Tournament Competition/Cooperation

[jimdmcevoy]

This is an idea that popped into my head a few days ago.

Everyone knows that in tournament play it can be favourable to avoid big pots even if you are a small favourite. A simple example:

Suppose you have three equaly skilled players who are the last three players in a tourney, and they all have the same amount of chips. Suppose third place pays $200, second place pays $400, and first place pays $600.

Now this hand comes down, two players are all in preflop, one has QQ and one has AK. What are the players EV's?

Well suppose that the AK wins 43% of the time and QQ 57% of the time (disregarding split pots).

EV of player with AK: $343
EV of player with QQ: $390
EV of player that is not in the hand: $467

So if the player with AK goes all in and then flips his hand face up, the player with QQ should fold if he is trying to maximize his EV, even though it would be correct to call in a cash game, and it would be correct to call if he wanted to maximize his chances of winning.

This principle of avoiding coin flips to maximize EV is well known. In tournaments each hand is not a zero-sum game in terms of money EV.

So I thought if hands are no longer zero-sum, then maybe there can be some degree of cooperation? There already exists cooperation between two players when they are in a pot and a third player is all in, sometimes the two players play slower in order to maximize the chance of the third player to lose the hand.

But what about when you just have two players involved in a hand? This is still not a zero-sum game (as opposed to all cash games where it is always zero sum not including rake).

So I thought one day of one way to cooperate when heads up: Suppose you are in a hand where you know you will not win, and you know that no matter what happens you will not try to bluff. An example:

You have 22 in the big blind, one limper came in and the board on the river is KK2KK (you tried to slowplay). Suppose for whatever reason that you decided not to bluff here, I reckon that you will increase your EV by folding your hand on the river even when you could have checked.

This loses no tournament chips EV.

The advantage of doing this is in the future if you are in the same situation but with a better hand, when you check instead of folding your opponent (if he knows how you play) will know that you don't have 22, and thus there is a slighty higher chance you have a better hand, and you want him to know this.

Using this method of folding when you could check when you know you will not win I think will keep pots a little smaller than normal, and I think by keeping pots smaller than normal you increase both you and your opponents EV a little.

[TStoneMBD]

assuming 3 equally skilled players, each with equal stacks and payout of 600:400:200;

lets assume QQ vs AK is a 50/50 dead even race for a minute. QQ calls the allin, and will therefore doubleup 50% of the time or bust winning $200. If he doubles up, he has twice as many chips as the other player left which means that his equity in the tournament is $533.3333 (600+600+400=1600/3). remaining players equity becomes 466.6666.

1/2 the time he wins $200. 1/2 the time he wins $533.3333.

if he folds his hand his equity is $400 (600+400+200=1200/3).

His equity for calling is, on average, $366.666666 (533.3333+200/2)

Calling here means a loss of $33.3333, or -17% equity.


Therefore, Hero must gain an extra 17% equity by calling the allin to break even. His immediate equity for a QQ vs AK race is 7%. Therefore, Hero must make 10% equity when accounting for dead money in the pot.

Under that assumption, If the blinds are 5/10 and Villain goes allin UTG with AK for 110chips, Hero can call in the BB with QQ getting 4:5 equity, or 20%.

His positve expected value for calling would be 10%, or $19.60. (0% equity= -33.33333; 17% equity =0; 27% equity=+19.60)

[jimdmcevoy]

Yep, looks good to me. But what do you think of the idea that sometimes folding when you could check can increase your EV?

[Paul2432]

I see several problems.

The first part of this analysis discounts the effect of antes and blinds. If the blinds/antes are large enough, then your example falls apart.

In the second part you say you will not bluff. Giving up bluffing is a huge leak IMO. Another problem, is that the situation you described may not occur very often. Even when it does occurr, your opponent may have no idea you are trying to do. Finally, even if he does understand, he may get knocked out or switched to a different table.

None of this really gets to the heart of the problem. The effect you describe only occurs in the very late stages of a tournament. Nearly all the time in a tournament, chipEV is pretty close to $EV.

Paul