14 research outputs found
The Secrets of Notakto: Winning at X-only Tic-Tac-Toe
We analyze misere play of impartial tic-tac-toe---a game suggested by Bob
Koca in which both players make X's on the board, and the first player to
complete three-in-a-row loses. This game was recently discussed on
mathoverflow.net in a thread created by Timothy Y. Chow
Misère quotients for impartial games
AbstractWe announce misère-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misère quotients—commutative monoids that encode the additive structure of specific misère-play games. We also introduce several advances in the structure theory of misère quotients, including a connection between the combinatorial structure of normal and misère play