Ruin Probability Under a Martingale Betting Strategy

A gambler uses a doubling strategy (Martingale system): she bets $\$1$ on a fair coin, and after each loss she doubles her bet, resetting to $\$1$ after any win. Her initial capital is $\$31$ and the table maximum bet is $\$16$ (so she can lose at most $4$ consecutive times before hitting the cap, since $1 + 2 + 4 + 8 + 16 = 31$). If the bet would exceed $\$16$, she bets her remaining capital instead. Her target is $\$42$ (a net gain of $\$11$). What is the probability she reaches $\$42$ before going broke?