Tic-tac-toe

Tic-Tac-Toe, also called Noughts and Crosses, is a classic game between two players, "O" and "X", who alternate in marking the spaces in a 3×3 board, trying to put three of their own marks in a horizontal, vertical or diagonal row.

For instance, the following game was won by the first player, "X":

 | |X   O| |X   O| |X   O| |X   O| |X   O| |X   O| |X
-+-+-   -+-+-   -+-+-   -+-+-   -+-+-   -+-+-   -+-+-
 | |     | |     | |     |O|     |O|     |O|O    |O|O
-+-+-   -+-+-   -+-+-   -+-+-   -+-+-   -+-+-   -+-+-
 | |     | |    X| |    X| |    X| |X   X| |X   X|X|X

The following game was won by the first player, "O":

 | |     |X|    O|X|    O|X|    O|X|    O|X|    O|X|
-+-+-   -+-+-   -+-+-   -+-+-   -+-+-   -+-+-   -+-+-
 |O|     |O|     |O|     |O|    O|O|    O|O|    O|O|O
-+-+-   -+-+-   -+-+-   -+-+-   -+-+-   -+-+-   -+-+-
 | |     | |     | |     | |X    | |X   X| |X   X| |X

In a normal 3×3 tic-tac-toe game, both players have a strategy to draw the game. In fact, any move by the first player leads to a draw with best play.

The corner opening has the disadvantage that the centre defense is well-known, and in many of the lines that follow, there is only one obvious move by respondant which doesn't lead to immediate defeat. Thus such games are easily drawn.

A better strategy might be to open on an edge. In this case, there are four responses with which the responder can force a draw - centre, opposite edge, or either adjacent corner. The play which follows is often subtler, with scope for either player to set traps for the other.

Variations

There are some variations: 4×4, N×N, 3D tic-tac-toe, 9-board tic-tac-toe and inverse tic-tac-toe. There are several games with an element of being the first to get n-in-a-row: Nine Men's Morris and relatives, Pente, Gomoku, Connect Four, and Score Four. See mnk-games for a family of such games.

A variant played in Argentina (and probably other countries too) is one in which both players have 3 pieces of different colors and a board with 9 places connected by horizontal and diagonal lines. Pieces are put on the board in turns. After the 3 pieces are put, the players can move them along the lines in the board. The one who has 3 in line wins. A winning strategy exists for the first player. He plays the first piece in the center. The opponent plays in any other place. The first player then puts a piece in the nearest place to the place opposite to where the second player has put her piece.

In 3D tic-tac-toe, when played on a 3×3×3 and 4×4×4 board, the first player can force a win.

On a 3×3×3 board it is relatively trivial to win, the first move should be in the centre, the third move should form a link of two in such a way that a blocking move will not allow the opponent to create two in a row, now a forking move will be possible such that on the players next move there will be two places they can go to win. The opponent will be able to block only one of these and thus the first player can take the other and win the game. The same applies for any number of dimensions (i.e 3×3×3×3, 3×3×3×3×3, etc).

The 4×4×4 board game has been solved. Victor Allis showed in 1994 that there are 76 different possible winning lines.

An interesting variant is inverse tic-tac-toe, in which each player tries to force the other to get N in a row.

Another interesting variant is 9 board tic-tac-toe. The nine boards are themselves arranged like a tic-tac-toe board. 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) - should all nine squares get taken on a board and the last square taken points to the full board(unlikely), the next move may go on any board. Victory is attained by winning 3 in a row on any board. This makes the game considerably longer and more involved, with a definite beginning, middle and endgame.

An interesting extension of this idea is the commercial game Quarto which is played on a 4×4 board. There are 16 pieces each with four aspects:

Height: short or tall
Color: dark or light
Cross-section: round or square
Texture: smooth or grooved

Play proceeds in turn by choosing a piece and handing it to the opponent. The opponent plays the piece. If the play results in four pieces which all share the value of one of the attributes, the person who plays the piece wins.