Clusters of rod/staff fails

[grumbleguts]

This was discussed in the 90s, but it still seems to be relevant today.

If you use a rod or staff which fails on the first attempt it seems more likely to fail on the second and subsequent attempts than the failure chance would imply.

So you have this rod with a 15% failure rate, and you zap it because you can't see a damn thing because you are blinded but the bloood pouring into your eyes from the deep gash which is seeping poison, and a little curing never hurt anyone.

You fail to zap the rod properly. OK fine, I still have some HP I can survive another hit
You fail to zap the rod properly.
You fail to zap the rod properly.
You fail to zap the rod properly.
You die.

Then there'll be 12 times in a row where it will work as advertised.

Has anyone else noticed this? Or is it confirmation bias?

[Pete Mack]

4 failures in a row is a 1 in 2000 chance. That is expected roughly every 5 games, assuming
a. you use devices about 400x per game.
b. You retry the device on failure.

A more useful estimate is 1 in 300 conditional chance of 3 failures in a row, following the first failure in the sequence. Not a bad risk, but still something you can't mess around with as a matter of course. Anything near 1% is a risk you should only take with deliberation. 4 fails in a row doesn't qualify. You had plenty of chances to heal, and certainly on the last fail you'd have died even if it was successful: the monster attack still would have killed you.

[PowerWyrm]

I've failed 1% fail spell 5 times in a row once. An average is an average on infinite tries, you can't expect x% fail to fail x times out of 100 for every 100 tries you do.

[grumbleguts]

The was brought up in the usenet group rec.games.rogue.angband, or whatever it was called, in the mid nineties, it seems a lot of people noticed failures come in clusters, I am well aware of the maths involved in calculating the probabilities, and strings of failures still today appear more often than their theoretical probabilities would suggest.

I got 11 failures in a row which is approximately 1 in 10.5 million.

Now I get that a 1 in 10.5 million still has that chance. But it happened twice in 45 minutes. And it was a phenomenon that people have noticed in the past.

[takkaria]

The was brought up in the usenet group rec.games.rogue.angband, or whatever it was called, in the mid nineties, it seems a lot of people noticed failures come in clusters, I am well aware of the maths involved in calculating the probabilities, and strings of failures still today appear more often than their theoretical probabilities would suggest.

I got 11 failures in a row which is approximately 1 in 10.5 million.

Now I get that a 1 in 10.5 million still has that chance. But it happened twice in 45 minutes. And it was a phenomenon that people have noticed in the past.

The RNG totally changed since the r.g.r.a days. Maybe twice. It's just confirmation bias.

[Pondlife]

Testing RNGs is quite difficult. A couple of test suites are:

Dieharder: A Random Number Test Suite:

http://webhome.phy.duke.edu/~rgb/General/dieharder.php

TestU01:

http://simul.iro.umontreal.ca/testu01/tu01.html

Running the angband RNG through something like the dieharder suite might give some assurance that there are no serious problems.

[takkaria]

Testing RNGs is quite difficult. A couple of test suites are:

Dieharder: A Random Number Test Suite:

http://webhome.phy.duke.edu/~rgb/General/dieharder.php

TestU01:

http://simul.iro.umontreal.ca/testu01/tu01.html

Running the angband RNG through something like the dieharder suite might give some assurance that there are no serious problems.

Angband uses the WELL1024a RNG. It is generally considered a pretty decent non-secure PRNG based on what I've read online, though admittedly I'm barely even an amateur when it comes to RNGs.

[Pondlife]

Yes, WELL looks fairly reasonable. I've used the similar but older mersenne twister in my own projects.

The fact that the Angband maintainer has taken the time to choose an independent RNG function is a good sign in itself. IME many software RNG problems stem from one of two causes:

a) The developer uses the languages' own rand() function, which is often poorly implemented with a linear congruential generator; or

b) They write their own random function, which is often poorly implemented with an LCG.