Machine Learning

, Volume 74, Issue 2, pp 159–189 | Cite as

Effective short-term opponent exploitation in simplified poker

  • Finnegan Southey
  • Bret Hoehn
  • Robert C. Holte


Uncertainty in poker stems from two key sources, the shuffled deck and an adversary whose strategy is unknown. One approach to playing poker is to find a pessimistic game-theoretic solution (i.e., a Nash equilibrium), but human players have idiosyncratic weaknesses that can be exploited if some model or counter-strategy can be learned by observing their play. However, games against humans last for at most a few hundred hands, so learning must be very fast to be useful. We explore two approaches to opponent modelling in the context of Kuhn poker, a small game for which game-theoretic solutions are known. Parameter estimation and expert algorithms are both studied. Experiments demonstrate that, even in this small game, convergence to maximally exploitive solutions in a small number of hands is impractical, but that good (e.g., better than Nash) performance can be achieved in as few as 50 hands. Finally, we show that amongst a set of strategies with equal game-theoretic value, in particular the set of Nash equilibrium strategies, some are preferable because they speed learning of the opponent’s strategy by exploring it more effectively.


Game-playing Opponent modelling Experts Bayesian Poker 

Supplementary material


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Finnegan Southey
    • 1
  • Bret Hoehn
    • 2
  • Robert C. Holte
    • 2
  1. 1.GoogleMountain ViewUSA
  2. 2.Dept. of Computing ScienceUniversity of AlbertaEdmontonCanada

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