Two expert and jaded tic-tac-toe players, after drawing for the n-th time, decided to add some randomness to their favorite game.

First, they used a coin to decide who would start. Then, that player would pick his initial move randomly. Next, the other player would also pick his answer randomly. Finally, from then on the game went on as usual, with each player playing in the best possible way.

For each player, what are the odds of winning, losing, or drawing?

Assuming X goes first: X wins 40/72, draw 32/72, O never wins.

X's first spot in 1 of 9 spots, O's in 1 of 8 spots => 72 possible starts.

If X starts in middle and O on corner: draw (4)
If X starts in middle and O on edge: Xwin (4)
If O starts in middle and X on corner: draw (4)
If O starts in middle and X on edge: draw (4)
X on corner and O on non-adjacent edge:Xwin (8)
X on corner and O on adjacent edge: Xwin (8)
O on corner and X on non-adjacent edge:draw (8)
O on corner and X on adjacent edge: draw (8)
X on edge and O on opposite edge: draw (4)
X on edge and O on adjacent edge: Xwin (8)
X on corner and O on opposite corner: Xwin (4)
X on corner and O on corner (!opposite):Xwin (8)

Hope this is right.

Posted by Rajal on 2004-10-04 12:33:00