The Misère Monoid of One-Handed Alternating Games
Rebecca Milley, Richard J. Nowakowski, Paul Ottaway · Zenodo (CERN European Organization for Nuclear Research) · 2012
Mis`ere games are notoriously more difficult to analyze than their normal-play counterparts. To deal with the inherent lack of structure, Plambeck (2005) considered restricted universes of games and developed the concept of indistinguishability, modulo a given universe; the resulting quotient semi-group is called the mis`ere monoid. Results for only three general universes are known. We introduce a fourth: the universe of alternating games and their sums. We find that the mis`ere monoid of one-handed alternating games is isomorphic to (Z, +).