Trihex

Equitable version of tic-tac-toe on a triangular field and nine lines.

The playing field encompasses nine rings located on nine lines, three on each of them. Two players take turns placing chips of their color on one of the rings. At the beginning of the game you have four white chips, your opponent has four black chips. The winner is the first person to occupy all three rings on a straight line. Players also take turns to start the game.

Thomas H. O'Beirne from Glasgow, author of Puzzles and Paradoxes (Oxford, 1965), experimented with topologically distinct patterns of nine rows to see which of these were suitable for a tic-tac-toe play. He found that on all regular configurations the starting player can win easily. The only exception is the configuration shown here.