When people make risky choices, two kinds of information are crucial: outcome values and outcome probabilities. Here, we demonstrate that the juncture at which value and probability information is provided has a fundamental effect on choice. Across four experiments involving 489 participants, we compared two decision-making scenarios: one in which value information was revealed during sampling (standard) and one in which value information was revealed after sampling (value ignorance). On average, participants made riskier choices when value information was provided after sampling. Moreover, parameter estimates from a hierarchical Bayesian implementation of cumulative-prospect theory suggested that participants overweighted rare events when value information was absent during sampling but did not overweight such events in the standard condition. This suggests that the impact of rare events on choice relies crucially on the timing of probability and value integration. We provide paths toward mechanistic explanations of our results based on frameworks that assume different underlying cognitive architectures.