Deepest "possible" stacks

[PokrLikeItsProse]

We could do a few special cases. (And by we, I mean someone besides me.)

Given two game theory experts, how deep do stacks have to be for the two players to not be all-in for the following cases:

1) They find themselves set over set on a J72 rainbow flop.

2) They both catch straight flushes on a 765 monotone flop.

[bluffcakes]

With any stacks less than infinite according to game theory you can always get all-in. Even with 1,000,000 BB stacks, you should eventually get all-in. For example say you have 83o on a J72r flop, if someone bets you should raise as a bluff a certain % of the time, they should then reraise as a bluff a certain % of the time, you should then rereraise...etc until someone is all-in.

[reidardahlen]

[ QUOTE ]
With any stacks less than infinite according to game theory you can always get all-in. Even with 1,000,000 BB stacks, you should eventually get all-in. For example say you have 83o on a J72r flop, if someone bets you should raise as a bluff a certain % of the time, they should then reraise as a bluff a certain % of the time, you should then rereraise...etc until someone is all-in.

[/ QUOTE ]

Hmmm... sounds weird but maybe that would occur, although maybe infrequently, even with astronomical stacks. This question is hard to specify! Would playing with say 1,000,000 BB stacks often result in many more raises per street? That looks like weird poker, with re-re-re-re-re-re-reraises being common.

[PokrLikeItsProse]

[ QUOTE ]
With any stacks less than infinite according to game theory you can always get all-in. Even with 1,000,000 BB stacks, you should eventually get all-in. For example say you have 83o on a J72r flop, if someone bets you should raise as a bluff a certain % of the time, they should then reraise as a bluff a certain % of the time, you should then rereraise...etc until someone is all-in.

[/ QUOTE ]

I really don't believe that. I don't have The Mathematics of Poker in front of me (have you read it?), but I want to say that there was a suggestion that seven reraises or so (some finite figure at least) was the maximum that two game theoretical players would go to with the nuts vs the second nuts. I'm willing to believe that the nut straight flush vs the second nut straight flush will go to more reraises than nut flush vs second nut flush with no straight flush possible or AA vs KK preflop, but I still think that there is a limit before a game theory expert will decide that his second-best hand can only be raised by the best possible and just call the last reraise (because the pot is so big).

And since we're talking no limit, the player with the nuts can't just shove because you can make the stacks so big relative to the size of the pot that the correct action is to fold anything but the absolute nuts.

[MARK R]

The money will always go into the middle when both players have the nuts on the river.

[SteenV]

If AA is out versus AA then all the money will probably go in preflop... Here, the bigger stacks doesn't change the EV but it changes the number of raises (and the variance)

[reidardahlen]

[ QUOTE ]
If AA is out versus AA then all the money will probably go in preflop... Here, the bigger stacks doesn't change the EV but it changes the number of raises (and the variance)

[/ QUOTE ]

Eh....what....

[Mook]

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[ QUOTE ]
With any stacks less than infinite according to game theory you can always get all-in. Even with 1,000,000 BB stacks, you should eventually get all-in. For example say you have 83o on a J72r flop, if someone bets you should raise as a bluff a certain % of the time, they should then reraise as a bluff a certain % of the time, you should then rereraise...etc until someone is all-in.

[/ QUOTE ]

Hmmm... sounds weird but maybe that would occur, although maybe infrequently, even with astronomical stacks. This question is hard to specify! Would playing with say 1,000,000 BB stacks often result in many more raises per street? That looks like weird poker, with re-re-re-re-re-re-reraises being common.

[/ QUOTE ]
Past a certain point, this won't happen even with game theoretic play, because there aren't enough distinct hand combinations in hold-'em.

What I mean is that in TMOP's {0,1} game, there are an infinite continuum of hands. And, yes, there would thus be a "theoretical range" in which X puts in, say, the 11th pot-sized raise for value while Y puts in the 12th pot-sized raise as a bluff (or whatever numbers would get such enormous stacks all-in). My guess is that the parlay would happen, say, once every several billion hands or so.

But in hold-'em, the number of distinct combinations of X's and Y's hole cards for a given board come up far, far, far short of this number. (I believe it's only about a few hundred thousand.) So, for practical purposes, the ranges in which this parlay would be expected to happen don't exist in real life. Any game with only a 52-card deck yields too "lumpy" a distribution of probable hands to ever make the "dozens of re-raises with less than the nuts" scenario possible, even using game theory.

Mook

[Dr. Tre]

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How would the flop action go with infinite stacks with AK v AK v QQ on a QJT board?

In a three way all in the QQ is a money favorite, but heads up it is an underdog. How would each player play their hand correctly? Each of the AK players would be making an "infinitely" big mistake to get all in on the flop, but the QQ would make an infinitely big mistake to get all in unless he was guarenteed to get two callers.

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Easy cop-out answer: with infinite stacks, nobody would get in preflop without AA.

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This is not true. With infinite stacks, only playing aces would be a mistake. It is easily exploitable by calling his preflop raise with ATC and bet/raise without the nuts on the flop. If he is only playing the nuts because it is infinite stacks, then he will be losing a lot of money by folding too much.
Even with extremely deep stacks, it is not necessary to play for only the nuts. Simply bluffing out the nits who will only play for the nuts can become very profitable in these games.