Lost in state space

You and your friend like to play tic tac toe, but are not very good at it. On each turn the player picks a random empty square to place their mark. The game ends when the first person gets three in a row, as usual. If you make the first move, what is the probability that you win the game? If the answer can expressed as \(\frac{a}{b}\), \(a\) and \(b\) coprime, find \(a + b\).

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