Lessons in Losing: An Introduction to Misere Game Theory

Abstract: A combinatorial game is a two-player game with no elements of chance, no hidden information, and no ties. Under "normal" rules, the player who makes the last move wins the game; under "misere" rules, whoever makes the last move loses. Normal-play games have been extensively analyzed and exhibit nice mathematical structure, including a notion of addition that forms the set of all games into an abelian group. Misere games have been much less studied, as almost all of the intuitive algebraic structure seems to fall apart when the loser is the player who moves last. This talk will introduce combinatorial games in general before highlighting some of the challenges inherent in misere play. We will then consider how restricting the game universe can allow for more useful analysis of misere games.