I have a question similar to, but different from, the martingale problem.
Assume you are a gambler willing to bet, say, $10\%$ of whatever amount you start with on a fair coin toss. Then, if at any time the number of tails (losses) exceeds the number of heads (wins) by $10$, you are out of the game.
It seems intuitive to me that as $N$ increases, the probability approaches $1.0$.
However, I don't know how to calculate the probability for any given $N$, say $10$ or $100$ or $1000$. If, in addition to a formula, someone also knows how to build a Monte Carlo simulation in Excel, that would be excellent! Thanks in advance for your insights and expertise.