 Both the Dutch Book theorem and its converse are sensitive to the formulation of the axioms, as well as to the understanding of ‘bet’, ‘sure loss’ and what it means for such a loss to be guaranteed. Special care must be taken with the characterization of the probability axioms when it comes to the Converse Dutch Book theorem. Given that the axioms are formulated such that the second axiom only requires that tautologies receive probability one, it is possible to satisfy the axioms, yet still be open to a sure loss. Consider the claim that if \(b\) has \(F\) then something has \(F\). This is not tautological, but betting against it would leave one vulnerable to a sure loss. Sometimes the second axiom is instead formulated as requiring that all logical truths receive probability one, but satisfying this constraint leaves open the possibility of a sure loss by betting against a necessary truth such as ‘nothing is both red and green all over’. Even with strengthening the second axiom to require that all necessary truths receive probability one, there is still a reading upon which the Converse Dutch Book theorem is false, since an agent will be vulnerable to a sure loss if she attaches a probability less than one to a known truth (or a probability greater than zero to a known falsehood). One response to this is to restrict ‘sure loss’ to those losses that do not depend on contingent facts. Instead the restriction could be made to losses that are ‘sure’ in the sense that there is a mechanical formula for inflicting the loss, thus removing the sort of counterexample to the Converse Dutch Book theorem with which we began, and the need to strengthen the axioms. A related move involves restricting the allowable bets, rather than limiting what counts as a sure loss.