I've been playing since Day 1 and missed out on the chance to get the ghorn from Xur.
Approximately, and conservatively 1000 hours (including deleted and new character made) put in yet no luck.
I am open to advice as this is just silly.
Note: I've broken down more multi tools, NLBs, uni remotes and Dragons than I care to consider...
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My advice: Don't think about it. Don't anticipate it dropping when finishing Night Falls, opening exotic chests, taking down raid bosses, or on Friday mornings when Xur is in town (especially when Xur is in town. Forget that). I was in your same boat. 800+ hours, 3 characters, doing all my weekly activities and always hoping and wishing one would drop. All my friends and raid buddies had it. Some would get multiples in front of me. Despair set in, I realized I was playing the game ONLY to get this weapon, and I wasn't enjoying it. I even stopped playing for a few weeks. Then I rejoined and just started playing the game for fun again. I would run VoG with my group not because I wanted a chance at the exotic chest or Atheon drop, but because it is a fun activity to play. Within a week of coming back, Ghorn dropped on an Atheon kill. I wasn't even thinking about it. Since then, I now have 3 maxed Ghorns. I am not saying once you stop thinking about it it will happen, just don't let that damn gun ruin your experience because you think about it all the time. It will drop eventually. Cheers.