Lotteries are commonly used to allocate big game hunting privileges. In this study, lottery demand and consumer surplus are modeled before and after policy changes designed to increase participation. The application is to New Mexico elk hunt lotteries. Given the volume and variety of hunts, we adopt a disaggregated and flexible count modeling approach. Two welfare measures are estimated: Marshallian surplus and a proposed measure that incorporates consumer uncertainty. The Marshallian measure produces smaller and slightly less precise estimates. However, regardless of the surplus measure examined, welfare increased significantly with the policy changes, while revenues changed by less than 1%.