Domineering

20x20square

20x20square

20x20square

20x20square

20x20square

Domineering is a strategy game played on a chessboard. It is a two-player game with the players taking turns to place their respective pieces on the board. One player controls the vertical moves (placing pieces vertically), and the other controls the horizontal moves (placing pieces horizontally). The game is also known by other names such as "Crosscram" and "Stopgate".

Gameplay

The game begins with an empty chessboard or a grid of squares. The two players decide who controls the vertical moves and who controls the horizontal moves. The player controlling the vertical moves places a domino vertically on two empty adjacent squares, and the player controlling the horizontal moves places a domino horizontally on two empty adjacent squares. The players alternate turns, each placing a domino on the board in their respective orientations.

The objective of the game is to block the opponent from being able to make a legal move. The game ends when one player cannot place a domino on the board due to lack of space or being blocked by the other player's dominos. The player who makes the last move is the winner, as they have effectively blocked their opponent from making a move.

Strategy

The strategy in Domineering involves planning ahead and trying to control more space on the board while limiting the opponent's options. Players must balance between aggressive moves to limit the opponent's space and defensive positioning to avoid being blocked themselves. Advanced strategies may involve sacrifice moves, where a player intentionally allows the opponent to block part of their territory to gain a strategic advantage elsewhere on the board.

Variants

Domineering can be played on different sizes of boards, from the standard 8x8 chessboard to larger or smaller grids. The game can also be modified by changing the shape of the board or adding obstacles, which can create new strategic challenges and opportunities.

Mathematical Aspects

Domineering has been studied in the field of combinatorial game theory, where it is analyzed in terms of winning strategies and mathematical properties. The game is a part of a larger family of games known as "blocking games," where the objective is to limit the opponent's moves. Researchers in combinatorial game theory have explored the concept of "strategy stealing," where one player can always guarantee at least a draw by mirroring the opponent's moves, and how it applies to Domineering.

Cultural Impact

While not as widely recognized as games like chess or checkers, Domineering has a niche following among board game enthusiasts and mathematicians interested in game theory. It is often used as a teaching tool in mathematics and computer science to illustrate concepts in combinatorial game theory and algorithmic thinking.