But your argument supports the opposite of the classic gambler's fallacy. The traditional mistake is to expect the 30th flip to be less likely to be heads, beca

But your argument supports the opposite of the classic gambler's fallacy. The traditional mistake is to expect the 30th flip to be less likely to be heads, because 30 in a row is rare. So peoples' intuition is even less appropriate to the real world than probability theory is.