new take on old game theory thing..misposted in mtt thread

[sheetsworld]

The situation has been brought up in different forms, but the basic premise is as follows..

You are playing a heads up freeze out NL holdem...blinds 10/20 and each has 10,000 chips. Player A, first to act, makes it 60 to go with AA, and exposes his hand to his opponent. For whatever reason, Player B makes it 120 to go. Now knowing that his opponent has seen his AA, it is player A's action.

How much, if any should A reraise?

sheets

[threeonefour]

i am not sure this has a really clean answer since player B has already made a mistake. so you are not necessarily dealing with an efficient or rational player.

[AaronBrown]

If A's goal is to maximize EV, assuming B makes the worst possible action from A's point of view, A should raise enough to make B fold any hand (except the other two Aces, which of course give B an even chance). I believe the best hand against AA is T9s, with the suit not matching either Ace. That's got 22.8% equity. With $400 in the pot after A calls B, A has to bet $168 or more to make sure B folds with any hand. The exact calculation might be more complicated if you consider post flop action, but $168 is close.

If A bets less than $168, B can profitably call, and that call comes out of A's EV. If A bets more than $168 and B calls, that increases A's EV above the profit she gets if B folds.

[pzhon]

Player A should push or at least raise enough to leave the other AA pot-committed on any flop. If B has AA, the equity is even. If B has other than AA, then B should fold and A picks up the whole pot. Player A can't do better than this against B's best strategy.

[threeonefour]

[ QUOTE ]
If A's goal is to maximize EV, assuming B makes the worst possible action from A's point of view, A should raise enough to make B fold any hand (except the other two Aces, which of course give B an even chance). I believe the best hand against AA is T9s, with the suit not matching either Ace. That's got 22.8% equity. With $400 in the pot after A calls B, A has to bet $168 or more to make sure B folds with any hand. The exact calculation might be more complicated if you consider post flop action, but $168 is close.

If A bets less than $168, B can profitably call, and that call comes out of A's EV. If A bets more than $168 and B calls, that increases A's EV above the profit she gets if B folds.

[/ QUOTE ]

this ignores implied odds. stacks are deep.

[AaronBrown]

[ QUOTE ]
this ignores implied odds. stacks are deep.

[/ QUOTE ]

Yes it does. That's what I meant by ignoring post-flop action. But I don't think it makes much difference, AA doesn't have to be afraid of many flops, and for most of them the danger is obvious. A can afford to go all in, even against an open ended straight flush draw.

A full game theory solution is pretty complicated for this case, I don't think anyone has ever done it.

[MathEconomist]

I agree with three. There's no reason a rational player would raise the AA here (in fact I think it's wrong for B to raise with any hand, even the other possible AA). Since we know B isn't rational, there's not really a well defined correct solution. If we assume that B "accidentally" raised and will play the rest of the hand rationally, then this becomes more complicated. It's not immediately apparent to me how to solve it even though in principle I know enough game theory to do it. Intuitively, I'm going to say the answer is "a lot". If this happended to me, I probably push all-in. You don't want to play the hand out with deep stacks and a huge informational disadvantage. I imagine you can raise a smaller amount in a nash equilibrium solution, but I don't know.

[restrikt]

Player B knows Player A's hand, and is willing to outplay him postflop. How is Player A to know whether Player B has flopped two pair? A set? He doesn't.

Player B, knowing this, attempts to build a slightly larger than normal pot. On the flop, if Player B shows any strength, Player A must fold - I mean, Player B knows Player A has aces, right?

[MathEconomist]

B can't raise for one obvious reason. If he does, he gives A the option of reraising A-I and insuring positive expectation for himself. So A must have positive expectation whatever course of action he undertakes (otherwise he'd use the A-I move as a fallback plan). So B should not be building the pot, because raising gives him negative expectation. Calling should give him a large positive expectation. So B isn't rational. This isn't a formal proof, but it captures the logic correctly.

[sheetsworld]

ok so B cant raise because it opens the door for a to reraose...but now that he has, what shoudl a reraise?

thats the point.

sheets