I've never hunted there, but am interested since my ID unit shares a border with MT.
I believe this CJ video will answer your question:
https://www.youtube.com/watch?v=t1UNpqpEL_U
Thanks. Corey is right. It used to be easy to get a tag as a non-resident in Montana. That is why we have went there for the last 6 years. Easy to get a tag, lots of elk and not as crowded as Colorado. That has defiantly changed in the last couple years. Tags are harder to get and there are a lot more hunters. At least where we are hunting.
Based on my limited knowledge of their system in Montana your odds will increase with a party application only of the other person in your party has more points than you have. If the weighted average of the parties points is higher than your number of points that should help you.