The point here isn’t just that I coolered him. I put him on either a big hand (which would probably include KK and AA) or a bluff. No matter which he has, I can just check-call my boat and let him stick the money in by the river, since that’s what he’ll do with either type of hand. Not only do I induce bluffs, but I also make it tougher for him to bluff and value bet me with a line like this in the future.

Before you start feeling too bad for this guy, realize that this was payback for the last time he re-raised me with garbage:

Full Tilt Poker, $5/$10 NL Hold’em Cash Game, 2 Players
LeggoPoker.com – Hand History Converter

Hero (SB): $3,829
BB: $2,000

Pre-Flop: J J dealt to Hero (SB)
Hero raises to $30, BB raises to $120, Hero calls $90

Flop: ($240) 3 2 T (2 Players)
BB bets $125, Hero calls $125

Turn: ($490) 5 (2 Players)
BB bets $365, Hero raises to $3,584 and is All-In, BB calls $1,390 and is All-In

River: ($4,000) 9 (2 Players – 1 is All-In)

Results: $4,000 Pot ($0.50 Rake)
Hero showed J J (a pair of Jacks) and LOST (-$2,000 NET)
BB showed 6 4 (a straight, Six high) and WON $3,999.50 (+$1,999.50 NET)

Honestly, this is a bad turn shove by me. Against a lot of people, it would be fine, but this guy really wasn’t aggressive enough to warrant it. JJ is good often enough, but my equity is so bad that I can’t profitably shove. Mayyyyybe I could get away with calling and then folding the river unimproved, but folding is probably the best option.

Hero (SB): $2,434.50
BB: $3,954.50

Pre-Flop: T K dealt to Hero (SB)
Hero raises to $30, BB raises to $100, Hero raises to $255, BB calls $155

Flop: ($510) 3 A 2 (2 Players)
BB checks, Hero bets $199, BB calls $199

Turn: ($908) K (2 Players)
BB checks, Hero bets $480, BB folds

Results: $908 Pot ($0.50 Rake)
Hero mucked T K and WON $907.50 (+$453.50 NET)

If he called the turn, I was shoving the river. Position, deep stacks, and judiciously employed small bets are a lethal combination. It’s exceedingly difficult for him to show up with enough big hands to prevent me from exploiting him with river shoves.

If both players employ game theoretically optimal strategy, the advantage will obviously go to the player in position. His EV in the game will be a function of the pot size and the number of betting rounds, meaning that it behooves him to structure the betting so that there is roughly a pot-sized bet remaining on the river. He can then maximize his edge by making better decisions than his opponent about when he wants that last bet to go into the pot.

The player out of position is fighting an uphill battle. To balance his range, he needs to slowplay big hands quite frequently, make some heroic call downs, and float the flop out of position with the intention of check-raising the turn on a bluff. Most players can’t do any of those things, let alone all three.

I entered the tournament with the expectation that I would play mostly normally for the first hour but push hard with draws or in spots that I thought were very slightly -EV and not make any big folds. I also reminded myself not to make any big bluffs, since theoretically others should be more willing to call down as a result of the Second Chance.

As the end of the two hours approached, if I was still in the neighborhood of 5000 chips, then I’d start getting crazier, eventually just open shoving in the hopes of either doubling up or using the free rebuy that was about to disappear.

With about half an hour left to go, I had over 8000 chips when I ran into this psychopath:

Full Tilt Poker, NL Hold’em Tournament, 60/120 Blinds, 8 Players
LeggoPoker.com – Hand History Converter

SB: 6,390
Hero (BB): 8,690
UTG: 9,080
UTG+1: 14,775
MP1: 5,756
MP2: 11,176
CO: 9,055
BTN: 6,018

Pre-Flop: (180) A 2 dealt to Hero (BB)
6 folds, SB raises to 480, Hero calls 360

Flop: (960) 4 5 9 (2 Players)
SB bets 840, Hero raises to 2,222, SB raises to 5,910 and is All-In, Hero calls 3,688

Turn: (12,780) T (2 Players – 1 is All-In)

River: (12,780) 8 (2 Players – 1 is All-In)

Results: 12,780 Pot
SB showed T A (a pair of Tens) and WON 12,780 (+6,390 NET)
Hero showed A 2 (Ace Ten high) and LOST (-6,390 NET)

Maybe I should have just shoved the flop. I thought this would look stronger, but the worst case scenario occurred where he shoved a dominating Ace that almost certainly would not have called all in.

