Tic-tac-toe
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.This game is won by the first player, X:
This game is drawn:
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.
The first two [[ply
But the very 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's 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).
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Variations
Many games share the element of trying to be the first to get n-in-a-row: three men's morris, nine men's morris, pente, gomoku, Connect Four, Quarto. The m,n,k-games are a family of generalized games based on tic-tac-toe.
- 3-dimensional tic-tac-toe on a 3×3×3 board is no fun: the first player has an easy win by playing in the centre. But the game on the 4×4×4 board (called Qubic) is much more subtle. It was solved by Victor Allis in 1994 (the first player can force a win) but is still interesting for humans.
- In misère tic-tac-toe you win if the other player gets n in a row. The 3×3 game is a draw.
- In nine board tic-tac-toe nine tic-tac-toe boards are themselves arranged in a 3×3 grid. The first player's move may go on any board; all moves afterwards are placed in the empty spaces on the board corresponding to the square of the previous move (that is, if a move were in the upper-left square of a board, the next move would take place on the upper-left board). If a player can't move because the indicated board is full, the next move may go on any board. Victory is attained by getting 3 in a row on any board. This makes the game considerably longer and more involved than tic-tac-toe, with a definite opening, middle game and endgame.
Alternative names
- Tic-tac-toe, tick-tat-toe, or tit-tat-toe (English - USA)
- Noughts and crosses or naughts and crosses (English - Great Britain and Ireland)
- Ta-te-ti (Spanish)
- Tres en raya ("three in a line") (Spanish)
- Gato (Spanish)
- Morpion (French)
- Kaesekaestchen (Cheese Squares) (German)
- Boter, kaas en eieren ("butter, cheese and eggs") (Dutch)
- Amőba (Hungarian)
- Kryds og bolle (Danish)
- Tripp trapp trull (Swedish)
- Ristinolla (Finnish)
- X şi zero (Romanian)
- Jogo da velha (Portuguese - Brazil)
- Τρίλιζα (Greek)
- Zero kata (Hindi)
- Phool aur chaukadi (Hindi)
- Maru batsu (円伐, "circle attack") (Japanese)
- Sanme narabe (三目並べ, "row of three") (Japanese)
- Морски шах ("sea chess") (Bulgarian)