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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.

Air Mike
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etienne53
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  • Are you asking for the probability that after $N$ coin tosses, the number of tails never exceeds the number of heads by 10? – Alan Abraham Sep 12 '20 at 16:08
  • Yes, that's it exactly. I was able to build a Monte Carlo simulation in Excel. Clumsy, but it works. I come up with around 60% to 67% going broke in a fair 50% game such as a coin toss after 2000 throws.I've done some reading online, but I don't really understand the formula for putting in real numbers, such as 10 throws, 100 throws, or 1,000 throws. – etienne53 Sep 13 '20 at 17:10

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