Optimal Bluffing Strategies in Poker

Lawrence Friedman
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Lawrence Friedman: Mathematica, Princeton, New Jersey

Management Science, 1971, vol. 17, issue 12, B764-B771

Abstract: Bluffing in poker is examined as a problem in game theory. A very common situation occurs where the "kitty" contains K, player B has the apparent high hand, and player A has an apparent probability, P, of having a better hand than B, and considers a bluff. Under these conditions it can be shown that A should raise 1 unit with probability (1/(1 + K))(P/(1 - P)) \cdot B, in turn, should call A's potential bluff with probability K/(1 + K). This says that in pot limit poker, if the potential bluffer has the appearance of having the winning hand with probability 0.25, he should bluff 1/2 \cdot 1/3 = 1/6 of the time. The optimal strategy is to call a potential bluffing hand half the time.

Date: 1971
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