Tic Tac Toe


Arcade Games

Tic-Tac-Toe

Tic-tac-toe, also called noughts and crosses (in the British Commonwealth countries) and X’s and O’s in the Republic of Ireland, is a pencil-and-paper game for two players, X and O, who take turns marking the spaces in a 3×3 grid. The X player usually goes first. The player who succeeds in placing three respective marks in a horizontal, vertical, or diagonal row wins the game.
Without taking symmetries into account, the number of possible games can be determined by hand with an exact formula that leads to 255,168 possible games (see Henry Bottomley, 2001[4], or Steve Schaeffer, 2002[5]). Assuming that X makes the first move every time:

131,184 finished games are won by (X)
77,904 finished games are won by (O)
46,080 finished games are drawn

If board symmetries are taken into account, two games are considered the same if the sequence of board modulo the symmetries is the same. With the use of computer, Steve Schaeffer determined in 2002[5] that the number of games in these conditions is 26,830.

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