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Tic-tac-toe variants
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Tic-tac-toe variants
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 also be generalized as a nd game. The game can be generalised even further from the above variants by playing on an arbitrary hypergraph where rows are hyperedges and cells are vertices.
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.
Variants of tic-tac-toe date back several millennia.
An early variation of tic-tac-toe was played in the Roman Empire, around the first century BC. It was called Terni Lapilli and instead of having any number of pieces, each player only had three; thus, they had to move them around to empty spaces to keep playing. The game's grid markings have been found chalked all over Rome. However, according to Claudia Zaslavsky's book Tic Tac Toe: And Other Three-In-A Row Games from Ancient Egypt to the Modern Computer, Tic-tac-toe could be traced back to ancient Egypt. Another closely related ancient game is three men's morris, which is also played on a simple grid and requires three pieces in a row to finish.
Three-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 two people are playing.
One can play on a board of 4×4 squares, winning in several ways. Winning can include: four in a straight line, four in a diagonal line, four in a diamond, or four 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.
The 3D tic tac toe variant does not always appear as 3 dimensional board. Some variants have different forms. For example in the case of Gobblet-like variant, Gobblet Gobblers and Otrio, the third element appears as variation in marker sizes (small, medium, large). Players can 'steal' the opponent spot by placing larger marker at the top of the opponent smaller marker or just simply competing with overlapping spot.
In misère tic-tac-toe, the player wins if the opponent gets n in a row. This game is also known as avoidance tic tac toe, toe-tac-tic, inverse tic tac toe, or reverse tic tac toe. A 3×3 game is a draw. More generally, the first player can draw or win the -in-a-row game on an board (of any dimension), when is odd, by playing first in the central cell and then mirroring the opponent's moves across the central cell. This mirroring strategy prevents the creation of any line through the center, and any other line would be created by the second player before it is mirrored by the first player.
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Tic-tac-toe variants
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 also be generalized as a nd game. The game can be generalised even further from the above variants by playing on an arbitrary hypergraph where rows are hyperedges and cells are vertices.
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.
Variants of tic-tac-toe date back several millennia.
An early variation of tic-tac-toe was played in the Roman Empire, around the first century BC. It was called Terni Lapilli and instead of having any number of pieces, each player only had three; thus, they had to move them around to empty spaces to keep playing. The game's grid markings have been found chalked all over Rome. However, according to Claudia Zaslavsky's book Tic Tac Toe: And Other Three-In-A Row Games from Ancient Egypt to the Modern Computer, Tic-tac-toe could be traced back to ancient Egypt. Another closely related ancient game is three men's morris, which is also played on a simple grid and requires three pieces in a row to finish.
Three-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 two people are playing.
One can play on a board of 4×4 squares, winning in several ways. Winning can include: four in a straight line, four in a diagonal line, four in a diamond, or four 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.
The 3D tic tac toe variant does not always appear as 3 dimensional board. Some variants have different forms. For example in the case of Gobblet-like variant, Gobblet Gobblers and Otrio, the third element appears as variation in marker sizes (small, medium, large). Players can 'steal' the opponent spot by placing larger marker at the top of the opponent smaller marker or just simply competing with overlapping spot.
In misère tic-tac-toe, the player wins if the opponent gets n in a row. This game is also known as avoidance tic tac toe, toe-tac-tic, inverse tic tac toe, or reverse tic tac toe. A 3×3 game is a draw. More generally, the first player can draw or win the -in-a-row game on an board (of any dimension), when is odd, by playing first in the central cell and then mirroring the opponent's moves across the central cell. This mirroring strategy prevents the creation of any line through the center, and any other line would be created by the second player before it is mirrored by the first player.
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