Close gambles in tourneys

[paulish]

Your in a live tourney and you're in the money 5 tables left, and avg stack is around T40.000

Full table, 9 players
SB = 1.000
BB = 2.000
ante = 100

Everybody folds to the Button, who pushes all-in with T16.000 without looking at his cards. SB folds, and you're in the BB.
You cover the Button.
[*] [2[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/heart.gif[/img]] is a slight favorite (EV=50.334%) over a random hand, and has an expectation of T3.063 (1,5xBB)[*] [T [img]/images/graemlins/club.gif[/img] 3[img]/images/graemlins/club.gif[/img]] is a 45.693% dog against a random hand, but still has an positive expectation of T1.490 (3/4xBB)

So in a cash game you would make a profit by calling with both [2[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/heart.gif[/img]] and [T[img]/images/graemlins/club.gif[/img] 3[img]/images/graemlins/club.gif[/img]]. But in a tournament you have to take into account the gap and survival concepts

TPFAP (Sklansky):
"Avoid close gambles with a slight advantage":[*] due to the way tournaments are paid. But this is really only apliable to certain final table situations.[*] If you are one of the best players, you should not gamble with a slight edge for a large portion of your chips. It can be mathematically correct to pass up a good bet if losing that bet can keep you from making an even better bet later on. Fold [4[img]/images/graemlins/diamond.gif[/img] 4[img]/images/graemlins/club.gif[/img]] if you know your opponent has [A[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/heart.gif[/img]] "if losing that pot would get you broke or near broke".

So both these two hands would make money in the long run, but you should fold them if calling would bust or criple you. Ok, so if you have enough chips, you call.
But let's get more specific.

<font color="red">Q How big stack would you need to gamble with the Button with these "positive-expectation-bets" in this particular situation?</font>

[AaronBrown]

As a practical matter, you seldom have enough information to make a close calculation anyway. If you play for maximum expected value, you won't go far wrong. The main reason people don't has nothing to do with the mathematics of tournaments, it's that the urge to postpone losing is stronger than the urge to win. That's a bad thing, and you should be careful that you're not using mathematics as an excuse for it.

If you did have full information, as in this problem, the two principles you mention work in opposite directions. If you're trying to maximize your expected tournament payout rather than your expected stack, you would avoid this gamble more with a large stack than a small one. There's no simple calculation to compute the break-even stack size, it depends on the exact distribution of stacks and your model of future play.

The desire to avoid going broke, or getting too short-stacked to exercise your superior Poker talent, operates more at lower stacks. I would say offhand that you would want something like $12,000 left; enough for three rounds of antes and blinds and 30% of the average stock; so you might make $28,000 the minimum holding to call.

There is a third important factor. If you take this bet and win you force out one player. This helps everyone else in the tournament, not just you. That probably overwhelms the statistical disadvantage of money you win being worth less than money you lose. Also, in my experience, players who are willing to gamble encourage reciprocation from other players. Remember, you're in the tournament to win, not to avoid losing. If you want to avoid losing, don't enter.

[Xhad]

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As a practical matter, you seldom have enough information to make a close calculation anyway. If you play for maximum expected value, you won't go far wrong.

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Actually a better way of looking at it is, since variance is inherently -EV in tournaments, anytime a decision looks close from a cEV standpoint, you should fold. The exact mathematical threshold for when a call becomes +EV depends on the specific prize structure, and how many players have to be eliminated before there is a prize jump, neither of which was included in the OP.

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There's no simple calculation to compute the break-even stack size, it depends on the exact distribution of stacks and your model of future play.

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Highlighted for emphasis. Since it's usually very easy to pilfer the blinds at this level, there's not much incentive to jeapordize your stack without a good hand since with the proper initiative you can make plenty of money on your bad ones in uncontested pots.

About the break-even stack size for a call; it depends on the prize structure, but generally it will be such that it isn't worth calling here; if people are playing tight, steal blinds when you get the chance. If they're playing loose, let them eliminate each other, or call you when you happen to catch a real hand.

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I would say offhand that you would want something like $12,000 left; enough for three rounds of antes and blinds and 30% of the average stock; so you might make $28,000 the minimum holding to call.

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Actually a stack of $28000 is already in the "not desperate but not happy" range. Having a stack of less than 20K is "push or fold" range. A stack of $12000 is "open-push any two and cross your fingers" range, hardly a comfortable amount to be left with after calling with T3s.

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There is a third important factor. If you take this bet and win you force out one player. This helps everyone else in the tournament, not just you.

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Eliminating players generally has little to no value until the final table; in this case you're sharing the reward with forty people, but taking the entire risk yourself.

