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An edge opening must be answered either with a center mark, a corner mark next to the X, or an edge mark opposite the X.

A combinatorics study of the game shows that when "X" makes the first move every time, the game is won as follows: All-pay auction Alpha—beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition First-move advantage in chess Game mechanics Glossary of game theory List of game theorists List of games in game theory No-win situation Solving chess Topological ceoss Tragedy of the commons Tyranny of small decisions.

Views Read Edit View history. For strategy purposes, there are therefore only three possible first marks: Then this game will be a draw, X cannot win. A teaching metaphor for superposition in quantum mechanics".

This section does not cite any sources.

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However, by rotating the board, we will find that in the first turn, every corner mark is strategically equivalent to every other corner mark.

Retrieved December 17, American Journal of Physics. The same is true of every edge side middle mark. Tic-tac-toe Abstract strategy games Mathematical games Paper-and-pencil games Solved games. Hence, tic-tac-toe is most often played by young children.

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The Theory of Gambling and Statistical Logic. Unsourced material may be challenged and removed. The different names of the game are more recent.

This section needs additional citations for verification. How to never lose at Tic-Tac-Toe.

The second player, who shall be designated "O", must respond to X's opening mark in such a way crosss to avoid the forced win. In fact, taking 9 is the best move, since a non-perfect player X may take 4, then O can take 7 to win.

## Tic-Tac-Toe

Harary's generalized tic-tac-toe is an even broader generalization. Although O takes the only good position 5 as first move, crose O takes a bad position as second move:. August Learn how and when to remove this template message.

A player can play a perfect game of tic-tac-toe to win or at least, draw if each time it is his ezro to play, he chooses the first available move from the following list, as used in Newell and Simon's tic-tac-toe program.

An Isomorph of Tic-Tac-Toe".

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Archived from the original on August 24, It is straightforward to write a computer program to play tic-tac-toe perfectly or to enumerate the essentially different positions the state space complexity or the 26, possible games up to rotations and reflections the game tree complexity on this space.

Arrow's impossibility theorem Aumann's agreement theorem Folk theorem Minimax theorem Nash's theorem Purification theorem Revelation principle Zermelo's theorem.

Tic-tac-toe is the game where n equals 3 and d equals 2. Pages using deprecated image syntax Articles needing additional references from August All articles needing additional references Articles needing additional references from May Tic-Tac-Toe as a Magic Square". The Tinkertoy computer, made out of almost only Tinkertoys, is able to play tic-tac-toe perfectly.

Any other responses will allow X to force the win.

Intic-tac-toe was also used by MIT students to demonstrate the computational power of Tinkertoy elements. University of Chicago Press.

The properties turns out, what that

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