 Finite frequentism gives an operational definition of probability, and its problems begin there. For example, just as we want to allow that our thermometers could be ill-calibrated, and could thus give misleading measurements of temperature, so we want to allow that our ‘measurements’ of probabilities via frequencies could be misleading, as when a fair coin lands heads 9 out of 10 times. More than that, it seems to be built into the very notion of probability that such misleading results can arise. Indeed, in many cases, misleading results are guaranteed. Starting with a degenerate case: according to the finite frequentist, a coin that is never tossed, and that thus yields no actual outcomes whatsoever, lacks a probability for heads altogether; yet a coin that is never measured does not thereby lack a diameter. Perhaps even more troubling, a coin that is tossed exactly once yields a relative frequency of heads of either 0 or 1, whatever its bias. Or we can imagine a unique radiocative atom whose probabilities of decaying at various times obey a continuous law (e.g. exponential); yet according to finite frequentism, with probability 1 it decays at the exact time that it actually does, for its relative frequency of doing so is 1/1. Famous enough to merit a name of its own, these are instances of the so-called ‘problem of the single case’. In fact, many events are most naturally regarded as not merely unrepeated, but in a strong sense unrepeatable — the 2020 presidential election, the final game of the 2019 NBA play-offs, the Civil War, Kennedy’s assassination, certain events in the very early history of the universe, and so on. Nonetheless, it seems natural to think of non-extreme probabilities attaching to some, and perhaps all, of them. Worse still, some cosmologists regard it as a genuinely chancy matter whether our universe is open or closed (apparently certain quantum fluctuations could, in principle, tip it one way or the other), yet whatever it is, it is ‘single-case’ in the strongest possible sense.