Exhaustive Search and Databases in the Application of Combinatorial Game Theory to the Game Amazons

The author describes the young and challenging tactical board game Amazons and his mathematical analysis of the game with the means of combinatorial game theory. The main tool of this analysis was the construction of a database of 66 million evaluated Amazons positions. This database was used to gather new statistical insights about exponential complexity of Amazons and to find positions with values heretofore unknown in Amazons. Among the more spectacular results was the discovery of the existence of *, a nimber, in Amazons and the construction of anAmazons representation for every day dyadic fraction. Both Amazons and combinatorial game Theory are introduced extensively, so that this book should be understandable for anybody with an academic mathematical background or even for mathematical laymen with a strong interest in both Amazons and combinatorial game theory.