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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?

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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.

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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

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It is always random. Depending on the skill of the player, it may be 0/100 or 100/0. Putting the X in the middle doesn't necessarily mean that you will have a higher chance of winning. In fact I've seen my fair share of people who put their X (if they go first) in the corner or on the sides.

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