Playing Konane Mathematically: A Combinatorial Game-Theoretic Analysis

This article presents a combinatorial game-theoretic analysis of Konane, an ancient Hawaiian stone-jumping game. Combinatorial game theory [Berlekamp et al. 19821 applies particularly well to Konane because the first player unable to move loses and because a game often can be divided into independent subgames whose outcomes can be combined to determine the outcome of the entire game. By contrast, most popular modern games violate the assumptions of combinatorial gametheoretic analysis. This article describes the game of Konane and the ideas of combinatorial game theory, derives values for a number of interesting positions, shows how to determine when a game can be divided into noninteracting subgames, and provides anthropological details about Konane.