 The question takes on a different character when we consider its consequence for decision making. According to the standard theory, a utility-maximizing Bayesian must find at least one side of any bet attractive. It is straightforward to check that if a bet that costs \($\ell\) and pays out \($w\) has negative expected utility, then the other side of the bet, that costs \($w\) and pays out \($\ell\), has positive expected utility. Since her credences in both cases are the same, whatever bet Sophia accepts on the next spin of the Euro, she must also accept on the ancient coin. So even though her beliefs about the Euro are more stable, this difference is not reflected in her betting behavior. Yet intuitively, it seems reasonable to refuse to bet on the ancient coin at all. A bet on the Euro is risky: the outcome of the spin is uncertain, but there is no uncertainty about the chance with which each outcome occurs. A bet on the ancient coin is ambiguous: the outcome of the spin is uncertain and there is significant uncertainty about the chance with which each outcome occurs. Many seemingly rational people take account of this distinction in their decision making (see the discussion of  Ellsberg decisions in the entry on   imprecise probabilities).  However, this distinction cannot be represented in the standard theory (see Buchak (2013)).