Jan 302012

The other day I was chatting with Mayhem about number theory, algorithms, and game theory. He was very excited to be learning some interesting math tricks that help with factorization.

Along the way we eventually got to talking about simple games and graph theory. That, of course, led to Tic-Tac-Toe. But not being content to leave well enough alone we set about reinventing Tic-Tac-Toe so that we could have a 3 way game between he and I and Chaos.

After a bit of cogitating and brainstorming we hit upon a solution that works for 3 players, preserves the game dynamics of the original Tic-Tac-Toe, and even has the same number of moves!

The game board is a fractal of equilateral triangles creating a triangular grid with 9 spaces. The tokens are the familiar X, O, and one more – the Dot.

The players pick their tokens and decide on an order of play. Traditionally, X goes first, then O, then Dot. Just like old-school Tic-Tac-Toe, the new version will usually end in a tie unless somebody makes a mistake. Unlike the old game, Tic-Tac-Toe-3 requires a little bit more thinking because of the way the spaces interact and because there are two opponents to predict instead of just one.

Here is how a game might go:

O makes a mistake, Dot wins!

At the end of the game shown, O makes a mistake and allows Dot to win by claiming 3 adjacent cells – just like old-school Tic-Tac-Toe. Hope you have as much fun with this as we did!