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 6×6 square, a rectangle, an entirely irregular 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.

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.

This is a 2×3 grid, which is even more complex, but, just like any Domineering game, it can be broken down by looking at what the various moves for Left and Right are.

Our 2×3 grid, then, is {2|−1⁄2}, which can also be represented by the mean value, 3⁄4, together with the bonus for moving (the "temperature"), 1+1⁄4, thus:

The Mathematical Sciences Research Institute held a Domineering tournament with a $500 prize for the winner.

The winner was mathematician Dan Calistrate, who defeated David Wolfe in the final.

In 2000, Dennis Breuker, Jos Uiterwijk and Jaap van den Herik computed and published the solution for the 8x8 board.

Then, in 2002, Nathan Bullock solved the 10x10 board, as part of his thesis on Domineering.

Some other known values for rectangular boards can be found on the site of Nathan Bullock.

The only difference in the rules is that each player may place their dominoes in either orientation.

It seems only a small variation in the rules, but it results in a completely different game that can be analyzed with the Sprague–Grundy theorem.