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Game comparison through play. (English) Zbl 1402.91090

Summary: 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 \(\mathbb U\), we define a dual normal-play game, called the left provisonal game \([G, H]\), and show that \(G \succcurlyeq H\) 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 \(\mathbb U\), and we define the associated categories \(\mathbf{LNP}(\mathbb U)\) .

MSC:

91A46 Combinatorial games
Full Text: DOI

References:

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