Two good tic-tac-toe players started a game, but the wind blew away their paper just after the second play. Given that the situation was as follows, who was to play next, O or X?

       |   |
    ---+---+---
     O |   |
    ---+---+---
     X |   |

If X had played the opposite corner, what would you say?

O was to play next.

Without any second thought, if X plays first and plays the corner, the optimal strategy is to play the center. We assume that since both players are "good," they will play the optimal strategy. If O plays first and selects the side middle, one of the optimal strategies is to play the X below it. There are many such strategies due to symmetry. Also, this will lead to a forced draw.

If O had played where it was and X played the opposite corner, X isn't an optimal player. Assuming O is still using an optimal strategy, then O has a forced win strategy.

Posted by Eric on 2004-07-19 07:51:11