The insight here is that, provided you are not certain of the fairness of the die, each roll would give you information about its fairness (and therefore about future rolls). The rolls themselves are still independent even on an unfair die, but you will develop progressively better estimates of the actual underlying probabilities.

(Of course, in basic statistics we ignore this sort of thing and just assume the die is fair or loaded in some known way. But this is an important caveat in real-world statistics!)