Poker Tourney III

A single-elimination poker tournament has $2^n$ players, each with a distinct rating. In each match, Assume that the player with the higher rating always wins against a lower rated opponent with probability $0.5 < p < 1$. The winner proceeds to the subsequent round. Find the probability that the second-highest rated player defeats the highest rated player in the final round of the tournament when $n = 7$ and $p = 2/3$. Round to the nearest hundred-thousandth.