Martingale Approach to Biased Ruin Probability

A gambler starts with $\$4$ and repeatedly bets $\$1$ on a biased coin that lands heads with probability $p = 0.55$. She gains $\$1$ on heads and loses $\$1$ on tails. The game ends when her fortune reaches $\$0$ or $\$10$. Using the martingale $(q/p)^{X_n}$ and the optional stopping theorem, find the exact probability that she reaches $\$10$ before going broke.