Spell Failure Rate Question

[Camcolit]

Hello everyone,

Just a quick question - I'm actually playing the Zangband tk variant but afaik the spell failure system is the same, maybe someone can confirm. My spell failure rate shows as the 5% minimum but I seem to fail a lot more than that. I get two failures in a row pretty often which is extremely unlikely at 5%. I'm not stunned or even in combat. Just randomly walking around the dungeon and I cast detect monsters and fail twice in a row. Any ideas? Thanks a lot.

[Zyphyr]

The RNG hates you. Don't take it personally though, it hates most people.

[Camcolit]

well it could be just bad luck, sure. It's natural to notice spells that fail a lot more than those that succeed. It's very hard to judge whether it's off or not, just seems that I've had a run of double-fails that's very improbable statistically if the rate is indeed 5%.

[jens]

Well, after each time you have a failed spell, you have a 1 in 20 chance to fail again. You are probably casting lots of spells, so it would not be all that uncommon...

[Camcolit]

Well I play a vampire warrior-mage that is more warrior than mage at the moment, so I don't cast that much. Just wanted to find out if there was any hidden factor that increased spell failure that everyone knew about (except me). Now that I know there isn't I'll just chalk it up to the RNG - thanks

[scud]

A couple of days ago I had a monumental sequence of Identifails at 33%. I'm quite used to six or more screw-ups, but this time I reckon I started counting at around 10-11 fails, and counted a further seven. Eighteen consecutive fails is a one in 38.7m chance (I've probably miscalculated).

I've also starved to death trying to satisfy hunger, having started spellcasting immediately I hit 'weak'.

I guess we don't remember to good rolls...

[zaimoni]

A couple of days ago I had a monumental sequence of Identifails at 33%. I'm quite used to six or more screw-ups, but this time I reckon I started counting at around 10-11 fails, and counted a further seven. Eighteen consecutive fails is a one in 38.7m chance (I've probably miscalculated).

Yes... (0.67)^18 ~ 0.074% i.e 1 in 1,351 chance for a theoretical uniform distribution.

[Timo Pietilä]

Yes... (0.67)^18 ~ 0.074% i.e 1 in 1,351 chance for a theoretical uniform distribution.

If I understood correctly that would be 18 consecutive successes, not failures. Failures would be 0.33^18 ~= 2.154*10^-9 which is about 1 in 464246974

[EpicMan]

Except that the older rng, which I believe is the one Zangband has, has some issues. One failure seems to make successive failures likely. That's why they changed the RNG in Vanilla.So your initial failure rate may be 5%, but a failure will make a second one much more likely.

[Derakon]

I don't know about "much". The RNG used in Vanilla now is slightly better than the old one, but it's not like the old one was bad. It compared decently well to the Mersenne Twister (I remember someone did a randomness study on the two awhile back). Yes, it's a bit prone to sequences of similar numbers, but IIRC not to the extent that you can blame every double-failure on it.

[Tiburon Silverflame]

IIRC, the old RNG was a linear congruential...and it compares *horribly* to MT, in a proper statistical analysis. Sure, over 10,000 trials, they probably give similar results...but LC is known to give particular shorter-term patterns.

You certainly can't blame every double failure on the RNG...and with combat spellcasting, it's probably true that you can blame only a few, unless the "spell success" method has an isolated RNG all to itself. If it doesn't, then in combat situations you'll have attack and damage rolls, presumably using the same RNG, and therefore your next spellcasting attempt won't be "consecutive" from the standpoint of the generated numbers.

[zaimoni]

IIRC, the old RNG was a linear congruential...and it compares *horribly* to MT, in a proper statistical analysis.

The old complex RNG was/is an addition-shift initialized by a linear-congruential.

Just about anything other than Mother-of-All compares horribly to Mersenne Twister for non-cryptographic purposes.

If it doesn't, then in combat situations you'll have attack and damage rolls, presumably using the same RNG, and therefore your next spellcasting attempt won't be "consecutive" from the standpoint of the generated numbers.

Which is why the important measure is correlation across phase shifts (which is precisely where linear-congruential is awful -- the best known LCG as of 2004 has detectable strong correlation at sampling interval 8, but not intervals 2..7).

By contrast, the old RNG was not empirically testable [on my end] as problematic for events with probability greater than 1/27.

[zaimoni]

If I understood correctly that would be 18 consecutive successes, not failures. Failures would be 0.33^18 ~= 2.154*10^-9 which is about 1 in 464246974

Yes, agreed.

[Mondkalb]

I have learned (through many many deaths of characters) that a failure rate of 5% means: Don't rely on it in critical situations. It will fail four or five times in a row, if necessary to kill your character. ^^

[Max Stats]

I'm glad I'm not the only one who thinks repeated failures are too common. I always wondered if the RNG was susceptible to occasional lack of independence between successive numbers. I assumed I was just noticing the failures and ignoring the successes, but maybe there is something to it.