If anyone is curious about the statistics, the formula for drawing a tag in a certain number of years is 100%*(1-((100-odds of drawing)/100)^number of years). Now to do this you have to make assumptions about what your odds will be in future years, but you can get a rough idea.
For example, I can look and see that I have a 1% odds of drawing a bighorn sheep tag in the Missouri Breaks with 11 bonus points. I estimate that with the squared points system in Montana that will go up to about 3% in 10 years, so i'll use a 2% odds for an average.
Then the odds of drawing in 10 years would be 100%*(1-((100-2)/100)^10)=18%. Assuming an average draw odds of 3% over the next 20 years the odds become 100%*(1-((100-3)/100)^10)=45%.
I'm starting to wonder if I should start applying for a more difficult hunt that I could probably get in my lifetime like the Spanish Peaks or the Upper Madison Range which for 11 bonus points have draw odds of 3.5-4%. Let's say that the odds of one of them is 6% on average for the next 10 years. Then the odds of drawing in 10 years would be 100%*(1-((100-6)/100)^10)=46%. Assuming an average draw odds of 8% over the next 20 years the odds become 100%*(1-((100-8)/100)^10)=81%. Lots to think about when you start doing the math.
Bottom line is that a resident will likely get some of the less desirable hunts in their lifetime but might never get the more desirable ones like the Missouri River Breaks. The only sure way to go sheep hunting is to buy a $15-20k Dall's sheep hunt. The best bet for a Bighorn is to apply for one of the easier to draw hunts every single year, and to support the conservation organizations that work to increase the Bighorn population.