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

If you flip a coin that you know is fair, then you would correctly expect even odds for heads and tails. You’d expect so even if you use a coin that has been flipped hundreds of times before. For a fair coin, the relation between past and future flips is entirely in your mind.

The probability of flipping 25 heads in a row is very low, but it’s only half as much as flipping 24 heads in a row, so the odds of flipping the 25th heads after already getting 24 is the same as getting heads once.