Yeah, by your logic, you're pretty much saying that we have a '50/50 chance of getting 20 heads in a row'.
That's not how probablity works.
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No I never meant it that way. I was saying the opposite actually. What I meant was that each "flip", in this instance, had a 50/50 chance, but landing on heads 2 times in a row doesn't change the 50/50 chance of the 3rd flip.