Best-response play in partially observable card games
Frans A. Oliehoek, Matthijs T. J. Spaan, Nikos Vlassis · 2005
We address the problem of how to play optimally against a fixed opponent in a twoplayer card game with partial information like poker. A game theoretic approach to this problem would specify a pair of stochastic policies that are best-responses to each other, i.e., a Nash equilibrium. Although such a Nash-optimal policy guarantees a lower bound to the attainable payo# against any opponent, it may not necessarily be optimal against a fixed opponent. We show here that if the opponent's policy is fixed (either known or estimated by repeated play), then we can model the problem as a partially observable Markov decision process (POMDP) from the perspective of one agent, and solve it by dynamic programming. In particular, for a large class of card games including poker, the derived POMDP consists of a finite number of belief states and it can be solved exactly.