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Optimal Bluffing Strategies in Poker

Author

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  • Lawrence Friedman

    (Mathematica, Princeton, New Jersey)

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.

Suggested Citation

  • Lawrence Friedman, 1971. "Optimal Bluffing Strategies in Poker," Management Science, INFORMS, vol. 17(12), pages 764-771, August.
    • Handle: RePEc:inm:ormnsc:v:17:y:1971:i:12:p:b764-b771
    DOI: 10.1287/mnsc.17.12.B764
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    Cited by:

    1. Steven D. Levitt & John A. List & David H. Reiley, 2010. "What Happens in the Field Stays in the Field: Exploring Whether Professionals Play Minimax in Laboratory Experiments," Econometrica, Econometric Society, vol. 78(4), pages 1413-1434, July.
    2. Fowler David S. & Musgrave Jon, 2020. "Revisiting Carr’s Business Bluff: Opinions on the Ethics of Playing the Game," Journal for Markets and Ethics, Sciendo, vol. 8(2), pages 1-3, December.
    3. Steven Levitt & John List & David Reiley, 2010. "What happens in the field stays in the field: Professionals do not play minimax in laboratory experiments," Artefactual Field Experiments 00080, The Field Experiments Website.

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