Good luck on that one Eric.  The draw out here in California is really, really tough, so I wouldn't go here.

There are not many tags, but there are tons of hunters.  And I am not sure, but I think they give them out just like any other tags for deer and elk, where all tags except one will go to people with max points.

So, you would go into the pool for the one tag available, along with anyone else.  Your odds would vary depending ont he unit, but as I said, the desert bighorn sheep tags here in California are very limited.

Actually, I have the big game digest right here in front of me at my desk.  It say that there 6 zones that had sheep tags.  As I said, there was only 1 tag in each zone that went to the random draw.  In total, there werre only 11 tags for the points draw.  That makes a total of 17 tags for the whole state.

You might want to try a different state...

After I submitted my answer, I just did a quick search.  I found that Montana has over the counter sheep tags available.

However, they say it's extremely remote area, and it's quota based, so once a level of harvest is reached, the hunt is closed.  Very similar to black bears here in California.

Anyway, if you want a low cost, low success, but OTC hunt, you could look there.

nevada gives out sheep tags in the draw, my odds as a resident are 1in146 for californa big horns and 1in56 for desert bighorns. i know rocky mnt bighorn odds are like 1in 600 thats why i dont apply for them. as for non res draw odds you might as well put a extra zero on the end of my odds there almost impossable to get. i think alaska would be your best bet for a tag it would be expencive though or maby arizona.

Have you ever considered a Montana Unlimited Sheep tag? http://fwpiis.mt.gov/content/getItem.aspx?id=37344 I haven't personally hunted these areas but from what I read over the years, it is possible to kill a legal ram in these areas and they do it quite often.

You might have a better shot at a ram tag if you find a state like oregon that will raffle one off every year, just buy a few raffle tickets . dont know what the odds are on that but it might be better than trying to draw out in various states.