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.