Wrath of God. Twice.

[Tiburon Silverflame]

http://www.lavarnd.org/what/nist-test.html

This page suggests that the Linux/BSD generators are probably OK for our very relaxed purposes, *in their current versions.* z-rand.c doesn't provide a point of reference for the version used as its basis, beyond the general copyright date. And the one time I did manage to find the code for one of the current versions, it didn't look methodologically similar.

http://www.iro.umontreal.ca/~simardr/indexe.html

has links to a number of tests and generators, including C code.

[Pete Mack]

@Zaimoni--
It plays well, so long as there aren't any 1/27 chances. (Rod activation comes to mind.)

[zaimoni]

I'm impressed - that's a brilliant piece of analysis. Bagsy not be the one to tell Takkaria that we have this problem!

Well, I'm not sure that it's a "problem". (This particular deviation plays well with untrained intuition about probability.)

[Magnate]

Well, the fact the RNG state is saved allows studying the RNG distribution by savescumming.

A particularly easy case, is low-probability enchantments. Recall the basic approximation from the first two weeks of a 700-level real analysis course,

(1-1/n)^(n-1) < 1/e < (1-1/n)^n .

The convergence of the upper and lower bounds is fairly rapid.

In particular, e^(-3) is approximately 0.0498 so for an event with probability 1/n, a run of 3n failures should be pretty close to a 5% probability event. e^(-4) is approximately 0.0183, so a run of 4n failures should be pretty close to a 2% probability event.

Empirically (my own testing, V3.0.9), the critical value appears to be near n=27. Runs of 3n failures suddenly become far more common than 5% of the time then.

[Protocol: save-load so that all copies of the game start from the same internal time. For each instance k, walk k-1 steps before reading the enchant scroll. A 1/26 enchant doesn't have a naked-eye discernible difference from a 5% chance to fail all 78 times; a 1/27 enchant empirically fails all 81 times about 1 in 3.]

I'm impressed - that's a brilliant piece of analysis. Bagsy not be the one to tell Takkaria that we have this problem!

[zaimoni]

Well, the fact the RNG state is saved allows studying the RNG distribution by savescumming.

A particularly easy case, is low-probability enchantments. Recall the basic approximation from the first two weeks of a 700-level real analysis course,

(1-1/n)^(n-1) < 1/e < (1-1/n)^n .

The convergence of the upper and lower bounds is fairly rapid.

In particular, e^(-3) is approximately 0.0498 so for an event with probability 1/n, a run of 3n failures should be pretty close to a 5% probability event. e^(-4) is approximately 0.0183, so a run of 4n failures should be pretty close to a 2% probability event.

Empirically (my own testing, V3.0.9), the critical value appears to be near n=27. Runs of 3n failures suddenly become far more common than 5% of the time then.

[Protocol: save-load so that all copies of the game start from the same internal time. For each instance k, walk k-1 steps before reading the enchant scroll. A 1/26 enchant doesn't have a naked-eye discernible difference from a 5% chance to fail all 78 times; a 1/27 enchant empirically fails all 81 times about 1 in 3.]

[Tiburon Silverflame]

I really want to do a RNG test where I take about 10 million rolls from 1-100 and measure both the probability of each number showing up (it'll probably be close enough to 1%) and the probability of each number showing up based on what the previous number is. It's pretty trivial to code...if I knew how to easily.

As in, you know the algorithm, but don't know C? The algorithm is trivial...the simplest approach is just create a 2D array, and increment the [prev,current] bucket.

But that isn't necessarily the only flaw. There are other forms of cyclic behavior. A very brief look at the RNG gives me pause; the root RNG is a linear congruential, which is an awful basis, but there's manipulation going on that may improve it. How good is it? Not sure. It claims a basis in Berkeley's random.c...but as of when? The web shows the 1995 Berkeley code in /dev/random.c, and suffice it to say, it looks NOTHING like the code in z-rand.c. Personally, I'd rather see something with proven-good performance...a fast version of Mersenne Twister, which can readily be found as freeware, or some of the more recent members of the same family such as WELL:

http://www.iro.umontreal.ca/~panneton/WELLRNG.html

WELL's a tiny lil guy...

I've definitely noticed too many cases of cluster behavior for me to think there isn't some memory in the RNG.

[Derakon]

The following items are native to dungeon level 100:

Power Dragon Scale Mail
Bladeturner
The One Ring
The Massive Iron Crown of Morgoth
The Mighty Hammer 'Grond'
Wrath of God

Now, Wrath of God is the most common of these items. But that still means that every monster except for Morgoth must pass an out-of-depth check to generate it, which significantly increases the effective rarity of the item.

