Pressures on natural resource stocks and habitats on public lands and waterways are resulting increasingly in the rationing of public access by lottery. Upon accounting for the uncertainties of random rationing, discrete choice models lend themselves to analyzing participation in public resource lotteries and estimating welfare changes. Key to the modeling is the estimation of individual-specific expected access-probabilities. In the application we model the discrete choices of more than 18,000 participants in a lottery system for harvest rights. Welfare estimates are obtained from simulated policy changes affecting individually and jointly the access probability and indirect utility.