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A related problem to the last post. You toss a fair coin, and keep going until the number of tails you’ve seen is n more than the number of heads. On average, how many times do you toss the coin before you stop?

Unlike the last problem, I don’t know the answer to this one, so I’d be interested in hearing anyone else’s approach. I believe that I have a good method for getting at the answer, but that I’m missing one crucial step that I haven’t yet been able to fill in.

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I have a lot of coin-tossing problems floating around in my head, of varying levels of difficulty. Here’s one which requires some thought, but shouldn’t present too much of a challenge if you’ve seen this kind of problem before.

You start flipping a fair coin, and keep going until you’ve seen n heads in a row, when you stop. On average, how many times do you flip the coin before stopping?