Triskaphobia

A tic-tac-toe variant where if you get 3 in a row, you lose!

O starts first, if the board gets full, new cells appear. Click and drag to move the board around, scroll to zoom.

This game is a small exploration into a thought experiment I had, is there a way to make the game infinite? Or must the game end? If it must end, then what is the maximum board size?