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 problem is not with stats, it’s with psychology.

Formation of life was impossible. Chances of a hole in one in golf are near impossible. Chances of winning a lottery are literally zero. But these things actually happened, right – **AND** – often enough!?

So your mind decides: Randomness is NOT random! I can find out some situations where it is NOT random at all!! The sniff of spotting that rare occurrence when random/unordered events are now due for a predictable order for a short while which YOU have spotted.

Our mind decides that it CAN figure out an order even in randomness. That’s what makes you do all kinda dumb shit.

A coin has no memory; but you with the memory of 24 consecutive heads do have a memory – so the coin is no longer random – it’s starting to get in tune – or IS in tune – with your memory of how randomness gotta catch up sooner or later.

But randomness has no memory. It has no idea when to catch up.