# What a game!

Two players, Nihar and I, are playing a game in which alternate tossing a fair coin and the first player to get a head wins. Given that I toss first, the probability that Nihar wins the game is $$\frac{\alpha}{\beta}.$$

If $$\alpha$$ and $$\beta$$ are coprime positive integers $$\alpha$$ and $$\beta$$, find $$\alpha + \beta$$.

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