domineering

Domineering is a two-player abstract strategy game played on a rectangular grid, typically m by n squares. The board starts empty and each square can be covered only once. One player, often called Left, places dominoes vertically; the other player, Right, places dominoes horizontally. Each move places a single 1-by-2 domino entirely within the board and over unoccupied squares. Once placed, a domino cannot be moved or removed.

The objective is simple: on your turn you must place a domino according to your orientation, and the player who makes the last legal move wins. If a player has no legal move on their turn, they lose under normal play. Because the two players have different allowed moves, Domineering is a partisan game rather than an impartial one.

Domineering is a classic object of study in combinatorial game theory. Positions are analyzed by considering the available left and right options, and some positions can be assigned CGT values. The outcomes depend on board size and shape, and researchers have determined results for many rectangular boards while other configurations remain more complex. The game is often used to illustrate how tiling constraints interact with player-specific moves and how game trees can grow quickly.

Variations include boards of different dimensions, boards with holes or missing squares, and alternative starting conditions or rules (such as misère play in some variants). The basic form, however, remains a test of spatial reasoning and strategic planning, highlighting the differences between the two players’ move sets and the influence of geometry on optimal play.