"The Wyoming draws between random and special and preference has me confused. "
Wyoming has "special" permits available that are drawn for a separate pool of applicants. They are more expensive. Draw odds are generally, but not always better.
You may, or may not wish to get preference points for Wyoming. If you have no preference points, you are in the "random" draw. If you have preference points, your odds are improved:
"e. Big Game Preference Points. The preference point system is designed
to improve your odds of eventually drawing a license in a hard-to-draw
hunt area. For Moose, Full Price Bighorn Sheep, Elk, Deer and Antelope,
75% of available licenses in each hunt area and license type combination
will be allocated to a “preference point draw.” Applicants with the highest
preference point totals will receive priority in the preference point draw.
The remaining 25% of available licenses will be allocated to a “random
draw.” In this manner, everyone who applies has at least some chance of
drawing a license regardless of their preference point total.