> > First of all, you have to know what you are > > averaging OVER. You are overaging over FLIPPERS, > > or flip-sequences.
email@example.com wrote: > He can average over whatever the heck he > wants to average over.
Bullshit. He SAID what he was averaging over (badly). Having stated a scenario and used the word "average" in the context of that scenario, he has to average over what the scenario says he's averaging over.
> He can take the longest initial match > over all flippers
Sure he can, BUT HE DIDN'T. The word "longest" does NOT appear in his question!
> and average that over however many times he wants > to do the whole experiment over.
But the prospect of doing the experiment over does NOT arise in his scenario. He didn't ASK about that. He ASKED about doing the experiment ONE time.
> > If he does that, he'll get something around 20 flips. > > Or he can take the the initial match and average > that over the million flippers.
Which was what the question was about.
> If he does that, he'll get something around 1 flip.
No, HE won't, because HE'S an idiot, as you can see from the fact that he's still arguing against high school math, and still deluding himself that he can divorce "on average" from the average.
> > You are averaging over a million > > things. > > No _YOU_ are averaging over a million things.
So is he.
> He's averaging over > something else.
No, he isn't. This is what he asked:
> ... 1,000,000 other people all flip 100 coins themselves. > on average, will someone flip the same 100 long > sequence I did? > how long a sequence will they match up to on average?
He is NOT asking for the LONGEST match. He is asking for the AVERAGE match.
> > > Furthermore, the AVERAGE, over all flippers, of the > > initial-length-of-match-you-prefix, is ALSO > > LESS THAN 1. > > But not measurably less than 1.
Well, if you can keep track of a million flippers flipping a hundred times, you can keep track of the number of decimal places where the first digit less than 9 is.