Project CEMAPRE internal
| Title | Mixture of winning conditions in combinatorial games |
| Participants | Tomoaki Abuku, Alda Carvalho (Principal Investigator), Richard J Nowakowski, Carlos P Santos, Koki Suetsugu |
| Summary | In combinatorial game theory, the two most commonly studied winning conventions are the normal play convention and the misère play convention. Under the former, the player who has no available moves on their turn loses; under the latter, the opposite holds — the player with no available moves wins. Numerous take-away games (pile games) have been analyzed in the specialized literature, with NIM and WYTHOFF NIM being the most paradigmatic examples. It is entirely natural to consider a mixture of these conventions. For instance, there may be piles of blue stones and piles of red stones. If the final move is made on one of the former, the player who makes that last move wins; if the final move is made on one of the latter, the player who makes that last move loses. The mathematics of such mixtures is surprisingly rich and sophisticated to analyze, both in terms of outcomes, periodicity, and algebraic structure in general. There are also connections with ancient games, notably the Japanese game GOISHI HIROI. |