can we look at the spell fail percentages

[Sky]

call me anal but if i see 34% spell fail i expect the spell to fail 34% of the time.

i managed to fail 5 times in a row a 24% spell fail. that happen .. maths .. 0.1% of the time. i would be ok with that if not that i keep failing strings of 3/4 failures on 5% spell fails. with ANY class, ANY spell. i zap a rod 6 times and fail the 5% activation 5 times out of 11 tries - that is NOT 5% fail.

how exactly are spell fail rates calculated? because i'm at the point that i already know a 50% spell fail will need to be tried at least 5 times before it passes.

[PowerWyrm]

RNG weirdness. I've managed to fail a 1% spell five times in a row once, which means the RNG rolled 0 five consecutive times when pulling randomly a number between 0 and 99.

[Sky]

just cast rememberance, 31% fail, 3 castings = 3 fails, 2 castings 2 fails, 3 castings 2 fails.
thats 7 fails to 1 pass. this are the only instances of my casting this spell; i'm not ignoring cases where the spell passes.

[Sky]

RNG weirdness. I've managed to fail a 1% spell five times in a row

and you don't think there's anything wrong with that ?
1/10,000,000,000 fail rate. i would think it's *more likely* that the fail rate RNG doesn't actually work the way it should.

[Derakon]

People have done in-depth analyses of Angband's RNG. It's really quite good. You just notice the strings of failures far more than you notice the strings of successes.

Every time I've decided to take notes on how frequently things actually succeed/fail over the long term, my results have closely matched the listed percentages.

[Pete Mack]

A .1% chance is actually pretty high. You should notice it roughly every 1000 times you make a decision--so about once a game. In any case, a 24% fail rate is not a spell you can count on during a fight. Getting ready for a fight, sure.

[kandrc]

i managed to fail 5 times in a row a 24% spell fail. that happen .. maths .. 0.1% of the time.

Actually, it's not. .24^5 ~= .0001 is the probability that if you flip your weighted coin exactly 5 times you will get exactly 5 heads (where heads is our failed roll case). It is not the probability of flipping 5 heads in a row over the course of n > 5 flips. That analysis is far more complicated. See this page:

http://www.askamathematician.com/2010/07/q-whats-the-chance-of-getting-a-run-of-k-successes-in-n-bernoulli-trials-why-use-approximations-when-the-exact-answer-is-known/

The exact solution (scroll down to "Jabberwocky" and see the last formulation above it) involves the difference of a pair of infinite series of a bunch of ugly binomial coefficients.

Now you can say, "But I started at zero when I tried to cast the spell, then I rolled 5 heads in a row, therefore .24^5." While this is not strictly incorrect, it is a biased observation. How many times does 1/1000 not happen in a game? This is Derakon's point. We (humans) evolved into pattern-recognizing machines because seeing patterns was good for our survival; it's easy to show that we err on the side of caution (seeing patterns where they don't actually exist). This is why you notice 5 fails in a row, but you fail to notice .76^n < .24^5 implies n >= 26 successes in a row.

[Sky]

if it were not that this is a spell which isn't cast in combat. i just now cast holy word 4 times (3 fails), then 4 times (3 fails). that's a 75% fail rate, and the game says 31%.

i've literally just used this spell under "test" conditions - due to the fail rate, the high mana cost, and the fact that it's only really useful when strongly wounded.

i understand the difference between an open set and a closed set. i failed consistently between 66% and 75% of the castings when the fail rate is 31%. or do you think every set i observe is an outlier?

[Gwarl]

You need a sample size of at least 25 before you can go about drawing conclusions from it. Also kandrc's explanation is very good.

[Sky]

no it's not, because we haven't drawn an infinite sequence. i.e. i have not "not taken into consideration all the time where the observed even DID NOT take place", but i ran a character from CL1 to CL47 and every time i cast high fail rate spells, it's never what's listed.
this, incidentally, applies to every character i play. yes i know what observation bias is.

[Derakon]

I encourage you to, for one level, record each time you attempt to cast a spell, whether it succeeded, and what the listed rate was. I don't think you're likely to convince anyone of anything without some hard data to back it up.

[Grimborn]

I've noticed this same exact thing. Seems most likely to me that there's a bug with the spell based RNG. Surprised to see so many people defending it. I noticed this on my Dunadan Rogue. Maybe it's a race/class/equipment specific bug, so it only shows up in certain cases, that's why other people aren't noticing it. Failing medium/low percentage spells numerous times in a row, with rests in between to generate mana. Definitely doesn't seem right.

[Sideways]

Everybody "notices" it and gets the feeling that spells fail way more often than they should, sometimes. I missed a spell with 3% fail three consecutive times the other day, which has a 1-in-37,000 chance of happening if you look at three random castings.

But when you actually keep track over the long-term and do the math, it's not a real effect. You just notice those streaks when they happen because of how annoying they are.

[Pete Mack]

When considering observation bias, it's useful to knock off one round of probability, so instead of three 3% events in a row, assume you're looking at two (or a 1/1000 chance.) The reason is, you don't even notice a failure until the second event, so there are a whole lot of single event failures you didn't notice along the way. This is mentioned in Rosencranz and Guildenstern, but of course it's hilarious when they discuss it--after around 80 consecutive "heads" in a row.

[kandrc]

Not only does everybody notice it, but somebody posts a new thread about it frequently. I wouldn't be surprised if there are 50 threads making the claim between here and r.g.r.a.