Flipping 5 tails in a row, it’s still a 50/50 chance to get a tail in the next flip?

Question

Flipping a tail is a 1/2 chance, but flipping 6 tails in a row is a 1/64, so if after flipping 5 tails, why is it incorrect to say that your chance of flipping another tail is now lower, like you’re “bound” to get a head? I know this is the gambler’s fallacy, but why is it a fallacy? I get that each coin flip is independent, but it feels right (as fallacies often do) that in consecutive flips the previous events matter? Please, help me see it in a different way.

In: Mathematics

Answer 1

>I know this is the gambler’s fallacy, but why is it a fallacy?

Because each flip is a discrete event, and the prior events have no impact on the future events. There’s no law or mechanism of the universe that’ll reach out and say “okay, that’s enough tails, now you get heads.”