Expected Utility Theory is of little use as a positive (or normative) model of decision making under uncertainty when the decision maker is sufficiently uninformed. We design an experiment in which subjects choose between two uncertain payoff distributions (which we call alternatives), only knowing the support of each. In the first round they choose one alternative and experience a payoff as a result. In the second round they decide whether to choose the same alternative, or switch. From each subject’s responses we construct what we call a response function, which serves as a simple model of decision making, and does not rely on Expected Utility Theory. We use a mixture model to classify each subject into one of several classes of response function. Further, we explain classes’ differing payoffs in terms of the interaction between the shapes of their response functions, and the properties of the payoff distributions that subjects’ choose between. We briefly explore why different individuals belong to different classes of response function. This work constitutes a first step in understanding decision making under uncertainty in environments where one does not have as clear an idea of alternatives’ outcome distributions as is commonly assumed, and where individuals can learn from only one experience.