Previous research has developed a variety of theories explaining when and why people's decisions under risk deviate from the standard economic view of expected utility maximization. These theories are limited in their predictive accuracy in that they do not explain the probabilistic nature of preferential choice, that is, why an individual makes different choices in nearly identical situations, or why the magnitude of these inconsistencies varies in different situations. To illustrate the advantage of probabilistic theories, three probabilistic theories of decision making under risk are compared with their deterministic counterparts. The probabilistic theories are (a) a probabilistic version of a simple choice heuristic, (b) a probabilistic version of cumulative prospect theory, and (c) decision field theory. By testing the theories with the data from three experimental studies, the superiority of the probabilistic models over their deterministic counterparts in predicting people's decisions under risk become evident. When testing the probabilistic theories against each other, decision field theory provides the best account of the observed behavior.