Domineering, also known as Crosscram
, is a two player, turn-based
, perfect information game. It is played on a grid
of squares which can be of any shape and size, but is most commonly played in competitive situations
on an 8x8 board (like a chessboard
The two players are hoRizontal and verticaL. On a square board, that doesn't matter, but on boards of other shapes, orientation is vital. At the beginning of the game, the winner of a coin toss decides either between R and L or between playing first or second.
Play proceeds as follows: on R's turn, R must place a "domino" horizontally on the board so as to cover two horizontally adjacent squares. Similarly, L must place a vertically oriented domino on the board on her turn. Once a square has been covered by a domino, it is no longer available for play, so the game is strictly reductive.
When the player whose turn it is cannot play, the game is over and that player has lost.
There are many particularities and points of mathematical interest that students of Domineering have discovered. For example, the winner of a domineering game on a board of any width and height up to five is known, with the exception of 4x19 and 4x21 boards. Solutions for square boards are known up to 9x9. Plenty is known about play on sums of boards; boards can be given numerical (or near-numerical) values according to combinatoric rules and then added to determine the winner on two or more disjoint boards.
Depending on who you ask, Domineering was invented by Goran Andersson in 1973 or has been around since at least the 1950s.