Game comparison through play

Absolute Universes of Combinatorial Games, as defined in a recent paper by the same authors, include many standard short Normal- Misere- 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 Misere-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). (C) 2017 Elsevier B.V. All rights reserved.