I examine the structure of random choice resulting from random expected utility maximization and a tie-breaking rule. I provide a partial identification result, characterizing the set of random expected utility models that could have generated the observed choice frequencies. I then consider a particular class of random choice rules for which it is possible to constructively identify the consistent random utility model that produces indifference the least. These random choice rules are characterized by breaking ties in favor of strict convex combinations. Towards proving these results, I introduce and axiomatize the notion of a choice capacity, representing the frequency of choice by strict maximization. Choice capacities, while not necessarily observable themselves, provide the technical machinery to translate arbitrary random expected utility models into choice behavior.