Winning the game: Due to the rules of ultimate tic-tac-toe, the global board is never directly affected. This makes the game tree difficult to visualize, possibly leaving many possible paths overlooked. Future board positions are no longer interchangeable, each move leading to starkly different possible future positions. Each move determines the next move, and therefore reading ahead-predicting future moves-follows a much less linear path. Visualizing the game tree: Visualizing future branches of the game tree is more difficult than single board tic-tac-toe. Therefore, players are forced to consider the larger game board instead of simply focusing on the local board. This might make moves that may be considered bad in normal tic-tac-toe viable, since the opponent is sent to another local board, and may be unable to immediately respond to them. Even though every move must be played in a local board, equivalent to a normal tic-tac-toe board, each move must take into account the global board in several ways:Īnticipating the next move: Each move played in a local board determines where the opponent's next move may be played. This is because of the complicated game branching in this game. Ultimate tic-tac-toe is significantly more complex than most other variations of tic-tac-toe, as there is no clear strategy to playing. The most recent move was O playing in the middle-left square of the top-middle grid, forcing X to play their next move in the middle-left grid. The board of an incomplete ultimate tic-tac-toe game (the large "X"s and "O"s representing local board games which have been won by that player). Game play ends when either a player wins the global board or there are no legal moves remaining, in which case the game is a draw. If a player is sent to such a board, then that player may play in any other board. Once the outcome of a local board is decided (win or draw), no more moves may be played in that board. If a move is played so that it is to win a local board by the rules of normal tic-tac-toe, then the entire local board is marked as a victory for the player in the global board. O can then play in any one of the nine available spots in that local board, each move sending X to a different local board. For example, if X played in the top right square of their local board, then O needs to play next in the local board at the top right of the global board. This move 'sends' their opponent to its relative location. The game starts with X playing wherever they want in any of the 81 empty spots. Compared to traditional tic-tac-toe, strategy in this game is conceptually more difficult, and has proven more challenging for computers.Įach small 3-by-3 tic-tac-toe board is referred to as a local board, and the larger 3-by-3 board is referred to as the global board. Players take turns playing in the smaller tic-tac-toe boards until one of them wins in the larger tic-tac-toe board. Ultimate tic-tac-toe also known as super tic-tac-toe, strategic tic-tac-toe, meta tic-tac-toe, or tic-tac-tic-tac-toe-toe is a board game composed of nine tic-tac-toe boards arranged in a 3-by-3 grid. If played properly, the game will end in a draw, making tic-tac-toe a futile game. Tic-tac-toe is the game where n equals 3 and d equals 2. Harary's generalized tic-tac-toe is an even broader generalization of 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×n board, with the goal of getting k of their own color in a row. It is straightforward to write a computer program to play tic-tac-toe perfectly or 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. Hence, tic-tac-toe is most often played by young children.īecause of the simplicity of tic-tac-toe, it is often used as a pedagogical tool for teaching the concepts of good sportsmanship and the branch of artificial intelligence that deals with the searching of game trees. Players soon discover that the best play from both parties leads to a draw. The following example game is won by the first player, X: The player who succeeds in placing three of their marks in a horizontal, vertical, or diagonal row wins the game. Tic-tac-toe (also known as noughts and crosses or Xs and Os) is a paper-and-pencil game for two players, X and O, who take turns marking the spaces in a 3×3 grid. Chapter 1 Overall overview 1.1 Tic-Tac-Toe
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