mathmatics of strategy: contradiction?

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As more and more players call you, your chances of winning can decline faster than the pot increases.

Suppose, for example, that four players call you with four different suited hands. Now any three-suited board beats you. It's the negative correlation between their hands that kills you. The same thing is true to a lesser degree if they are just holding different ranks.

Of course, all four players might be suited in the same suit, or holding the same ranks. But this is less likely than the opposite.


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OK this makes sense, but like the original poster said what is the math that backs it up?

My math is pretty poor in this area so I may be wrong but I think:

If your at a table with 10 people and you hold AA and everyone goes all in, your chance of winning is pretty slim , but this still gives you better positive odds because your getting 9:1 on your money and I think you will win more than %11 of the time, I'm not sure on the actuall math but I think thats what the original poster was asking for.

[AaronBrown]

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OK this makes sense, but like the original poster said what is the math that backs it up?

My math is pretty poor in this area so I may be wrong but I think:

If your at a table with 10 people and you hold AA and everyone goes all in, your chance of winning is pretty slim , but this still gives you better positive odds because your getting 9:1 on your money and I think you will win more than %11 of the time, I'm not sure on the actuall math but I think thats what the original poster was asking for.

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If everyone goes all-in blind, AA has about a 31% chance of winning. If everyone starts with the same stack, your expected profit is about twice the stack. That's obviously great.

But suppose you raise and nine good players call you. Now you cannot assume random hands. The first and maybe even the second caller might have top pairs, you play well against these. But the later callers are going to throw away their JJ and TT hands. They're probably playing suited connectors, which play well in multiway pots. A pair of Aces is no better against a flush or straight than a pair of 2's or no pair. Also, there's a chance someone else holds AA, the one hand that's never folded preflop. That kills your odds because you cannot improve, and the best you can do is split the pot (except for a rare flush).

Nine good players coming in is unrealistic, so lets consider four callers. Against four random callers, AA wins 56% of the time, but against four good players calling, 40% is a better guess. Moreover, those good players are likely to either beat you or fold after the flop.

Against one player, AA wins 85% of the time against a random hand, and not much worse against any hand. If someone's holding a top pair, you could get called to the river, even raised.

Guessing some numbers, AA against one hand might win 4 BB 85% of the time and lose 4 BB 15% of the time for an expected profit of 2.8 BB. AA against four hands might win 6 BB 40% of the time (more bettors preflop, but most hands dropping at the flop) and lose 4 BB 60% of the time (because you go to the river when you lose). That's zero expected profit.

Obviously you can play with the numbers and make things closer, but you'll generally find that AA plays better when one good player calls than when four good players do.

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OK this makes sense, but like the original poster said what is the math that backs it up?

My math is pretty poor in this area so I may be wrong but I think:

If your at a table with 10 people and you hold AA and everyone goes all in, your chance of winning is pretty slim , but this still gives you better positive odds because your getting 9:1 on your money and I think you will win more than %11 of the time, I'm not sure on the actuall math but I think thats what the original poster was asking for.

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If everyone goes all-in blind, AA has about a 31% chance of winning. If everyone starts with the same stack, your expected profit is about twice the stack. That's obviously great.

But suppose you raise and nine good players call you. Now you cannot assume random hands. The first and maybe even the second caller might have top pairs, you play well against these. But the later callers are going to throw away their JJ and TT hands. They're probably playing suited connectors, which play well in multiway pots. A pair of Aces is no better against a flush or straight than a pair of 2's or no pair. Also, there's a chance someone else holds AA, the one hand that's never folded preflop. That kills your odds because you cannot improve, and the best you can do is split the pot (except for a rare flush).

Nine good players coming in is unrealistic, so lets consider four callers. Against four random callers, AA wins 56% of the time, but against four good players calling, 40% is a better guess. Moreover, those good players are likely to either beat you or fold after the flop.

Against one player, AA wins 85% of the time against a random hand, and not much worse against any hand. If someone's holding a top pair, you could get called to the river, even raised.

Guessing some numbers, AA against one hand might win 4 BB 85% of the time and lose 4 BB 15% of the time for an expected profit of 2.8 BB. AA against four hands might win 6 BB 40% of the time (more bettors preflop, but most hands dropping at the flop) and lose 4 BB 60% of the time (because you go to the river when you lose). That's zero expected profit.

Obviously you can play with the numbers and make things closer, but you'll generally find that AA plays better when one good player calls than when four good players do.

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Ok thanks, I know the situation with the whole table was ridiculos but I just used it because it was easy. Ok I see what your saying in that Aces play perticularly well against the type of hand you would call a big raise with AA KK QQ AKs but when you have play multiway pot with suited connectors it sucks. Im still thinking on this though, its wierd stuff.