Abstract

Amazons is a young, abstract, strategic, two-player game, in which the first player unable to move loses. We present a database for small Amazons positions, which for every position holds the canonical combinatorial game theory values, its thermograph and the corresponding move for every canonical option. Such a database is useful to find values and structures in games that were unknown before and hard or impossible to find or verify by hand. In Amazons we were able to prove the existence of nimbers, of fractions down to 1 64 and of various infinitesimals, but these results also suggest that there is no easy construction for most of these values. The database also demonstrates how complex canonical forms in Amazons can be and that many Amazons positions have properties and values that are totally counterintuitive.

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