Taming the wild in impartial combinatorial games
arXiv:math/0501315
Abstract
We introduce a misere quotient semigroup construction in impartial combinatorial game theory, and argue that it is the long-sought natural generalization of the normal-play Sprague-Grundy theory to misere play. Along the way, we illustrate how to use the theory to describe complete analyses of two wild taking and breaking games.
35 pages. Accepted by INTEGERS: The Electronic Journal of Combinatorial Number Theory. See also http://www.plambeck.org/oldhtml/mathematics/games/misere