Finding Optimal Strategies for Imperfect Information Games

Ian Frank, David A. Basin, Hitoshi Matsubara

Abstract: We examine three heuristic algorithms for games with imperfect information: Monte-carlo sampling, and two new algorithms we call vector minimaxing and payoff-reduction minimaxing. We compare these algorithms theoretically and experimentally, using both simple game trees and a large database of problems from the game of Bridge. Our experiments show that the new algorithms both out-perform Monte-carlo sampling, with the superiority of payoff-reduction minimaxing being especially marked. On the Bridge problem set, for example, Monte-carlo sampling only solves 66% of the problems, whereas payoff-reduction minimaxing solves over 95%. This level of performance was even good enough to allow us to discover five errors in the expert text used to generate the test database.