Second seed upsetting the top seed in a 16-player final

A knockout tournament with a random bracket has $2^n$ players of distinct ratings, so it lasts $n$ rounds including the final. In any game the higher-rated player wins with probability $p$, where $\tfrac12<p<1$. Write the probability that the second-ranked player beats the top-ranked player in the final as a function of $n$ and $p$, and evaluate it for $n=4$ and $p=\tfrac34$.

$243/10240$. They must start in opposite halves (probability $\tfrac{2^{n-1}}{2^n-1}$), each must win all $n-1$ earlier games ($p^{2n-2}$), and then the underdog must win ($1-p$). For $n=4$, $p=\tfrac34$: $\tfrac{8}{15}\left(\tfrac34\right)^6\tfrac14=\tfrac{243}{10240}$.