alt Hacker NewsIsn't 100 / 100 the most likely outcome for a fair coin? Sure it's unlikely that you hit exactly that result, but every single other result is even less likely.
What I'm trying to say: if you get 100 / 100, that's not a sign of an unfair coin, it's the strongest sign for a fair coin you can get.
Replies
I would guess that a single trial of 200 flips can be treated as one event, so getting 100/100 is but one outcome. It may be the most likely individual outcome, but the odds of getting that exact result feel less likely than all of the other possible outcomes. The 100/100 case should be seen the most over repeated trials, but only marginally over other nearby results.
Intuitively, this seems right to me, but sometime statistics do not follow intuition.
"fair coin" refers to both the probability of heads and tails being equal (which is still justified) as well as the trials being independent (unlikely with 100/200; more likely the "coin" is some imperfect PRNG in a loop)
Well, yes. But the expected deviation from the mean is still ≈7.07. And the probability that the outcome will be either 93/107 or 107/93 is (slightly) higher than the outcome being exactly 100.
> every single other result is even less likely.
But the summed probability of the “not too far away results” is much higher, i.e. P([93, 107]\{100}) > P([100]).
So if you only shoot 100/100 with your coin, that's definitely weird.