You will have a hard time drawing a sheep tag without making a real financial commitment to doing so. For a guy starting out, Idaho is probably the best bang for the buck with all things considered (draw odds, license fees, tag fees, etc).
In Nevada I recall you can have the hunting license fee refunded if you don't draw, but then you won't accumulate bonus points. Without accumulating points your draw odds will be very minimal. Nevada squares their points plus a point for the current year, so imagine a guy who has been applying...for say 20 years...he will have 401 chances in the draw (20 x 20 +1). Without points you will have ONE chance in the draw. If you really want to improve your chances to draw in NV you need to buy a license each year and stick with it.
New Mexico has no point system, so you are in with everyone, but you have to front the significant tag fee ($3000+). I recall you have to buy a hunting license to apply but can have that refunded if you don't draw.
Wyoming, you have to front the tag fee to have a chance to draw. I recall 25% of the tags go in the random drawing. It is also a preference point state, and issues a LOT of sheep tags, so the top point pools are actually drawing out. They keep $100 each year you apply.
Montana, one of the cheapest states to apply in but you still have to front the tag fee. Amazing sheep, terrible draw odds...unless of course you go to the unlimited area. It is a bonus point state, and they square the bonus points, so guys who have been at it for the past 10+ years have by far the best odds.
Oregon, you hafta buy a hunting license to apply, but you can apply for $8 I recall, and pay the tag fee after drawing. There is not point system, so you have as good of odds as the next guy. But for a non-resident draw odds are roughly 0.2% to 0.5%.
Colorado, you won't draw until you have built at least 3 points built up. You have to front the tag fee to apply.
Idaho, you have to buy the hunting license and front the tag fee. There is no preference system, some of the best draw odds. If you stuck with it and applied in the easier to draw units you would have draw odds from 1% to about 8% in a given year.
Utah has very poor draw odds as a non-resident and you have to buy a license to apply. It is a bonus point state, so sticking with it increases your odds.
Arizona, you have to buy the license to apply. You can apply on-line and only pay the application fee, and have your credit card charged if you draw. I recall you can decide to not keep the license, but if you don't, you won't accumulate bonus points and that will create even longer odds in the years to come when competing with applicants who are building points.
One other thought, the popularity for ewe licenses seems to be on the increase, in order to experience the hunt, without the long odds for a ram tag.
