Rock Paper Scissors Tournament

You are one of 2,048 participants in a bracket tournament of rock-paper-scissors. In the tournament, participants are matched in pairs and throw until a winner is decided, with the winner moving to the next round. This process repeats until one champion is determined. What is the probability that you win the tournament, assuming that all participants throw completely randomly? The answer is in the form $\frac{\alpha}{\beta}$ for coprime positive integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.