Misère canonical forms of partizan games

Details Misère canonical forms of partizan games Misère canonical forms of partizan games

2007-03-20

arxiv.org/abs/math/0703565v1

Mathematics

Combinatorics

12 pages

Scientific paper

We show that partizan games admit canonical forms in mis\`ere play. The proof is a synthesis of the canonical form theorems for normal-play partizan games and mis\`ere-play impartial games. It is fully constructive, and algorithms readily emerge for comparing mis\`ere games and calculating their canonical forms. We use these techniques to show that there are precisely 256 games born by day 2, and to obtain a bound on the number of games born by day 3.

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