Domineering

Domineering, also called Stop-Gate or Crosscram, is a mathematical abstract strategy game played on graph paper grids of any shape. Two players alternately place dominoes to cover two adjacent squares, with one player restricted to placing tiles vertically and the other horizontally; the first player unable to make a legal move loses. Because each player uses a different orientation, the game is partisan rather than impartial, distinguishing it from its impartial relative Cram, in which either player may place a domino in either orientation. Domineering can be played on standard square boards, rectangles, polyominoes, or combinations of these shapes, and involves no element of chance, resting entirely on strategic placement. It is played by two players and is studied in combinatorial game theory for its rich range of positions on differently shaped boards.