An alternating grid-removal game in which choosing an occupied cell removes it and every occupied cell above and to its right. The player who removes the designated lower-left poison cell loses. Reachable occupied-cell sets are order ideals for coordinatewise order. A nonempty reachable position always contains the poison cell, and removing that cell empties the board. The monotone boundary representation of a grid order ideal supports compact board updates.
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Combinatorial game theory is a branch of mathematics and theoretical computer science that studies games with perfect information, where two players take turns making moves and there is no element of chance. It focuses on two-player games that are typically played to a conclusion, meaning that the game ends in a win, loss, or draw. Examples of such games include chess, Go, Nim, and various other abstract and strategic games.