The future citizens, planners, and policy makers in our geoscience courses need to visualize the long-term consequences of living in hazardous situations to reduce their risk without excessive cost. However, the statistics emphasized in many courses do not provide a good basis for visualizing risk. For example, students may learn that the "50-year flood" on Brandywine Creek at Chadds Ford, PA is one that exceeds 23000 cfs once every 50 years on average. If they try to thoughtfully apply the definition they should have additional questions: "If 50 years is the average, how much does the actual recurrence period vary?" "By how much can the 50-year flood be expected to exceed 23000 cfs?" "How does the 50-year flood help me understand my risk over the next 20 years?"

To provide insight into such questions, I use recurrence relations to generate stochastic simulations of hazardous processes. For example, a recurrence model for Brandywine Creek can be used to generate a sequence of maximum annual floods for a given period of time. However, a single simulation is just one possible "future" of indeterminate significance. Ensembles of large numbers of simulations demonstrate important features of the recurrence of floods and other hazards. I introduce students to the concept of stochastic simulation with reference to graphical models of recurrence probability such as dartboards (Lutz, JGE, 2001) that can be understood without formal training in the statistics of extreme value distributions. The main advantage of simulations is that they create intuitive, visual representations of the underlying probability model. Simulations can be incorporated into spreadsheets so that students can set up, create, and interpret their own ensembles. The presentation includes examples based on the statistics of floods, earthquakes, and a simplified cost-benefit scenario.