Domineering | Topological Games

The players take turns linking pairs of dots on a grid. The first player unable to move loses.

History

The game was originally proposed by Göran Andersson, and was described by Martin Gardner as the game Crosscram in "Mathematical Games: Cram, Crosscram and Quadraphage: New Games having Elusive Winning Strategies." Scientific American 230, 106-108, Feb. 1974. It can also be played using dominoes to cover up squares on a checkerboard, hence the name Domineering by which it is now more generally known.
It is related to the less-interesting game Cram, in which each player can make either vertical or horizontal moves.
It was described and analysed in the book "On Numbers and Games" by John Horton Conway, Academic Press, 1976.

Description

The game is played on a matrix of dots.
The players take turns in linking a pair of adjacent dots. The first player, Blue, always makes a vertical link, and the other player, Red, always makes a horizontal link. No dot can be linked more than once.
The first player unable to move loses.

Example

In the following game Red is unable to move, and so loses:

Tags: Pencil and Paper games,topological games