RamDreamer... great ram... what are those spots on his coat?
Regarding a desert sheep draw, I don't believe that anyone should expect to draw a permit within their lifetime. One problem is that you can only apply once per year per state, and no one lives forever. Even if you begin young, say at the legal minimum age, you still only get 50 or so draws before you're done. That said, I began applying my son and several nephews in all of the sheep states when they first became legally eligible. If you are just beginning, you should definitely begin applying in AZ, NM, NV and UT. Someone has to get lucky.
Another problem for the future is that human populations across the West are exploding, and resident hunters will continue to put pressure on their Game & Fish departments to further restrict non-resident tags to increase opportunities for residents. That factor, combined with increasing encroachment by development on sheep habitat, makes the outlook for non-resident draws somewhat bleak.
I began applying for sheep tags fifteen years ago, about the time that some of the states began their bonus/preference point systems. I got lucky and drew a Colorado bighorn tag in the mid-1990's, and took a 177 ram. The draw odds then were about 80 to 1. I also took two dall rams in the 90's, the first at 158 and the second at 168, and a stone ram at 170, leaving me at 3/4 status.
About five years ago I finally faced the grim reality of the worsening odds for drawing a desert permit, and with that, along with my advancing years, I "bit-the-bullet" on a desert tag in my home state and took a nice 168 ram. I hope that this does not sound like bragging, but I am proud to have a 680+ slam, with only five rams total. I have been a very lucky sheep hunter.
I believe the advice from the post above is on target for a sheep hunter from a non-sheep state, like MN. Unless you move out West, you're never going to get the advantage of resident odds (which are not great, and getting worse every year), so if you really want to hunt sheep, you need to make some money, save some of it, and invest wisely.
But get in the game. No one can know what the future holds. It may be that as this current "sheep-hunting" generation ages, and more guys face the reality that they can no longer climb well enough to do a sheep hunt justice, that the odds may begin to improve. And if you're there, with many years of bonus/preference points in your pocket, you just might get drawn.
Good luck.
Your personal case of sheep fever has not fully set in yet. I know quite a few people who have hunted sheep and only a very small percentage say that one was enough, regardless of species. I killed my desert 20 years ago and my California 12 years ago (both as a Nevada resident). I am 49 years old and if I could I would trade all future elk, antelope, bear, moose, whatever, hunts just to hunt sheep once more in Nevada. 
