 There is reason to accept the conclusion of the DBA that one ought to satisfy the probability axioms so as to avoid a Dutch Book only insofar as satisfying the axioms affords at least the possibility of avoiding exposure to a sure loss (Hájek 2005; 2008a,b). Here, the Converse Dutch Book theorem, proven independently by Lehman (1955) and Kemeny (1955), plays an important role. Roughly stated the result is that