2011/12/15 by Will Johnson, Johnson, Will
Computer Science · Mathematics · #91A46 #Artificial Intelligence in Games #Combinatorics (math.CO) #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #cs.GT #math.CO #msc:91A46
paper · pdf · doi:10.48550/arxiv.1112.3610
60 pages, 21 figures
arxiv created 2011/12/15 · openalex publication_date 2011/12/15 · arxiv updated 2011/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the class of "well-tempered" integer-valued scoring games, which have the property that the parity of the length of the game is independent of the line of play. We consider disjunctive sums of these games, and develop a theory for them analogous to the standard theory of disjunctive sums of normal-play partizan games. We show that the monoid of well-tempered scoring games modulo indistinguishability is cancellative but not a group, and we describe its structure in terms of the group of normal-play partizan games. We also classify Boolean-valued well-tempered scoring games, showing that there are exactly seventy, up to equivalence.