Domineering (also called Stop-Gate or Crosscram) is a mathematical game that can be played on any collection of squares on a sheet of graph paper. For example, it can be played on a 6ÃÂ6 square, a rectangle, a polyomino, or a combination of any number of such components. Two players have a collection of dominoes which they place on the grid in turn, covering up squares. One player places tiles vertically, while the other places them horizontally. (Traditionally, these players are called "Left" and "Right", respectively, or "V" and "H". Both conventions are used in this article.) As in most games in combinatorial game theory, the first player who cannot move loses.
Domineering is a partisan game, in that players use different pieces: the impartial version of the game is Cram.
Other than the empty game, where there is no grid, the simplest game is a single box.
In both games, clearly, neither player can move. Since these are a second-player win, they are zero games.
This game is a 2-by-1 grid. There is a convention of assigning the game a positive number when Left is winning and a negative one when Right is winning. In this case, Left has no moves, while Right can play a domino to cover the entire board, leaving nothing, which is clearly a zero game. Thus in surreal number notation, this game is <nowiki>