Variations 📈

Many board games share the element of trying to be the first to get n-in-a-row, including three men's morris, nine men's morris, pente, gomoku, Qubic, Connect Four, Quarto, Gobblet, Order and Chaos, Toss Across, and Mojo. 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. 

Harary's generalized tic-tac-toe is an even broader generalization. The game can be generalised even further by playing on an arbitrary hypergraph, where rows are hyperedges and cells are vertices.

Other variations of tic-tac-toe include:

• 3-dimensional tic-tac-toe on a 3×3×3 board. In this game, the first player has an easy win by playing in the centre if 2 people are playing.

One can play on a board of 4x4 squares, winning in several ways. Winning can include: 4 in a straight line, 4 in a diagonal line, 4 in a diamond, or 4 to make a square.

Another variant, Qubic, is played on a 4×4×4 board; it was solved by Oren Patashnik in 1980 (the first player can force a win). Higher dimensional variations are also possible.

• In misère tic-tac-toe, the player wins if the opponent gets n in a row. A 3×3 game is a draw. More generally, the first player can draw or win on any board (of any dimension) whose side length is odd, by playing first in the central cell and then mirroring the opponent's moves.

• In "wild" tic-tac-toe, players can choose to place either X or O on each move.

• Number Scrabble or Pick15 is isomorphic to tic-tac-toe but on the surface appears completely different. Two players in turn say a number between one and nine. A particular number may not be repeated. The game is won by the player who has said three numbers whose sum is 15. If all the numbers are used and no one gets three numbers that add up to 15 then the game is a draw. Plotting these numbers on a 3×3 magic square shows that the game exactly corresponds with tic-tac-toe, since three numbers will be arranged in a straight line if and only if they total 15.

• Another isomorphic game uses a list of nine carefully chosen words, for instance "try", "be", "on", "any", "boat", "or", "mare", "by", and "ten". Each player picks one word in turn and to win, a player must select three words with the same letter. The words may be plotted on a tic-tac-toe grid in such a way that a three-in-a-row line wins.

• Numerical Tic Tac Toe is a variation invented by the mathematician Ronald Graham. The numbers 1 to 9 are used in this game. The first player plays with the odd numbers, the second player plays with the even numbers. All numbers can be used only once. The player who puts down 15 points in a line wins (sum of 3 numbers).

• In the 1970s, there was a two player game made by Tri-ang Toys & Games called Check Lines, in which the board consisted of eleven holes arranged in a geometrical pattern of twelve straight lines each containing three of the holes. Each player had exactly five tokens and played in turn placing one token in any of the holes. The winner was the first player whose tokens were arranged in two lines of three (which by definition were intersecting lines). If neither player had won by the tenth turn, subsequent turns consisted of moving one of one's own tokens to the remaining empty hole, with the constraint that this move could only be from an adjacent hole.

• There is also a variant of the game with the classic 3×3 field, in which it is necessary to make two rows to win, while the opposing algorithm only needs one.

• Quantum tic tac toe allows players to place a quantum superposition of numbers on the board, i.e. the players' moves are "superpositions" of plays in the original classical game. This variation was invented by Allan Goff of Novatia Labs.