 Suppose we accept the claim that infinite precision is not required in decision theory. This would entail, per Smith’s argument, that it is rationally permissible to ignore probabilities smaller than \(\epsilon\). However, to ensure that the decision maker never pays a fortune for playing the St. Petersburg game it seems that Smith would have to defend the stronger claim that decision makers are rationally required to ignore small probabilities, i.e., that it is not permissible to not ignore them. Decision makers who find themselves in agreement with Smith’s view run a risk of paying a very large amount for playing the St. Petersburg game without doing anything deemed to be irrational by RNP. This point is important because it is arguably more difficult to show that decision makers are rationally required to avoid “infinite precision” in decisions in which this is an attainable and fully realistic goal, such as the St. Petersburg game. For a critique of RNP and a discussion of some related issues, see Hájek (2014).