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

The thing about coin flipping is that there are only two possible states it could realistically land on: heads or tails. Even though initially your results may show it favoring one side over the other, the longer you perform the experiment, the closer the average result is going to be 50%.