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Exhaustive Search in the Game Amazons

Amazons is a young “real world” game that fulfills all defining constraints of combinatorial game theory with its original rule set. We present a program to evaluate small Amazons positions with a given number of amazons on game boards of restricted sizes with canonical combinatorial game theory values. The program does not use an analytical approach, instead it relies on exhaustive search in a bottom-up strategy. Here it is applied on all positions on game boards which fit into an underlying game board of size 11 by 2. The results show that even under these restrictions Amazons offers a wide spread of game theoretic values, including some very interesting ones. Also the canonical forms of the values can be very complicated.