Ordinary Tic-Tac-Toe has 9 spaces and 8 lines. It’s been played for a while, and you probably already know the optimal strategy for it. This post will go through a few Tic-Tac-Toe variants.
The Fano plane has 7 spaces and 7 lines. It’s not a very good variant, because if the first player blocks the second player’s lines at all, the first player wins. The same applies to a 3 by 3 torus (9 spaces, 12 lines).
Next, an infinitely large variant. Spaces are integers, and lines are sets of three that add to zero. This one actually has some interesting strategy, and I called it The Zero Game. (Infinite spaces, infinite lines.)
What if we were to base the layout on the lines? How about 4 lines, and each pair of lines has one space that precisely those lines go through, totaling 6 spaces? That turns out to only be ties as well.
We’ve also got a few with longer line lengths: for length 4 we have the 4 by 4 torus (16 spaces, 16 lines) which is pretty balanced, as well as the finite projective plane of order 3 (13 spaces, 13 lines). For length 5 there’s Torus Games’s implementation of Gomoku (36 spaces, 144 lines), and regular Gomoku (Infinite spaces, Infinite lines).
Here are a few more gimmicky ones that don’t really fit into the established system above, of which I invented two:
Tic-Tac-Veto – On your turn, you pick two of your possible moves and your opponent picks which one happens.
Politic-Tac-Toe – There are three players, the board is 5 by 5, the lines are 5 long (including diagonals!), and wins are shared by two players if a line fills up with only those two players’ symbols.
HeXO – Infinite hexagonal grid, 6-in-a-row wins, every turn after the first lets you place two of your symbol.
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