“Preference point” lotteries—under which the probability an individual is drawn increases with their stock of preference points earned over time by being unsuccessful in past drawings—are widely used to allocate access to many economically important natural resources (e.g., big game hunting opportunities). Lotteries form a natural choice experiment: by observing the opportunities for which an individual applies, the alternatives not chosen, the associated costs, the probability of winning a permit, etc., statistical inferences can be made about how individuals trade off site characteristics for cost. Knowledge of these trade-offs can then be used to estimate applicants’ willingness to pay for site quality characteristics and site access. Two key features of recreationalists’ choices under preference point lottery are (i) forward-looking behavior (since the odds of winning a permit depend on the accumulated stock of preference points) and (ii) equilibrium sorting (whereby individuals decide where to apply based on their expectations of others’ choices and vice versa). We develop a novel revealed preference method for estimating individuals’ willingness to pay for access to recreational opportunities allocated by preference point lottery that accounts for these two features. We apply our model to the case study of black bear hunting in Michigan. We estimate total willingness to pay for access to a small site to be nearly $150,000.