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Old November 9, 2017, 22:01   #11
Derakon
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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.
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Old November 10, 2017, 00:05   #12
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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.
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Old November 10, 2017, 00:19   #13
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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.
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Old November 10, 2017, 00:44   #14
Pete Mack
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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.
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Old November 10, 2017, 01:08   #15
kandrc
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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.
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Old November 10, 2017, 02:11   #16
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At this point, I have no reason to doubt that the RNG is producing sufficiently random numbers. If someone supplies me with more than anecdotal evidence, I'm happy to look into it in more depth. Specifically, that evidence would have to be something like
  • Sufficient data - say 40-50 attempted casts, although 100 or more would be better - with a record of how many attempts it took to cast the spell successfully, and
  • Analysis of the results, preferably with a chi-squared test of the observed distribution vs the expected (which should probably be a Poisson distribution).
I intend to point back to this post every time this subject comes up
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Old November 10, 2017, 04:07   #17
Pete Mack
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It's worth noting noting that sequential casts aren't actually sequential RNG rolls, because there are other things going on like noise and random monster generation, as well as cast vs. move choices for LOS monsters. It's exceedingly unlikely that a series of failures is in any way correlated with some periodic misbehavior of the RNG. To be convincing, any analysis has to include an autocorrelation as well, using (say) mod 100 arithmetic to simulate spell-casting.
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Old November 10, 2017, 09:31   #18
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What would happen if instead of using the RNG directly for rolling d100 you had it backed up with an array of numbers between 1 and 100, using the RNG to pick up one of these numbers and removing it from the array until the array is empty? You would guarantee that a x% fail spell actually fails x% of the time, but of course you would bias the RNG by giving a straight linear distribution of values. Could be done for spells only if players are actually caring about spell fail rates.
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Old November 10, 2017, 09:37   #19
PowerWyrm
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Quote:
Originally Posted by Pete Mack View Post
It's worth noting noting that sequential casts aren't actually sequential RNG rolls, because there are other things going on like noise and random monster generation, as well as cast vs. move choices for LOS monsters. It's exceedingly unlikely that a series of failures is in any way correlated with some periodic misbehavior of the RNG. To be convincing, any analysis has to include an autocorrelation as well, using (say) mod 100 arithmetic to simulate spell-casting.
If you want to see an actual bias in the RNG, just use the Stair Creation spell. I can guarantee you, that deep in the dungeon, the spell will produce an incredible amount of up staircases before you can get a down staircase. And that's supposed to be a coin flip. To counter that, I had to actually code something in PWMAngband that counts the number of up staircases in a row generated by the spell and force placing a down staircase instead after 3-5 unsuccessful tries.
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Old November 10, 2017, 09:57   #20
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Powerwyrm: if you are always looking for down staircases, and always pick the first one, the expectation is 2x more up than down observed. That said, it's quite possible that there's a bug in the low order bit. But I would not count on it.
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