Inverse Tic-Tac-Toe and Other Variants

Some historians believe that Tic-Tac-Toe dates back to the Roman Empire. Others place it further back, to ancient Egypt. But the real problem lies in the modern version of Tic-Tac-Toe: It is predictable and boring. With the right moves, it is impossible to lose. That indicates a fundamental flaw in Tic-Tac-Toe, and the only way to correct it is to modify its rules, creating completely new variants.

The WOPR supercomputer already said it at the time: The best move is not to play. That same conclusion is reached by Tic-Tac-Toe once we have enough experience. Maybe we lost a game or two as children, but with such basic and limited rules, the only optimal solution is to force a draw again, and again, and again, and again, and again… or ignore the game altogether.

Now, what is the underlying problem in Tic-Tac-Toe? Mathematician Thane Plambeck explains it simply in an old Numberphile video: The inevitability of the draw is what breaks the game. Therefore, any attempt to fix it must eliminate the draw as a valid option. How to achieve this? A logical leap would be to expand the Tic-Tac-Toe board to 4x4, 5x5, or larger. Another possibility is to add a third dimension, although the 3x3x3 configuration guarantees the first player's victory (in a two-player game) if they take the center position.

However, there is a much more interesting path, known as Inverse Tic-Tac-Toe or "misère". What's different? First, whoever places three in a row loses. Second, there is an impartial variant in which both players can only play with X. Even so, it is not a complete solution: All the first player has to do to win under those conditions is take the center position and mirror the opponent's moves (normal misère), or respond following an L pattern if it is impartial misère (like the knight in chess).

Plambeck's proposal… is Notakto. What makes it special? The basic rules of Notakto are identical to impartial misère Tic-Tac-Toe... but it is played on three boards at once. Every time Tic-Tac-Toe is formed on a board, it is declared 'dead', and the winner is determined by the result of the last board in play. This opens up a wider range of possibilities, since a player can adopt a more aggressive stance and 'kill' the first two boards quickly, to avoid Tic-Tac-Toe on the third.

A Notakto expert should be able to recognize different X patterns on the boards, and take advantage of each opponent's mistake. Interested? There's an app for that! Notakto is available on iOS and Android, free of charge. And what about the rest?

Numeric Tic-Tac-Toe

An attractive alternative is Numeric Tic-Tac-Toe. Instead of X and O, players use numbers from 1 to 9. One plays with evens, the other with odds (repeating numbers is not allowed), and the goal is to sum 15 points in a line, or we can play misère and invert that condition. Numeric Tic-Tac-Toe is a creation of Ron Graham, and this document includes more variants.

Wild Tic-Tac-Toe

Also known as Devil's Tic-Tac-Toe, this variant adds a layer of flexibility, allowing players to use X and O whenever they see fit. With twice the options to consider and the possibility of playing misère, it is a far superior option to normal Tic-Tac-Toe.

Super Tic-Tac-Toe

A giant Tic-Tac-Toe board, and each of its squares contains a miniature Tic-Tac-Toe. To mark an X or O on that giant Tic-Tac-Toe, players must win the small one first... or lose if that is their strategy. The X determines the board on which O has to play (in other words, it 'follows' the move), and vice versa. For example: If X starts in the top-left corner of the central board, O must play somewhere on the top-left board.

And there you have it. From something boring and predictable like normal Tic-Tac-Toe, true nightmares can emerge that will make you and your opponents suffer for days. Enjoy!

Download Notakto: Click here