Cram (game)

Cram is a two-player mathematical game played on a grid, in which the players take turns placing dominoes on empty squares until no domino can be placed; the player unable to move loses under normal play rules, or wins under the misere variant. It is the impartial version of the game Domineering, distinguished by allowing either player to place a domino in either orientation, horizontal or vertical, rather than restricting each player to one orientation. Boards can be rectangular grids of various sizes, irregular polygons, or even cylindrical shapes, and the game has also circulated under names such as plugg and dots-and-pairs. Mathematician and writer Martin Gardner popularized the game for a wide audience through his Mathematical Games column in Scientific American. Because Cram is an impartial game, symmetry strategy determines many outcomes: the second player can guarantee a win on boards with even dimensions on both sides by mirroring the first player's moves, while the first player can win on boards with one even and one odd dimension by opening in the center and then mirroring.