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Incidence structure for tic-tac-toe. The game can be generalized to an m,n,k-game, in which two players alternate placing stones of their own color on an m-by-n board with the goal of getting k of their own color in a row. Tic-tac-toe is the 3,3,3-game. [5] Harary's generalized tic-tac-toe is an even broader generalization of tic-tac-toe.
A complete game of Notakto, a misère variant of the game. 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]
3-D Tic-Tac-Toe played with glass beads. 3D tic-tac-toe, also known by the trade name Qubic, is an abstract strategy board game, generally for two players. It is similar in concept to traditional tic-tac-toe but is played in a cubical array of cells, usually 4×4×4. Players take turns placing their markers in blank cells in the array.
Each box had a code number, which was keyed into a chart. This chart had drawings of tic-tac-toe game grids with various configurations of X, O, and empty squares, [4] corresponding to all possible permutations a game could go through as it progressed. [11]
In game theory, a game tree is a directed graph whose nodes are positions in a game (e.g., the arrangement of the pieces in a board game) and whose edges are moves (e.g., to move pieces from one position on a board to another). [1] The complete game tree for a game is the game tree starting at the initial position and containing all possible ...
The game ends when all the boards contain a three-in-a-row of Xs, [4] [5] [6] at which point the player to have made the last move loses the game. [7] However, in this game, unlike tic-tac-toe, there will always be a player who wins any game of Notakto. [8] Notakto is an impartial game, where the allowable moves depend only on the state of the ...
Quantum tic-tac-toe is a "quantum generalization" of tic-tac-toe in which the players' moves are "superpositions" of plays in the classical game. The game was invented by Allan Goff of Novatia Labs , who describes it as "a way of introducing quantum physics without mathematics", and offering "a conceptual foundation for understanding the ...
The rating of best Go-playing programs on the KGS server since 2007. Since 2006, all the best programs use Monte Carlo tree search. [14]In 2006, inspired by these predecessors, [15] Rémi Coulom described the application of the Monte Carlo method to game-tree search and coined the name Monte Carlo tree search, [16] L. Kocsis and Cs.