Tic Tac Toe

It is straightforward to write a computer program to play tic-tac-toe perfectly or to enumerate the 765 essentially different positions (the state space complexity) or the 26,830 possible games up to rotations and reflections (the game tree complexity) on this space.[1] If played optimally by both players, the game always ends in a draw, making tic-tac-toe a futile game.[2]



The game can be generalized to an m,n,k-game in which two players alternate placing stones of their own color on an m×n board, with the goal of getting k of their own color in a row. Tic-tac-toe is the (3,3,3)-game.[3] Harary's generalized tic-tac-toe is an even broader generalization of tic-tac-toe. It can also be generalized as a nd game. Tic-tac-toe is the game where n equals 3 and d equals 2.[4] It can be generalised even further by playing on an arbitrary incidence structure, where rows are lines and cells are points. Tic-tac-toe is the game given by the incidence structure shown to the right, consisting of nine points, three horizontal lines, three vertical lines, and two diagonal lines, each line consisting of at least three points.