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Tic-tac-toe. Tic-tac-toe (American English), noughts and crosses (Commonwealth English), or Xs and Os (Canadian or Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid with X or O. The player who succeeds in placing three of their marks in a horizontal, vertical, or diagonal row is ...
Tic-tac-toe is an instance of an m,n,k-game, where two players alternate taking turns on an m × n board until one of them gets k in a row. [1] Harary's generalized tic-tac-toe is an even broader generalization. The game can also be generalized as a n d game. [2] The game can be generalised even further from the above variants by playing on an ...
Perfect play. In game theory, perfect play is the behavior or strategy of a player that leads to the best possible outcome for that player regardless of the response by the opponent. Perfect play for a game is known when the game is solved. [1] Based on the rules of a game, every possible final position can be evaluated (as a win, loss or draw).
Notakto is a tic-tac-toe variant, also known as neutral or impartial tic-tac-toe. [1][2] The game is a combination of the games tic-tac-toe and Nim, [1][3] played across one or several boards with both of the players playing the same piece (an "X" or cross). The game ends when all the boards contain a three-in-a-row of Xs, [4][5][6] at which ...
Ultimate tic-tac-toe (also known as super tic-tac-toe, meta tic-tac-toe or (tic-tac-toe)²[1]) is a board game composed of nine tic-tac-toe boards arranged in a 3 × 3 grid. [2][3] Players take turns playing on the smaller tic-tac-toe boards until one of them wins on the larger board. Compared to traditional tic-tac-toe, strategy in this game ...
Combinatorial Games: Tic-Tac-Toe Theory. Combinatorial Games: Tic-Tac-Toe Theory is a monograph on the mathematics of tic-tac-toe and other positional games, written by József Beck. It was published in 2008 by the Cambridge University Press as volume 114 of their Encyclopedia of Mathematics and its Applications book series ( ISBN 978-0-521 ...
Harary's generalized tic-tac-toe or animal tic-tac-toe is a generalization of the game tic-tac-toe, defining the game as a race to complete a particular polyomino on a square grid of varying size, rather than being limited to "in a row" constructions. It was devised by Frank Harary in March 1977, and is a broader definition than that of an m,n ...
The Matchbox Educable Noughts and Crosses Engine (sometimes called the Machine Educable Noughts and Crosses Engine or MENACE) was a mechanical computer made from 304 matchboxes designed and built by artificial intelligence researcher Donald Michie in 1961. It was designed to play human opponents in games of noughts and crosses (tic-tac-toe) by ...