Risk involves exposure to a chance of injury or loss. The fact that risk inherently involves chance leads directly to a need to describe and to deal with uncertainty. Corps policy has long been (1) to acknowledge risk and the uncertainty in predicting floods and flood impacts, and (2) to plan accordingly. Historically, that planning relied on analysis of the expected long-term performance of flood-damage-reduction measures, on application of safety factors and freeboard, on designing for worst-case scenarios, and on other indirect solutions to compensate for uncertainty. These indirect approaches were necessary because of the lack of technical knowledge of the complex interaction of uncertainties in predicting hydrologic, hydraulic, and economic functions and because of the complexities of the mathematics required to do otherwise.