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I don't think that's true. I think that the average number of flips before _stopping_ might be 3, but it doesn't become more likely to get HT simply because you're also looking for HH (or vice versa).

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It turns out that the average number of flips to get HH and HT is 3 - someone else on the thread described it well - on average, the number of flips to get to a "H" will be 2, and then you will always stop on the next flip - 50% at flip 3 with a HT, and 50% at flip 3 with a HH. Explained that way, it makes sense that the average number of flips is 3.

But, I still find it strange that if you are flipping with one particular scenario in mind, HT or HH, that the average number of flips goes from 3 to 4 or 6, even if I can reason it out with a bit of thinking.

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