  Chance, it is commonly said, is ‘single-case objective probability’. Philosophers haven’t been very clear on what is meant by ‘single-case’, and the terminology is slightly misleading, as it falsely suggests that perhaps multiple cases have less claim to their chances. The most minimal version of the claim is that, at least sometimes, an outcome can have a chance to be a result of an instance of a given kind of process, or trial, even though no other trials of that process occur. This is what we will mean by ‘single case’ chance. (A stronger claim is that the chance of an outcome resulting from a given process is an intrinsic property of a single trial. The stronger claim is inconsistent with standard versions of the frequency theory, and indeed it can be difficult to see how chance and frequency might be connected if that stronger claim were true.) Some have claimed that single-case chance is no part of objective probability; for example, von Mises (1957: p. 11) remarks that the ‘concept of probability … applies only to problems in which either the same event repeats itself again and again, or a great number of uniform elements are involved at the same time.’. However, this is a theoretical judgment on von Mises’ part, based on difficulties he perceived in giving an account of single-case chance; it is not a judgement derived from internal constraints on the chance role. And how could it be? For