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Tuesday, November 14, 2006

Tic-Tac-Toe - Shall we Play a Game?

Tic-Tac-Toe, also called Noughts and Crosses, X’s and O’s, X-e O-zees, Boxin’ Oxen, Tickle My Tackle With Your Toe, Hugs and Kisses or many others is universally know by children and adults throughout the English speaking world.

The exact origin of Tic-Tac-Toe is unknown, but variations such as “Three Man’s Morris” were popular in England in the 1300’s.

The game is a simple pen and paper game for two players, O and X, who take turns to mark the spaces in a 3 x 3 grid. The first player who succeeds in connecting 3 marks in a row wins.

The simplicity of Tic-Tac-Toe makes it ideal for teaching concepts of combinational game theory and the branch of artificial intelligence that deals with the searching of game trees. It is fairly easy to write a computer program to play Tic-Tac-Toe perfectly, to incorporate the 765 essentially different positions (the state space complexity), or the 26,830 possible games (the game tree complexity) on this space. Ignoring symmetry, there are 255,168 possible games. Taking into account both rotational and mirroring symmetry, there are 31,896 possible unique games.

The first know computer game, OXO (or Noughts and Crosses) was written in 1951 with the EDSAC computer playing perfect games of Tic-Tac-Toe against human opponents.

The game remained the same, but computers progressed from 1951’s EDSAC compared to 1983’s WOPR in the cult movie War Games. Tic-Tac-Toe was utilized as an allegory for nuclear war when Matthew Broderick’s character makes the missile defense computer WOPR play against itself. As each game ends in a draw, WOPR makes the association between the two and declares that “The only winning move is not to play.”

You can challenge this computer and decide for yourself if it’s ok to play or not.

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