A theoretical and empirical investigation of search in imperfect information games

We examine search algorithms for games with imperfect information. We rst investigate Monte Carlo sampling, showing that for very simple game trees the chance of nding an optimal strategy rapidly approaches zero as size of the tree increases. We identify the reasons for this sub-optimality, and show that the same problems occur in Bridge, a popular real-world imperfect information game. We then analyse the complexity of the underlying problem, proving it to be NP-complete and describing several polynomial time heuristics. We evaluate these heuristics theoretically and experimentally, demonstrating that they signi cantly out-perform Monte Carlo sampling. Indeed, on a set of Bridge problems drawn from a de nitive expert text, our heuristics consistently identify strategies as good as, or superior to, the expert solutions | the rst time a game-general tree search algorithm has been capable of such performance.