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Old March 10, 2008, 09:14   #1
The Sparrow
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Where are all those vaults?

I have a question about Vaults. I am well versed in the basics of the game, having beaten Moria a few times, but I just started playing Angband the last couple of months, so I am not familiar with everything.

Anyhow, my question is about how common vaults are. I have been playing for a couple of months and have had about a dozen characters reach the over level 20 and two reach over level 32, and have gotten those two as deep as 1900'. I have not seen a single Greater Vault at all, and MAYBE about a half dozen lesser vaults in all (I dont keep count, but it is rare enough to me that I would be suprized if ive seen over 6 in two months). I dont stair scum, and I dont dive quickly, playing rangers, I like to use patience. So where should I start seeing Greater Vaults?
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Old March 10, 2008, 14:19   #2
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With autoscum on, I generally find only a couple of greater vaults in a winning game. The first seems to be in the 1500-2500 range, so you aren't quite deep enough. Greater vaults cannot be created before level 10 (500').

What follows may be considered spoilers, but the bottom line is this: fewer than 1 in 1000 level 30 dungeons will have a greater vault.
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The numbers below are fairly accurate for the first room created on a level. Rooms cannot overlap (or even share an 11x11 area), which drop the odds of successfully creating a big room later.

The odds of even attempting to create a greater vault is (dlvl*dlvl) in 400,000. So, at dungeon level 10, there is a 1/4000 chance of *trying* to make a greater vault. Level 20 -- 1/1000. Level 40 -- 1/250. Level 100 -- 1/40.

The greater vault will not be created 3/6 the time because it goes past the top or bottom of the level, and 5/18 because it goes off the left or right. Together, these make greater vaults fail in 69 of the 108 11x11 areas, so the effective odds are about a third of what I said above.

Lesser vaults are attempted dlvl*dlvl in 266,666 times (plus any time a greater vault fails), and fail in 28 of 108 areas. Monster pits (e.g. orc) are tried dlvl*dlvl in 266,666 times (plus any time a lesser vault fails), and fail 12/108 areas. Monster nests (e.g. jelly) are tried dlvl*dlvl in 400,000 times (plus any time a pit fails), and fail 12/108 areas.

For a given level, the probability that the first room is of each type is below. The distribution for subsequent rooms is similar, with a shift toward more-boring rooms.
Code:
Lvl Greater Lesser  MonNest MonPit  PitLike Crossed L-Shape Normal
 20  0.04%   0.16%   0.18%   0.11%   2.05%   2.23%   4.70%  90.53%
 30  0.08%   0.36%   0.41%   0.25%   2.95%   3.16%   7.05%  85.75%
 40  0.14%   0.63%   0.73%   0.44%   3.76%   3.97%   9.38%  80.94%
100  0.90%   3.96%   4.57%   2.73%   6.82%   6.31%  23.23%  51.48%
Kevin
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Old March 10, 2008, 14:26   #3
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A request -- before re-publishing these numbers, please let me know. There are a couple of subtle approximations I'm using here, but I can re-do this precisely.

Thanks,
Kevin
roustk@alumni.caltech.edu
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Old March 10, 2008, 15:25   #4
The Sparrow
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Thanks for all the info....reading these boards you dont get the feeling that they are that rare. For some reason I see orc nests ALL the time and orc, troll and jelly pits fairly often. Well I hope I get lucky with my next character then. Though that is not likely...I never seem to survive past about level 10 or so with Kobold Rogues
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Old March 10, 2008, 16:44   #5
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Greater vaults are extremely rare before 1500', and fairly rare before 2500'.
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