(No item is native to a depth below level 100)

[TJS]

Is WoG that rare? I noticed earlier I had 5 copies from just walking about at the higher levels for a while and sold 3 of them.

[fizzix]

Definitely. I just saw an AMHD in pit-like special room (not a vault) at 1550'. AMHD is dlvl 2150' monster, so it was 600' OOD. I thought that wasn't possible. Apparently it is. In starting room there was some lonely tiny monster (can't remember what), and it dropped Bard. I was very very tempted to try to kill AMHD, but realized that at this point even with resists (I have rpoison from the only elvenkind I have seen yet) it can still kill me instantly. Then I realized that I don't have any arrows, so whole temptation was a moot point.

A recent character of mine was killed by an unvaulted Azriel at dlevel 52. Azriel was 12 levels OoD. Definitely possible.

[ewert]

I also like what this change has done to black market. There's lots of useful stuff, and much more stat potions in there. Even though I am selling less "junk" (as way less armor/weapons are generated) and thus as a compulsive pick&sell guy spending less time shopping, I actually wait for checking black market after a sortie, especially if have the 24k+ whatever needed for stat potions, as they are quite plentiful in BM now. Just saw a potion of augmentation in there too, drool, just didn't have the erm, was it what 160k ... =(

[Timo Pietilä]

Yeah my priest was like that too, kept waiting for the sudden one in a billion insta death. =P

This new paladin and I'm again feeling like I am getting lots of artifacts. Then I finally kinda figured it out I think. It is just the lack of JUNK armor/weapons. Those amounts of junk take rl time to sort through, pick up, etc., so I think it just feels so much more plentiful because one is not sorting through that junk and actually playing even faster in rl time because of it.

That might be it. I'm also feeling that I'm getting a lot of artifacts, but in fact I'm not. I have pretty ordinary set considering my turncount and depth.

[ewert]

Yeah my priest was like that too, kept waiting for the sudden one in a billion insta death. =P

This new paladin and I'm again feeling like I am getting lots of artifacts. Then I finally kinda figured it out I think. It is just the lack of JUNK armor/weapons. Those amounts of junk take rl time to sort through, pick up, etc., so I think it just feels so much more plentiful because one is not sorting through that junk and actually playing even faster in rl time because of it.

[Timo Pietilä]

Okay you are killing the OoD checks, lol.

Definitely. I just saw an AMHD in pit-like special room (not a vault) at 1550'. AMHD is dlvl 2150' monster, so it was 600' OOD. I thought that wasn't possible. Apparently it is. In starting room there was some lonely tiny monster (can't remember what), and it dropped Bard. I was very very tempted to try to kill AMHD, but realized that at this point even with resists (I have rpoison from the only elvenkind I have seen yet) it can still kill me instantly. Then I realized that I don't have any arrows, so whole temptation was a moot point.

This is going to be one seriously odd game. I don't know if RNG loves me or hates me, but she certainly is playing tricks to me.

I wish every game would be like this has been this far. I don't remember when I have had this many surprises last time. It's invigorating.

[ewert]

Okay you are killing the OoD checks, lol. Considering my warrior who got to Sauron saw 1 rod of detection, that has less allocation rarity but shallower dlvl, so I'm still willing to bet on RNG funkiness. Personally I have felt that artifacts have increased, but it just can't affect that in such a way except for the rare base items (the code is totally separate aside base item for artifact check, and there are LESS base items generated with the modified allocation file!?). On the other hand, with current overall amounts of rarity in the file, I'm thinking of going over the list again after my next char and tune some of the more powerful items a smidgen down, and some maybe a smidgen up like rod of detection (the other rods do not appear after dlvl 80, and my warrior actually lost his treasure rods before finding detections and he had like a stack of 4 kept up till 80).

[Timo Pietilä]

Hello.

I'm playing Dwarf Priest and just found my second Wrath of God. Nothing special, you think? Well, first one was in dlvl 850' lesser vault. Second is in BM when I'm still diving to stat-gain (not yet at stat-gain: 1250' recall depth). No other dungeon book seen yet.

Weirdness continues. Now I got Godly Insights at 1550'. After that Ethereal Openings at BM.

This Ewert change that affects TMJ -problem (almost removes it) has made useful stuff a bit more common than I expected: lowering weapons and armors increases everything else, and that is showing pretty obviously. Consumables are definitely not a problem with these changes.