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Tic-tac-toe A completed game of tic-tac-toe Other names Noughts and Crosses Xs and Os Genres Paper-and-pencil game Players 2 Setup time Minimal Playing time ~1 minute Chance None Skills Strategy, tactics, observation 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 ...
The first two plies of the game tree for tic-tac-toe. The diagram shows the first two levels, or plies, in the game tree for tic-tac-toe. The rotations and reflections of positions are equivalent, so the first player has three choices of move: in the center, at the edge, or in the corner.
Tic tac toe is a classic game. How to win tic tac toe requires strategic thinking and planning to win the game or force a draw. When you’re the first one up, there is a simple strategy on how to ...
The game tree size is the total number of possible games that can be played. This is the number of leaf nodes in the game tree rooted at the game's initial position.. The game tree is typically vastly larger than the state-space because the same positions can occur in many games by making moves in a different order (for example, in a tic-tac-toe game with two X and one O on the board, this ...
Diagram showing optimal strategy for tic-tac-toe.With perfect play, and from any initial move, both players can always force a draw. In combinatorial game theory, a two-player deterministic perfect information turn-based game is a first-player-win if with perfect play the first player to move can always force a win.
In wild tic-tac-toe, players can choose to place either an X or O on each move. [7] [39] [40] [41] It can be played as a normal game where the player who makes three in a row wins or a misere game where they would lose. [7] This game is also called your-choice tic-tac-toe [42] or Devil's tic-tac-toe. [citation needed]
One game in which the backward induction solution is well known is tic-tac-toe. Reinhard Selten proved that any game which can be broken into "sub-games" containing a sub-set of all the available choices in the main game will have a subgame perfect Nash Equilibrium strategy (possibly as a mixed strategy giving non-deterministic sub-game decisions).
The classic example of a positional game is tic-tac-toe. In it, X {\displaystyle X} contains the 9 squares of the game-board, F {\displaystyle {\mathcal {F}}} contains the 8 lines that determine a victory (3 horizontal, 3 vertical and 2 diagonal), and the winning criterion is: the first player who holds an entire winning-set wins.