  A fundamental problem with RCT seems to emerge when we consider the fate of hypothetical frequentism as a theory of chance. For there seems to be no fact of the matter, in a case of genuine chance, as to what sequence of outcomes would result: as Jeffrey (1977: 193) puts it, ‘there is no telling whether the coin would have landed head up on a toss that never takes place. That’s what probability is all about.’ Many philosophers (e.g., Hájek 2009) have followed Jeffrey in scepticism about the existence and tractability of the hypothetical sequences apparently required by the right hand side of RCT. However, there is some reason to think that RCT will fare better than hypothetical frequentism in this respect. In particular, RCT does not propose to analyse chance in terms of these hypothetical sequences, so we can rely on the law of large numbers to guide our expectation that chance processes produce certain outcome frequencies, in the limit, with probability 1; this at least may provide some reason for thinking that the outcome sequences will behave as needed for RCT to turn out true. Even so, one might suspect that many difficulties for hypothetical frequentism will recur for RCT. However, these difficulties stem from general issues with merely possible evidential manifestations of chance processes, and have nothing specifically to do with randomness. The objections canvassed below are, by contrast, specifically concerned with the interaction between chance and randomness. So these more general potential worries will be set aside, though they should not be forgotten—they may even be, in the end, the most significant problem for RCT (if the right kind of merely possible sequence doesn’t exist, we must retreat to CTa or CTb and their problems).