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Old March 4, 2011, 18:49   #21
camlost
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Quote:
Originally Posted by myshkin View Post
This is not a simple calculation. The value for a speed ring is 5 + MB(5) + supercharges. MB(5) is a pseudo-normal distribution capped at four standard deviations. At dlvl 91, where his ring dropped, its mean is 3 with probability 71/128 and 4 with probability 57/128, while its standard deviation is 1 with probability 3/4 and 2 with probability 1/4. The code then supercharges the value by one every time it passes a one-in-two test.

I am presently too lazy to run an exact calculation, but some Monte Carlo tests indicate that the probability that a speed ring dropped on dlvl 91 has pval >= 21 is about 0.0002. (By comparison, P(pval >= 15 | dlvl 91) is about 0.0136.)
Assuming random number generation. IIRC, an old version of Angband had some trouble with getting trapped in a low-probability loop.
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Old March 4, 2011, 20:57   #22
Timo Pietilš
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Quote:
Originally Posted by PowerDiver View Post
I think you miscounted the 0s and it is 1 in 5000. Still pretty rare.
Oops, so I did. So not that rare, but still rare. I think The One Ring had once rarity of 1/1000000. Literally. It basically existed in game, but nobody found it. Since then artifact generation has been revised several times.
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Old March 5, 2011, 00:20   #23
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Quote:
Originally Posted by camlost View Post
Assuming random number generation. IIRC, an old version of Angband had some trouble with getting trapped in a low-probability loop.
My simulation used the actual random number code that the latest Angband has, although an actual game would have less predictable numbers of RNG calls between speed rings. A few months ago, d_m converted z-rand.c to the WELL1024a RNG (see this paper for a description), and it seems pretty solid.
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