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The present study reviews the literature about dynamic decision-making and judgment of low-probability, high-consequence events. The specific features of this situation under risk and uncertainty imply an anomaly: while the single probability of an event with high negative consequences may be small, being exposed to the same situation repeatedly over time, however, makes the one-time occurrence of this event highly probable. Evidence is presented which demonstrates that people violate the principles of rationality in dynamic settings and make their decisions in isolation instead of integrating all future consequences. Moreover, systematic biases and errors in belief formation lead to judgments which do not coincide with those obtained by probability theory and Bayesian updating. The fundamental proposition of this literature review is that policy-makers can benefit from an integrated view of psychological factors and economic (non-)rational choice behavior. A profound understanding of how people think and make decisions concerning repeated risks of low-probability events conceivably leads to effective policies and risk management strategies ...