Hacker News Reader

Yeah, but say 1,000 people each flipped a coin 10,000 times and one of them once got a streak of 29 heads out of 30 flips. Can we assume anything then?

Nope. A previous flip has no bearing on the next flip.

You can calculate the probability of having a fair coin and as N(Heads) increases that probability goes down. Each flip is indeed independent but the distribution of flips tells you something about the coin.

We aren't predicting flips based on "a" previous flip. We're predicting them based on the set of ALL KNOWN previous flips, which allows a statistical model.

The odds of that happening by chance is so astronomical it involves a number you've probably never even heard of.

'If you flipped a coin 100 times and all you got are heads you'

By starting the sentence with if, you are selecting the occurrence to look at.

If you said I am about to look at the results of this coin toss that happened yesterday, if it is all heads then I am going to assume it was not random, then you are making the claim before you have seen the results. You can still be wrong, but the chances of you being wrong is the rarity of the event.