Assuming you are hyper efficient at chaining nightmare dungeons back-to-back and get an average of 1 unique per hour…
With 1:800,000 odds of getting an uber unique as compared to normal uniques, you are looking at 800,000 hours of playtime, or 33,333 days, or 91 years.
Given that 91 years is close to the upper limit of average life expectancy, and that you can only farm for 18 hours per day (assuming that you need at least 6 hours to sleep and eat, although your quality of life and health will be miserable), you only have 597,870 hours to farm an uber unique. That’s well below the expected 800,000 hours.
tl;dr, if you dedicate your entire life to farming uber uniques and nothing else, you still likely won’t see one.
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And you can still get one from the first capable mob you kill. Its just RNG. But the idea is not farming them. You either get one in the season, or not. Thats the catch and fun
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that doesn’t sound like fun. Imagine finding one only to start a new season a couple months later. what a waste.
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Whut? You must be new to ARPG’s. Seasons have been a thing, will always be a thing. You know that your seasonal character gets rolled back up into the eternal realm, yeah?
I fairness most other ARPGs don’t have this level of scarcity for their top uniques. Some even have ways to actually target farm them, so you can get one if you’re willing and able to put in the effort, regardless of how scarce they are.
and you must be new to reading
You said “Imagine finding one only to start a new season a couple months later what a waste”.
How is that a waste? You just put that uber on your new character that rolled up from a season to eternal. What is happening here? Do you think your eternal realm characters are a waste? What are you talking about here? These forums are filled with ridiculousness…
Like POE? How many mirrors do you have? D2, how many ZOD runes are you holding onto?
Uber uniques dropped on helltides like candy, so this post is uber copium.
You still going on about that?
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Do you know what a chase item is? On my Necro(s) im still going for a ring of mendeln. Druid, tempest roar. Those are chase items, its something you can find, but is rare. We aren’t talking about uber uniques where 99.9999 percent of the games population will never see…that isn’t a chase, its a fart in the wind.
There are plenty of chase items in the game, what are you talking about?
I have 5 doombringers. I have 1 in my living room, 1 in my bathroom…
I don’t have any mirrors, but then I wouldn’t consider them to be a chase item since they have a restricted use in game. I have enough currency in my standard league stash to buy one, if I wanted to, but I don’t play standard, so there’s no point.
And as I said, “if you’re willing and able to put in the effort”. I’m not going to grind for 30-40 hours to get a Headhunter, but you absolutely can, IF you’re willing to put in the time.
apparently you fail to grasp the little point that once season is over, your character goes to eternal realm. included all non seasonal items. as a uber unique. that is permanently yours.
You don’t understand statistics
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funny thing is , i found a ZOD runes during the very first week of D2R release 
(never used it though, but was funny to find and even made a post about it at the time considering how confused i was to have found one on my very first hell cow run in a group)
because of a bug, brilliant attempt at trolling but i’m going to have to 0/10 it
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This items are so rare , if you find one you will probably want to sell your account.
No account is worth more than 3000 dollars.
This system is so dumb 
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the people that got bugged Grandfathers and Shakos sold their accounts lol