Your best bet would probably be to hunt the general season in the west half of the state. It's tough hunting but you can hunt for branch antler bull elk every year, no draw required. The east side of the state is open only for spike bulls during the general season.
The other option would be to try drawing an archery permit for the east side. They have reasonable odds but still you should expect to wait at least ten years. A permit for rifle season, I'd say plan on waiting 20 to 30 years. Yeah, not really worth it. It would be cheaper to pay for a guided hunt.