Damage vs Accuracy

[Ighalli]

Originally Posted by Derakon

Yes, many times. It is on average quite random. Humans are bad at recognizing randomness.

What seems stranger than the allegedly streaky RNG is how frequently the fairness of it is questioned.

[Pondlife]

Originally Posted by Ighalli

What seems stranger than the allegedly streaky RNG is how frequently the fairness of it is questioned.

I think the mathematical definition of random differs from the "common sense" definition of random. See for example "The Black Swan: The Impact of the Highly Improbable" by Nassim Nicholas Taleb; or Apple's decision to change the shuffle algorithm from true random because that didn't "feel" random to users.

I beleive the Angband RNG is random in the mathematical and statistical sense; but often it seems "unfair" or "streaky" to humans.

[Pete Mack]

Um. No pseudorandom RNG is "random in the mathematical sense." And there are a whole lot of statistical ways to analyze a sequence for randomness. I suspect the angband RNG is good under some of the basic ones, which is usually good enough.

[Gordon]

Well, 1 in 18593 is slightly less probable than flipping a coin and having it come up heads 14 times in a row. I think any intelligent being would look upon that coin with suspicion. That said, I was glad to hear that this RNG had been tested for correlation. Serial correlation analysis is just as important as uniformity analysis when evaluating a RNG and is often neglected.

[Pete Mack]

When evaluating likelihood of an event like repeated fails on a 5% throw, it's better to ignore the first failure, as you are looking at a case where there is at least one failure. So the first failure should be considered a prior. 1 in 18000 isn't all that unlikely when integrated over all games and players.

[t4nk]

Originally Posted by Gordon

One other thing. When I was looking for a monster to try the Wand of Annihilation on, I ran into Ariel, Queen of Air. Seeing as I knew that the wand wouldn't work on her, I cast Mana Storm instead. It failed five times in a row. With @'s current 14% chance of failure for this spell, the probability of that happening by chance is 1 in 18593. Has anyone checked the RNG used for spell failure for correlation?

This is a fun question. I searched the internet for answers and this article seems pretty good: http://www.askamathematician.com/201...swer-is-known/
I skipped the formulas, of course (maybe Nick can verify them ). But there are also some human language examplanations and even some code. So I played a bit with it on my machine. If you cast mana storm 100 times, you'll get a streak of 5 or more failures in a row with about 1% probability. 18000 casts give you more than 50% chance of getting a bad run.
I guess there is a useful lesson here - always be prepared for the worst

[Gordon]

Here is a prettied up version of a python script for calculating this that I found on a link on that site.

import argparse

argparser = argparse.ArgumentParser(description='Calculate the probability of run of n events in m trials where p is the probabilty of an event')
argparser.add_argument('-n', type=int, required=True, help='run length')
argparser.add_argument('-m', type=int, required=True, help='number of trials')
argparser.add_argument('-p', type=float, required=True, help='probability of an event')
args = argparser.parse_args()

N = args.n
M = args.m
p = args.p
q = 1-p #probability of failure

#setting up P_i (P[i] will be the probability that we see a run of length n in i flips)

P = [None for i in range(0,M+1)] #initialize list to all Nones

for i in range(0,N): #set boundary conditions, (not including P_N (r)
    P[i] = 0

P[N] =p**N #P_N (r) is now equal to p^N


#now for main recursion (using a loop here instead)
for i in range(N,M):
    P[i +1] = P[i] + (1-P[i-N]) * q * P[N]

print 'A run of',N, 'events of probability',p, 'has a chance of 1 in',1.0 / P[M], 'of occuring in',M, 'trials'

[Chud]

The other thing people often lose track of (or don't think about in the first place) is just how many trials are really being run in a typical game. I'll bet it's a *lot* more than most people realize, so when you do the math and come up with a 1 in 18,000 chance of something, you think "come on, that'll never happen" when in fact there are so many trials that it's to be expected a lot more than you think.