Games at Grenfell:

Mini Workshop on "Misere Placement Games"

September 20-21, September 2014, Sir Wilfred Grenfell College.

Contact: Rebecca Milley or Richard Nowakowski for more details.

A combinatorial game is a two-player game of perfect information and no chance. Under normal play, whoever gets the last move wins, while under misere play, whoever gets the last move loses. There is a large body of knowledge for normal-play games; the structure underlying these games is intricate and elegant, with notions of addition, negation, and equality. When the ending condition is changed to misere, however, most of this structure falls apart. For example, the negative of a game is no longer its additive inverse, and so a game G satisfies the unsettling equation G − G ≠ 0. Most of the intuition from normal-play theory is also lost in misere games. For these and other reasons, misere play has been much less studied than normal play.

Placement games can be informally defined as games in which players take turns placing pieces on a board. Such games have much stricter structure than general games and so are excellent candidates for misere analysis. One property of a placement game is that a player who currently has no legal move will never again be able to move; this is the property we have termed dead- ending, and the set of dead-ending games has proven to be rich in interesting results for misere play. As a subset of dead-ending games, placement games should be even more open to misere analysis; as a broad and naturally-occurring subset of games, this analysis would be a significant contribution to misere game theory.

The objectives of the mini workshop are to work towards a useful definition of placement games, to explore solutions to specific examples of placement games, and to generate results for placement games in general.