This article models the cognitive processes underlying learning and sequential choice in a risk-taking task for the purposes of understanding how they occur in this moderately complex environment and how behavior in it relates to self-reported real-world risk taking. The best stochastic model assumes that participants incorrectly treat outcome probabilities as stationary, update probabilities in a Bayesian fashion, evaluate choice policies prior to rather than during responding, and maintain constant response sensitivity. The model parameter associated with subjective value of gains correlates well with external risk taking. Both the overall approach, which can be expanded as the basic paradigm is varied, and the specific results provide direction for theories of risky choice and for understanding risk taking as a public health problem.