IMHO Kano is correct, and I don't see the relevance of the
Central Limit Theorem to the question of whether bad luck
in the past will be compensated for
in the future. The idea that tossing a fair coin and getting, say, six heads in a row will be "evened out" by disproportionally more tails in future tosses is known as the
Gambler's Fallacy. If you've had bad [or good] luck in the past, then your lifetime expectation for luck is bad [or good]; you cannot change the past -- it is the baseline for your future. More generally, probability theory deals with unknown (often future) events, not known past events.
No, of course not "compensated" as a reaction to the bad luck streak. But "evened out" in the sense that this single bad luck streak has less and less influence as the time or number of draws rise.
I am pretty sure we all are more or less talking about the same thing, and actually agreeing. How about we say "there are bad times, there are good times, everything is fine", and leave that page-long non-p2pool-related statistics/probability stuff?
The still unanswered question remains:
Is p2pool in fact statistically "working", in the sense that 100 Th will yield the [statistically] same amount of blocks as 100 Th on a single bitcoind or centralized pool?
Ente