Strategy Purification

There has been significant recent interest in computing effective practical strategies for playing large games. Most prior work involves computing an approximate equilibrium strategy in a smaller abstract game, then playing this strategy in the full game. In this paper, we present a modification of this approach that works by constructing a deterministic strategy in the full game from the solution to the abstract game; we refer to this procedure as purification. We show that purification, and its generalization which we call thresholding, lead to significantly stronger play than the standard approach in a wide variety of experimental domains. First, we show that purification improves performance in random 4x4 matrix games using random 3x3 abstractions. We observe that whether or not purification helps in this setting depends crucially on the support of the equilibrium in the full game, and we precisely specify the supports for which purification helps. Next we consider a simplifed version of poker called Leduc Hold'em; again we show that purification leads to a significant performance improvement over the standard approach, and furthermore that whenever thresholding improves a strategy, the biggest improvement is often achieved using full purification. Finally, we consider actual strategies that used our algorithms in the 2010 AAAI Computer Poker Competition. One of our programs, which uses purification, won the two-player no-limit Texas Hold'em bankroll division. Furthermore, experiments in two-player limit Texas Hold'em show that these performance gains do not necessarily come at the expense of worst-case exploitability and that our algorithms can actually produce strategies with lower exploitabilities than the standard approach.