[AaronBrown]

Of course, you know the tournaments you play in best, but I have never known this hyperconservative style to succeed. Generally the bad and some of the loose players wash out first, while the blind-stealers who avoid all contested pots, and refuse to risk their stack or try to eliminate anyone, survive. But as things get closer to the money, the survive-at-any-price players fall out for a variety of reasons.

If this style does get you in the money in the tournaments you play in, then I agree there is no reason to take chances. But I think most of us have to take some gambles to win, and it rarely makes sense to pass up a positive expected value gamble. When you do, you usually find yourself later forced to take a gamble at worse odds.

[Xhad]

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Of course, you know the tournaments you play in best, but I have never known this hyperconservative style to succeed.

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I suggest doing a search in the STT forum for anything with the word "bubble" in the subject line. This is not "hyperconservative", it's widely considered correct play.

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Generally the bad and some of the loose players wash out first, while the blind-stealers who avoid all contested pots, and refuse to risk their stack or try to eliminate anyone, survive. But as things get closer to the money, the survive-at-any-price players fall out for a variety of reasons.

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This isn't surviving at any price. You lose almost nothing by folding a coinflip. Furthermore, assuming the other players know what they are doing, it's more EV just to wait until it's your turn to steal the blinds so someone else can fold a coinflip.

When things get close to the money, and two players get in an all-in confrontation, the confrontation itself is often more EV for the other players than it is for the people playing in the pot (for an illustration see Tournament Poker for Advanced Players, or try fiddling with the ICM calculator).

Again, if your opponents are good players, you can just blind steal. They won't call because they know they shouldn't. If they are bad weak-tight players, calling here is absurd because A: He has a hand and B: You can blind steal even more. If they are bad loose players, they'll hang themselves by playing pots together when they shouldn't, and you'll probably still get in situations where you can blind steal, just be careful that either you're in late position or your hand is semi-decent before you try because your fold equity will be diminished.

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If this style does get you in the money in the tournaments you play in, then I agree there is no reason to take chances. But I think most of us have to take some gambles to win, and it rarely makes sense to pass up a positive expected value gamble.

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cEV, or expected value in tournament chips, is common notation in both tournament forums. This is to differentiate it from $EV, or expected value in prize dollars, because they are known not to be the same in all situations.

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When you do, you usually find yourself later forced to take a gamble at worse odds.

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Highlighted again for emphasis; this is the fallacy. If your opponents are playing mathematically correctly, they are also avoiding showdowns, meaning your blind steals are insanely likely to work. Meaning calling off too many of your chips here is giving up many EV bets because you're trashing your fold equity. Blind stealing in a situation where your opponent will fold AKs* is more +EV than calling half your stack as an underdog getting just above even money. Your fold equity of future blind steals more than makes up for the fraction of a big blind in cEV you give up by folding.


*probably never correct in a multi-table tournament paying many spots, but sometimes it does happen in an SNG when someone has a very small stack and the money is very close.

[KingDan]

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So in a cash game you would make a profit by calling with both [2[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/heart.gif[/img]] and [T[img]/images/graemlins/club.gif[/img] 3[img]/images/graemlins/club.gif[/img]]. But in a tournament you have to take into account the gap and survival concepts

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Just to clear up, this doesn't have anything to do with the gap concept. That is stating you need a bigger hand to raise than to call a raise because a raise means he has a good hand (better than random)However, if there is no action to you, you are facing random hands, your own hand relative to your opponents hand is better.
In this case, he raised blind so he still has a random hand.

[Xhad]

The Gap Concept still matters because the raiser has a chance to win the pot uncontested, while a caller does not. Late in some tournaments it can be correct for the button to raise all-in with any two cards, but incorrect for the big blind to call with non-monster hands.

[Xhad]

http://forumserver.twoplustwo.com/sh...t=all&amp;vc=1

Notice the post where someone calculated that getting all-in against complete trash is less EV than just going all-in and hoping everyone folds. Also notice the implicit assumption that the reraiser's doing this with trash does not necessarily make this a call.

[AaronBrown]

I'm not disagreeing with you, I just think we play different tournaments. I absolutely agree that if you can win without taking gambles, you should do it. That's the difference between Poker and gambling.

I also agree your strategy "widely accepted" in the sense that many players play this way. Some of them no doubt do it because it wins for them. However, I see a lot of people playing this way who end up surviving longer but still finishing out of the money. That doesn't invalidate the strategy, but it's prudent to warn people that a lot of people who try it, fail. Of course, a lot of people who just play for EV fail as well, but in my personal experience (obviously different from yours) some of them also win.