Dots and Boxes

Dots and boxes is a pencil-and-paper territory game for two players, played on a grid of dots, in which players take turns drawing a single line between two adjacent dots, and a player who completes the fourth side of a box claims that box and takes an extra turn, with the game ending when the grid is full and the player who claimed the most boxes winning. The game was described and analyzed by the French mathematician Edouard Lucas in the late nineteenth century, under whose name it is sometimes still known, and it remains a common introductory example in combinatorial game theory because of the surprising depth of strategy hidden in its simple rules.