Classic Type Game Theory Problem

[Jerrod Ankenman]

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I came to the conclusion that the ideal strategy for A is to stand pat on all hands where 1.0 - B < A.

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That is part of the optimal strategy in some cases, when b > [sqrt(2)-1], which is around .4142. There, B always draws when A does.

But the interesting cases are when b < [sqrt(2)-1], where it turns out A stands pat when his hand exceeds [1 - sqrt(1-2b)]. This value is above b, so it does contain an element of bluffing. Furthermore, B randomizes between standing and drawing. Use the usual indifference conditions for these cases.

alThor

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I posted the solution in the Poker Theory forum, but I've now seen TWO references to this [1 - sqrt(1-2b)] thing, and I'm trying to understand why on earth this would come up.

Suppose there existed a strategy where if b < .5, A could make money by standing pat with a hand less than .5. Then B could respond to this strategy by simply redrawing all the time with b < .5. Then B would make money because A would have stood pat with a hand weaker than .5

Hence, no such strategy can be optimal.

Jerrod Ankenman