Gambler's ruin: Probability heads exceed tails by $X$ or more as $N$ increases.

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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.