Playing "Invisible Chess" with Information-Theoretic Advisors

Making decisions under uncertainty remains one of the central problems in AI research. Unfortunately, most uncertain real-world problems are so complex that any progress in them is extremely dif cult. Games model some elements of the real world, and offer a more controlled environment for exploring methods for dealing with uncertainty. Chess and chess-like games have long been used as a strategically complex testbed for general AI research, and we extend that tradition by introducing an imperfect information variant of chess with some useful properties such as the ability to scale the amount of uncertainty in the game. We discuss the complexity of this game which we call invisible chess, and present results outlining the basic values of invisible pieces in this game. We motivate and describe the implementation and application of two information-theoretic advisors that assist a player of invisible chess to control the uncertainty in the game. We describe our decision-theoretic approach to combining these informationtheoretic advisors with a basic strategic advisor. Finally we discuss promising preliminary results that we have obtained with these advisors.