Game comparison through play

Absolute Universes of Combinatorial Games, as defined in a recent paper by the same authors, include many standard short Normal- Misère- and Scoring-play monoids. Given G and H in an Absolute Universe U, we define a dual Normal-play game, called the Left Provisonal Game [ G, H ], and show that G ≽ H if and only if Left wins [ G, H ] playing second. As an example of our construction, we show how to compare Dicot Misère-play games in Siegel's computer program CGSuite and illustrate by including the partial order of all games of rank 2. We also show that Joyal's Normal-play Category generalizes to every Absolute Universe U, and we define the associated categories LNP ( U ).

Authors

• Urban Larsson
• Richard J. Nowakowski
• Carlos P. Santos

Keywords

• Absolute universe
• Category theory
• Combinatorial game space
• Dicot misère-play
• Play game-comparison