I contacted my friend in Flagstaff and he confirms the deer and elk hunting is a lottery system.
In 35 yrs. he has never drawn a elk tag. Took him 7 years to draw a deer tag and nothing in the last 5 yrs. He doesn't even bother anymore.
But he knows guys who draw a elk and deer tags almost every year. He just thinks he's unlucky.
Arizona is a lottery for most places but they also have OTC tags for certain zones and times. However all those zones either have few animals or scrub bucks etc. I think there's roughly 90 zones across the state. It's also a group lottery. Up to 5 guys can go in as a group for a zone. If one of them gets drawn they all get a tag. That increases your chances by 4x over a guy applying alone.
I like any area of Nebraska along the Platte River. The areas around Denver are nice, but not my cup of tea. Northern Michigan is probably where we will wind up some day. The fishing is great, and I just like the area!