An analysis of physical geology textbooks used in introductory courses shows that there is a systematic lack of clarity regarding flood risk. Some problems originate from confusion relating to statistical terms such as "100-year flood" and "100-year floodplain." However, the main problem is conceptual: statistics such as return periods and annual probabilities do not portray the variability inherent in flood recurrence and lead to misconceptions. An alternative conception of risk is proposed based on the analogy between playing a game of chance and living in a hazardous situation. This concept leads to the introduction of statistical ensembles as a means to characterize risk as a function of the duration of exposure to a hazardous situation. Presenting risk in relation to exposure time places floods in the framework of planning and problem-solving: how does the risk that arises from where we build relate to how long we want to be there? Methods and materials in the paper show how game play and ensembles can be introduced in the classroom. A supplemental Excel spreadsheet provides the means to generate ensemble diagrams from commonly available stream data and gives instructors the potential to customize their course materials by using data from local streams.