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

Ish?

Which is more random:

HHHHTHTTHTTHHTHTHTT

OR

HHHHHHHHHHHHHHHHH

OR

HTHTHTHTHTHTHTHTHTH

?

They are all equally random. The chance of flipping a million heads in a row, is just as likely to occur as any million state sequence of coin flips. They occur at PRECISELY the same rate. Namely, almost never.

That being said, what’s the chance that if you flip it a million times, you’ll achieve SOME 1 million state sequence?

100%.

SOME sequence WILL result. (Note: SEQUENCE, not PATTERN)

Astronomically improbable things happen regularly. Almost exclusively. There are more probable things that happen, than probable things that happen.. since there are theoretically only a finite number of improbable things, and an infinite number of astronomically improbable things that could happen.

No SPECIFIC improbable thing ever happens. But it would be infinitely impossible for astronomically improbable things to NEVER happen. Given the sheer volume.

Matt Parker did a video on this… but I’m running late to a family function… If I find it, I’ll post it…