Chance of Winning In Tic Tac Toe

Question

I'm sure everyone knows how to play the game of tic-tac-toe.

I have just been wondering what's the probability of winning if one player started his or her move by putting his mark in the middle?

Answer 1

If the other player plays properly, zero. The game is known to be a draw. If you want to assume random play by both sides, you could make a tree and calculate it. There are only two responses to a center opening-a corner or a side, but then more branches to the tree after that because the symmetry is broken.

Answer 2

I believe there is always a way to end the game in a tie, so the chance of winning would be zero. (assuming the opponent knew what move to make in response to your move)

This might be relevant: http://www.cs.jhu.edu/~jorgev/cs106/ttt.pdf