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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