Two hands later, I found a great spot where I would have gambooooooooool shoved any two cards. Shockingly, the two Villains, both of whom were decent tournament regulars, folded.

Full Tilt Poker, NL Hold’em Tournament, 60/120 Blinds, 9 Players
LeggoPoker.com – Hand History Converter

CO: 12,780
Hero (BTN): 2,240
SB: 8,960
BB: 13,805
UTG: 5,756
UTG+1: 11,176
UTG+2: 9,055
MP1: 13,186
MP2: 10,287

Pre-Flop: (180) J A dealt to Hero (BTN)
3 folds, MP1 raises to 300, MP2 calls 300, CO folds, Hero raises to 2,240 and is All-In, 4 folds

Results: 1,080 Pot
Hero mucked J A and WON 1,080 (+780 NET)

The next time I shoved over a raise, my K2 ran into AA and I got to rebuy up to 5000, which is where I ended the “rebuy period”. I never got anything going afterwards, though, and within an hour I lost a flip for the rest of my chips.

I read with interest the blog in which you say that you use AQ as a four / five bet semi bluff.

With what hands are you getting called with?

I ask, because in analyzing how to play against Harringbots, I discovered that there are some unusual hands that do well against standard Harrington hand ranges. For example, KJs is almost as good against AQ+/77+ as AQo. The benefit of playing KJs is that opponents will automatically add KQ and AJ to your range which will presumably make the AA/KK hands even more profitable. Of course, KJs does not occur as often as AQo but playing AQo 2/3 of the time and KJs 100% of the time would give you the same semi-bluff frequency.

I think this is an interesting idea, particularly because of the deception it creates. As the commenter points out, people may assume that if you showed up with KJs you will also be shoving hands like AJ and KQ. I was frankly a little surprised when I ran the numbers and saw that the equity difference between AQo and KJs vs a range of TT+ and AK (in answer to the first question, it depends on the spot, but in general my 4-bets aren’t getting called by 77-99) was less than 1%.

That difference gets a little bigger as you strengthen Villain’s range. It’s about a 1.5% difference for a range of JJ+ and AK.

I like this suggestion and don’t have a lot to add to why it could be good. I will add a few caveats though:

1. 1-1.5% is not as trivial as it sounds. Given that you are only looking at 25-30% equity in the first place, that means AQo is actually 3-5% stronger than KJs in such spots.

2. You won’t usually be 4- or 5-betting without first 2- or 3-betting. I’m somewhat more likely to make that first raise or re-raise with AQo than with KJs.

3. 76s actually performs about 4% better than KJs against tight calling ranges. Again, though, you’re less likely to be making the initial re-raises with it.

4. The suited is what’s making the biggest difference here. If you compare AQs to KJs against a few ranges, you see differences of 4-5%, which means it’s 12-20% better. For me at least, I think the takeaway lesson is that it’s fairly important to be suited when 4- or 5- (or 6-, I suppose) bet shoving light.

Thanks for the comment, and sorry for the delay in addressing it!

What’s really important in these closer spots is how good your opponents are. Remember that most players are going to make bigger post-flop mistakes when stacks are deep relative to the pot size than when they are shallow. This is especially true when you have position, though you may also find that against better players you 3-bet hands like KQo from out of position in order to make the stacks shallower for your own benefit whereas you are more comfortable making post-flop decisions out of position against less-talented opposition.

Full Tilt No-Limit Hold’em, $20.00 BB (2 handed) – Full-Tilt Converter Tool from FlopTurnRiver.com

Hero (SB) ($6099)
Button ($4299)

Preflop: Hero is SB with Q, 5
Button raises to $54, Hero calls $34

Flop: ($108) 5, 10, A (2 players)
Hero checks, Button checks

Turn: ($108) J (2 players)
Hero checks, Button checks

River: ($108) 2 (2 players)
Hero checks, Button bets $55, Hero raises to $345, 1 fold

Total pot: $218 | Rake: $0.50

Hero: LOL

You may wonder why I say I think he has some kind of hand here. It’s because he’s passed on two good bluffing opportunities on the flop and turn. That tells me has something, and based on how he’d been playing, I expected him to try for thin value with a lot of his range on the river.

