Behavioral decision theories aim to explain human behavior. Can they help predict it? An open tournament for prediction of human choices in fundamental economic decision tasks is presented. The results suggest that integration of certain behavioral theories as features in machine learning systems provides the best predictions. Surprisingly, the most useful theories for prediction build on basic properties of human and animal learning and are very different from mainstream decision theories that focus on deviations from rational choice. Moreover, we find that theoretical features should be based not only on qualitative behavioral insights (e.g. loss aversion), but also on quantitative behavioral foresights generated by functional descriptive models (e.g. Prospect Theory). Our analysis prescribes a recipe for derivation of explainable, useful predictions of human decisions.