For Ramsey and de Finetti, the point of appealing to a Dutch Book argument was to establish probabilistic constraints using precise terms that were tied to verifiable conditions, making it crucial that the bets constituting a book are given definite payoff conditions and can be settled. However, the book against the violator of the Principal Principle involves bets on chances, which lack the definitive settlement conditions that would produce a sure loss. To the extent that the underlying problem associated with Dutch Book vulnerability lies with the agent’s evaluations rather than merely with their pragmatic consequences, as discussed previously, the lack of a sure loss here may not be crucial. Still, the motivation for taking the Dutch Book vulnerability in cases where the probability axioms are violated as an indication of irrationality appears to derive from the idea that it leads to a sure loss, so that the merely expected loss associated with violating the Principal Principle, is less clearly irrational. In particular, credences that are associated with a mere expectation of loss, rather than a sure loss, are less clearly held to indicate an inconsistency in the agent’s action guiding evaluations. Such credences may still be irrational, but clarifying the source seems to require appealing to the nature of chance, which remains unsettled.