Note that I laugh at him when he folds. He may or may not interpret it this way, but my intent was to mock him for trying to get thin value and allowing me to check-raise him huge. This is important to set up his subsequent call:

Full Tilt No-Limit Hold’em, $20.00 BB (2 handed) – Full-Tilt Converter Tool from FlopTurnRiver.com

Hero (SB) ($6158)
Button ($4238.50)

Preflop: Hero is SB with K, 2
Button raises to $54, Hero calls $34

Flop: ($108) 2, 9, A (2 players)
Hero checks, Button bets $65, Hero raises to $199, Button calls $134

Turn: ($506) 8 (2 players)
Hero checks, Button bets $325, Hero calls $325

River: ($1156) 2 (2 players)
Hero checks, Button bets $640, Hero raises to $5580 (All-In), Button calls $3020.50 (All-In)

Total pot: $8477 | Rake: $0.50

This one isn’t that much of an overbet I guess, but I would have played it the same if the stacks were twice as deep. He called with AQ but unfortunately quit immediately after getting stacked.

Big bets are simply harder to play against than smaller bets. Any edge that you have over an opponent, whether it is position, better cards, or superior skill, is magnified by pot and bet size. This doesn’t mean that every bet you make should be all in. But if you believe that an opponent will make comparable mistakes whether you bet 70% of pot or 125% of pot, the latter option will be far more profitable.

A good rule of thumb about overbetting is that the larger your bet, the more likely it is to induce a raise-or-fold response from your opponent and the less likely it is to be simply called. How exactly you use that information will depend on factors like your hand, your opponent, and the size of the effective stacks.

As I discussed in a previous post, your objective on early streets may actually be to get called. Since you are going to be bluffing later anyway, it behooves you to build a bigger pot to steal. Your other objective on early streets is to lay the groundwork that will enable you to represent a monster by the river. That means your betsizing must be consistent with the hand(s) you want to represent.

On the river, your objective is to make the most +EV bluff that you can. Remember that this is not always the bluff that succeeds most often. Tripling your bet size to double your fold equity is not a winning proposition.

Let’s start by looking at how not to do that. I played this hand against a very good player, one of the best at these stakes:

Full Tilt Poker, $5/$10 NL Hold’em Cash Game, 6 Players
LeggoPoker.com – Hand History Converter

CO: $1,022
Hero (BTN): $2,349.75
SB: $2,169
BB: $3,128
UTG: $779.75
MP: $1,309

Pre-Flop: 8 T dealt to Hero (BTN)
3 folds, Hero raises to $35, SB folds, BB raises to $130, Hero calls $95

Flop: ($265) 4 K 6 (2 Players)
BB checks, Hero bets $111, BB calls $111

Turn: ($487) 4 (2 Players)
BB checks, Hero bets $333, BB calls $333

River: ($1,153) 2 (2 Players)
BB checks, Hero bets $1,275, BB calls $1,275

Results: $3,703 Pot ($3 Rake)
Hero showed 8 T (a pair of Fours) and LOST (-$1,849 NET)
BB showed K Q (two pair, Kings and Fours) and WON $3,700 (+$1,851 NET)

First off, this isn’t the greatest spot for a triple barrel bluff. My opponent is announcing that he has a medium-strength hand, but he’s also playing it in a way that will invite bluffs. And this particular opponent definitely has the hand-reading skills and the stomach to call down.

Since there aren’t any plausible two pair combinations, the river overbet represents either a full house or air (or 53 for a straight, I suppose). And Villain probably expects me to 4-bet KK pre-flop often, so really I can only have three combinations of 66, one combination of 44, or the rare 22 that was bluffing and then backed into a boat. Since he’s played his hand to entice a bluff, he’s got an easy call with KQ.

I like this one better, even though it didn’t work:

Full Tilt Poker, $5/$10 NL Hold’em Cash Game, 2 Players
LeggoPoker.com – Hand History Converter

BB: $2,203.50
Hero (SB): $6,798

Pre-Flop: 7 9 dealt to Hero (SB)
Hero raises to $30, BB calls $20

Flop: ($60) 4 2 8 (2 Players)
BB checks, Hero bets $44, BB raises to $144, Hero raises to $366, BB calls $222

Turn: ($792) Q (2 Players)
BB checks, Hero bets $444, BB calls $444

River: ($1,680) J (2 Players)
BB checks, Hero bets $888, BB calls $888

Results: $3,456 Pot ($0.50 Rake)
BB showed 7 7 (a pair of Sevens) and WON $3,455.50 (+$1,727.50 NET)
Hero showed 7 9 (Queen Jack high) and LOST (-$1,728 NET)

First off, my range is intrinsically much wider because we are heads up. It’s not inconceivable that I have 84, 82, or 42 for two pair. My smallish bet sizing on future streets is consistent with this; by the river, 82 can expect to be best but can’t expect worse hands to call a big bet. I also felt this bet sizing would be consistent with air that turned or rivered a pair and is now making a thinnish value bet.

