My data is dated, but I made two antelope hunts in Wyoming back in the 1990's. I don't recall any "points" being necessary in those days. We just applied, listing our preferences for area and got our 2nd choice. We hunted west of Casper, near the Powder River.
Our first hunt was terrific. We did it ourselves Just my hunting partner and myself. I had a good map of the BLM lands. We drove out there, and set up a tent camp on the wide open prairie. We could sit in camp and glass small pods of pronghorn at a distance all around us. We had a ball stalking and trying to sneak up as close as possible to them. I was successful in taking one at 192 paces. My partner, however, was unable to score.
Our second hunt out there was miserable. We were in a slightly different area this time. My map showed a huge area of BLM land that we planned to hunt. However, upon our arrival in the area we found that public land was completely surrounded with private ranches. The one and only road to get to it ran through private property and the owner had put up a big billboard-like sign saying "No Trespassing". The sign also listed his phone number to call for permission to enter.
I called. The guy wanted $100. for us to drive across approximately 1 mile of his land on a good gravel road that was used and maintained by a gas and oil company. I expressed my surprise and amazement, and the guy hung up on me.
We found another section of BLM land with easy access, but we never saw a pronghorn there.
Then, to top off the trip, it started to rain. It rained for 3 days and nights. We were well off road, camping again, and the prairie had turned into gumbo. I think we were lucky to make it out of the muck.