2015/09/04 by Gabriel Renault, Renault, Gabriel
Computer Science · #Artificial Intelligence in Games #Computability, Logic, AI Algorithms #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Logic, programming, and type systems #cs.DM
paper · pdf · doi:10.48550/arxiv.1509.01576
arxiv created 2015/09/04 · openalex publication_date 2015/09/04 · arxiv updated 2015/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In normal version of combinatorial game theory, all games are invertible, whereas only the empty game is invertible in misère version. For this reason, several restricted universes were earlier considered for their study, in which more games are invertible. We here study combinatorial games in misère version, in particular universes where no player would like to pass their turn In these universes, we prove that having one extra condition makes all games become invertible. We then focus our attention on a specific quotient, called QZ, and show that all sums of universes whose quotient is QZ also have QZ as their quotient.