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Tic-tac-toe, also called noughts and crosses, hugs and kisses, and many other names, is a pencil-and-paper game for two players, O and X, who take turns marking the spaces in a 3×3 grid. The player who succeeds in placing three respective marks in a horizontal, vertical or diagonal row wins the game. This game is won by the first player, X This is a "cat's game", that is, a draw Players soon discover that best play from both parties leads to a draw. Hence, tic-tac-toe is most often played by very young children; when they have discovered an unbeatable strategy they move on to more sophisticated games such as dots and boxes. This reputation for ease has led to casinos offering gamblers the chance to play tic-tac-toe against trained chickens. The simplicity of tic-tac-toe makes it ideal as a pedagogical tool for teaching the concepts of combinatorial game theory 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.
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