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

I find it easier to comprehend it this way:

So you have an old but otherwise regular coin. You flip it. What are the chances of a heads? 50% right? Now, remember, this coin has been around for a while, exchanged hands, so it’s probably been flipped a good number of times, right? Your flip wasn’t its first flip. It could’ve been flipped thousands of times for all you know. But you have no problem with believing it’s still 50/50 because you simply didn’t consider its past results, right? Well, that’s the thing, statistics never considers the last results either.