Unbounded Tic-Tac-Toe 1.1
Unbounded Tic-Tac-Toe is an implementation of a popular game.
The goal of Unbounded Tic-Tac-Toe is to get five marks in a row, either horizontally, vertically, or diagonally. The twist is that the board is infinite.
The computer plays the opponent.
Tic-tac-toe, also called noughts and crosses and many other names, is a paper and pencil game between two players, O and X, who alternate in marking the spaces in a 3×3 board. A player wins by getting three of their own marks in a horizontal, vertical or diagonal row.
Players soon discover that best play leads to a draw, regardless of where the first player plays. So tic-tac-toe is most often played by very young children; when they have discovered an unbeatable strategy they move on to more sophisticated games such as dots and boxes.
This reputation for ease has led to Las Vegas casinos offering gamblers the chance to play tic-tac-toe against trained chickens.
The first two ply of the game tree for tic-tac-toe.
Enlarge The first two ply of the game tree for tic-tac-toe.
The simplicity of tic-tac-toe makes it ideal as a pedagogical tool for teaching the concepts of game theory and the branch of artificial intelligence that deals with the searching of game trees.
It is straightforward to write a computer program to play tic-tac-toe perfectly, to enumerate the 765 essentially different positions (the state space complexity), or the 26,830 possible games (the game tree complexity) on this space.
Ignoring symmetry, there are 255,168 possible games.
The first known computer game, OXO (or Noughts and Crosses, 1952) for the EDSAC computer played perfect games of tic-tac-toe against a human opponent.