  The natural response is to reject the idea that short sequences are apt to be random. The right hand side of RCT makes room for this, for we may simply insist that unrepeatable events cannot be repeated often enough to give rise to an adequate sequence (whether or not the inadequate sequence they do in fact give rise to is random). The problem here is that we can now have chance without randomness, if there is a single-case unrepeatable chance event. Difficulties in fact seem unavoidable. If we consider the outcomes alone, either all short sequences are random or none of them are; there is no way to differentiate on the basis of any product-based notion between different short sequences. But as some single unrepeatable events are chancy, and some are not, whichever way we opt to go with respect to randomness of the singleton sequences of such events we will discover counterexamples to one direction or another of RCT.