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 easiest way to look at this is on a grand time scale, say 1 trillion outcomes (or infinity if it suits your fancy). During that amount of flips it should not seem unusual that you could have several million heads flipped in a row and the same for tails at some point. Probabilities are always figured so that the outcome gets closer to the theoretical (0.50 in this case) as you approach infinity. Taking a small sample size of 25 means nothing.