Unfortunately, this was another poorly chosen opponent. He wasn’t so much a good hand-reader as he was just plain old-fashioned stubborn. Oh well.

There are two seminal books that address the value of tournament chips: David Sklansky’s Tournament Poker for Advanced Players and Mason Malmuth’s Gambling Theory and Other Topics. I haven’t read Malmuth’s book, but my understanding is that both make a similar argument that this value is non-linear. Another words, your last chip is worth more than your second to last chip is worth more than your third to last chip etc. Each chip you add to your stack increases the value of your stack, but by less than the preceeding chip did. So if you have on chip worth x, and you double up, your stack is worth marginally less than 2x. And if you double again, your stack will not be worth 4x. This is because survival has value in a tournament where all of the prize pool is not paid to the winner.

The countervailing principle is that chips are worth more in the hands of a skilled player than an unskilled player. This is because better players will have the opportunity to use those chips to win more chips. They contain within them the player’s expected value for the tournament. In FTOPS Event 4, the first 2000 chips, which cost $300, were probably worth $750 or so to the best player in the field. Conversely, they were probably worth about $50 to the worst player.

You can see that at this rate, it is clearly correct for the best players to rebuy immediately in a tournament that allows unlimited rebuys. Even though his second $300 buys him less than his first expenditure, it still buys him more than $300 worth of value. Conversely, it is incorrect for the worst players to rebuy. In fact, it is incorrect for them to play at all.

When only a single rebuy is permitted, this could at least theoretically change. If a skilled player uses his rebuy immediately to double his starting stack, he risks losing all 4000 of his chips at once. Although his rebuy was a good investment, he missed out on the opportunity to make an even better investment in a second tournament life. Remember, going from 0 to 2000 is worth more than going from 2000 to 4000. By opting for the latter, the player cost himself the chance to do the former a second time.

However, this must be balanced against the risk of immediately getting over 2000 chips, remaining there for the entire rebuy period, and thus losing the opportunity, to invest that second $300 at all.

The one other thing I haven’t mentioned yet is that it matters how many chips the other players at your table have and how good they are. A player cannot realize the extra value that his skill imparts to his 4000 chip stack if no one else at the table has more than 2000. If several bad players to his right all rebought immediately, then the good player should do so as well, so that he will have the opportunity to invest his additional 2000 chips well against those weak players. If several very good players to his immediate left rebought to 4000, the same player might be better off saving his rebuy as an insurance policy against elimination. Otherwise, he risks playing larger pots out of position against very good players- a scenario where those additional chips would not be invested well. If the first hour is drawing to a close and his stack is below 2000, he can always take his second rebuy then.

Unlike an unlimited rebuy tournament, where it generally makes sense to push any edge during the rebuy period since survival is never at risk, this structure makes survival during the first hour particularly important. This is because the player will have the opportunity at the end of the first hour to buy chips at a discount. $300 will buy him, not 2000 chips, as with the rebuys, but 2500 chips for an add-on. It is pretty much always profitable for a good player to add-on, and if he is eliminated in the first hour, he won’t have a chance to take this good investment.

I include this exegesis on rebuy tournament theory because I have nothing interesting to say about the tournament itself. No one at my table rebought immediately, so I didn’t either. I lost my first 2000 chips with two pair in a limped pot at the 10/20 level. My opponent seemed like a fish, so I thought he would call me down with worse, but he ended up having a better two pair. Then I rebought, added on, lasted for about an hour more despite missing tons of flops, shoved over a very weak limper with K7s, and got called by one of the blinds who had AK.

I’m not all that good at PLO, but I do want to learn, and I’m sure it will be a weak field, so I’ll probably play today’s 2:00 $500 PLO 6-Max. I’ll be playing the Stars $300 anyway. Then at 4:30 there’s a $100 rebuy FTOPS that I’ll play if I’m not sick of poker by then.