Re:The gambler's fallacy is not a fallacy?
by aidenn0 on Wednesday April 13, 2022 @11:11PM
(#31023050)
Perhaps this will help:
The odds of getting the sequence HTTHT are exactly the same as the odds of getting HHHHH, and similarly the odds of getting HTTHTH are exactly the same as HHHHHH.
Another way of thinking of it is that there's roughly a one in a thousand chance of getting 10 heads in a row; there's a one in two-thousand chance of getting 11 heads in a row, but if you've already gotten 10 heads in a row, you've already ruled out the ~1998/2000[1] possibilities that can't ever result in 11 heads (because they didn't start out with 10 heads in a row), so you only need to rule out one of the ~2/2000 remaining possibilities.
The odds of getting the sequence HTTHT are exactly the same as the odds of getting HHHHH, and similarly the odds of getting HTTHTH are exactly the same as HHHHHH.
Another way of thinking of it is that there's roughly a one in a thousand chance of getting 10 heads in a row; there's a one in two-thousand chance of getting 11 heads in a row, but if you've already gotten 10 heads in a row, you've already ruled out the ~1998/2000[1] possibilities that can't ever result in 11 heads (because they didn't start out with 10 heads in a row), so you only need to rule out one of the ~2/2000 remaining possibilities.
1: Actual numbers is 2046/2048 and 2/2048