Odds for Wyoming residents are about 50% for drawing antelope in units 90, 92, 93, and 96 (based on 2003 results). For a non-resident the odds are a lot thinner: Unit 90 is 14%, Unit 92 is 13%, Unit 93 is 11%, and Unit 96 is 11%.
You could try Unit 24 or 23 which has a substantial chunk of public land in the form of Thunder Basin National Grasslands. These units have large numbers of permits allocated, and hence drawing odds are good for non-residents. The down side is that there may be large numbers of hunters in that Thunder Basin public land. One strategy would be to hunt late -- perhaps two weeks after the opening of the season -- and to hunt mid-week rather than the weekend. Alternately, some ranchers let you hunt on their properties for reasonable trespass fees. I hunted a property close to Gillette in Unit 23 this year and paid a $125 trespass fee to hunt.
