How is the gambler’s fallacy not a logical paradox? A flipped coin coming up heads 25 times in a row has odds in the millions, but if you flip heads 24 times in a row, the 25th flip still has odds of exactly 0.5 heads. Isn’t there something logically weird about that?

Question

I know it’s true, it’s just something that seems hard to wrap my head around. How is this not a logical paradox?

In: Mathematics

Answer 1

Flipping 25 heads in a row (24 heads in a row followed by 1 more heads) has *exactly* the same odds as flipping 24 heads in a row followed by 1 tails.

So after you’ve flipped 24 heads in a row, it should make sense that the next flip has equal odds of being heads or tails.