Dots and Boxes

Dots and boxes is a paper and pencil game for two players.
The game is first published in 1889 by mathematician Édouard Lucas.
Starting with an empty grid of dots, players take turns, adding a single horizontal or vertical line between two unjoined adjacent dots.
A player who completes the fourth side of a 1×1 box initials that box and adds another line.
In standart play, a player who can complete a box is not obliged to do so. In a variant of the game, however, this obligation is imposed.
The game ends when all boxes have been completed.
Whoever has initialed more boxes is declared the winner.
The board may be of any size, typically between 2×2 and 5x5.
The diagram above shows a game played on the 2×2 board, where player A wins against player B, 3-1.
An online version of the game is available here.
If you are keen on diving deeper into mathematics and winning strategies of the game, then check out Elwyn Berlekamp’s book below.