Noughts and Crosses

Tic-tac-toe

A completed game of Tic-tac-toe
Genre(s)	Paper-and-pencil game
Players	2
Setup time	Minimal
Playing time	~1 minute
Random chance	None
Skill(s) required	Strategy, tactics, observation
Synonym(s)	Noughts and crosses Xs and Os

Tic-tac-toe (also known as noughts and crosses or Xs and Os) is a paper-and-pencil game for two players, X and O, who take turns marking the spaces in a 3×3 grid. The player who succeeds in placing three of their marks in a horizontal, vertical, or diagonal row wins the game.

The following example game is won by the first player, X:

Players soon discover that best play from both parties leads to a draw. Hence, Tic-tac-toe is most often played by young children.

Because of the simplicity of tic-tac-toe, it is often used as a pedagogical tool for teaching the concepts of good sportsmanship and the branch of artificial intelligence that deals with the searching of game trees. It is straightforward to write a computer program to play tic-tac-toe perfectly, 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.

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.Harary's generalized tic-tac-toe is an even broader generalization of tic tac toe. It can also be generalized as a n^d game. Tic-tac-toe is the game where n equals 3 and d equals 2.

An early variation of tic-tac-toe was played in the Roman Empire, around the first century BC. It was called Terni Lapilli and instead of having any number of pieces, each player only had three, thus they had to move them around to empty spaces to keep playing. The game's grid markings have been found chalked all over Rome. However, according to Claudia Zaslavsky's book Tic Tac Toe: And Other Three-In-A Row Games from Ancient Egypt to the Modern Computer, Tic-tac-toe could be traced back to ancient Egypt. Another closely related ancient game is Three Men's Morris which is also played on a simple grid and requires three pieces in a row to finish.