Re: Another One Card Game Theory Problem
Let a be A's card and b be B's card. B needs at least 1/3 chance of winning to call A's bet of the pot.
If b < 1/3, then A should always bet and B should always fold.
If b > 1/3, the A should bet if a > (3b-1)/2. Actually, it doesn't matter what numbers A bets on if a < b, only how often he bets. So we could just as well say A should bet if a > b or a < (1-b)/2. If A doesn't bet, he should draw, then follow the same betting rule again.
A's expected value for given b is 3(1-b)(1+3b)/4, or 1 if b < 1/3, times the size of the pot. A's unconditional expected value (before she looks at B's card) is 29/36. B's breakeven card is 0.804738.
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