 De Finetti speaks of “an arbitrary sum” as the prize of the bet on \(E\). The sum had better be potentially infinitely divisible, or else probability measurements will be precise only up to the level of ‘grain’ of the potential prizes. For example, a sum that can be divided into only 100 parts will leave probability measurements imprecise beyond the second decimal place, conflating probabilities that should be distinguished (e.g., those of a logical contradiction and of ‘a fair coin lands heads 8 times in a row’). More significantly, if utility is not a linear function of such sums, then the size of the prize will make a difference to the putative probability: winning a dollar means more to a pauper more than it does to Bill Gates, and this may be reflected in their betting behaviors in ways that have nothing to do with their genuine probability assignments. De Finetti responds to this problem by suggesting that the prizes be kept small; that, however, only creates the opposite problem that agents may be reluctant to bother about trifles, as Ramsey points out.