  RCT is intuitively appealing, even once we distinguish process and product randomness in the way sketched above. It receives significant support from the fact that fair coins, tossed often enough, do in our experience invariably give rise to random sequences, and that the existence of a random sequence of outcomes is compelling evidence for chance. The truth of RCT explains this useful constraint on the epistemology of chance, since if we saw an actual finite random sequence, we could infer that the outcomes constituting that sequence happened by chance. However, in the next two sections, we will see that there are apparent counterexamples even to RCT, posing grave  difficulties for the Commonplace Thesis. In  §4  we will see a number of cases where there are apparently chancy outcomes  without randomness, while in  §5  we will see cases of apparent randomness where there is no chance involved.