XuaXua wrote:Yea, clustering illusion. Sure.
So the following isn't at all possible, then:
System picks out 10 uniques to throw at you.
5 of these uniques happen to have a max depth of, I don't know how it works, but 9.
System rolls for the uniques to generate for 1-8, but no one shows up, system gets desperate since it has this load of max-depth 9 uniques, so it craps them all out at 9.
You get to 9 and suddenly, uniques out the ying-yang.
That's how it feels.
Let's try a specific example. For simplicity let's say Sigmund, Jessica, Ijyb, Grinder, Terence, and Edmund all generate somewhere between D2 and D7. Six possible levels for each of them to show up, and there are six of them. Suppose Sigmund randomly happens to show up on D2 this game. There's a 5/6 chance Jessica won't accompany Sigmund, but there's a 1/6 chance she does, just by random chance. But Ijyb also has a 1/6 chance to accompany Sigmund, and so do the other three. All totaled, there's a (5*5*5*5*5)/(6*6*6*6*6) chance of Sigmund *not* getting at least one buddy to fight with, or 3125/7776 == 40%. Sigmund will get at least one buddy in three out of five games! That's a clear majority.
Suppose you lucked out and you're playing a game where Sigmund is all by his lonesome. Next up is Jessica at D3. Maybe she got a buddy? Given the fact that they didn't generate with Sigmund, there are still four possible partners for her. Each of them have a 1/5 chance of spawning on her level, since we've already determined that they don't spawn on Sigmund's level. So that's a (4*4*4*4)/(5*5*5*5) chance of Jessica *not* getting at least one buddy to fight with, or 256/625 == 40%. So in three out of five of the games where Sigmund does not get a buddy, Jessica will instead. We're already down to a 16% chance, and we're only through the first two! Ijyb on D4 has a chance to get a buddy, and then Grinder on D5, and so on.
In the end, even this highly simplified example is very likely to end up with some levels that are empty of uniques and some that have multiples. Worse, we don't just have these six uniques on the shallow levels, there's also Menkaure, Dowan&Duvessa, Pikel, Blork, Crazy Yiuf, Eustachio, Prince Ribbit, and Purgy crowding onto the same band of about ten pre-Lair levels, plus occasional guest appearances from midgame uniques like Erolcha or Gastronok at the low end of their range.
Unique clustering is expected just by random chance.