RoS +19 -- is this a record?

[Jay]

After I killed Carcharoth at level 94, he dropped something I've never seen in my years of Angband-ing: a +19 RoS! I can't recall seeing anything over +15 in the past.

So, like the subject line says: Is this a record? How did this happen? What are the odds? I seem to recall reading here at some point that there was theoretically no limit to how high the bonus number could get but the chances of the number going up gets significantly smaller with each subsequent increase. True? Oh, and this is with 4.2.5.

[PowerDiver]

By a remarkable coincidence, I was searching for some old exploit just *yesterday*, and I came upon https://angband.live/ladder/ladder-show.php?id=21757
from PowerWyrm mentioning RoS +24.

[backwardsEric]

The bit of blather below was from conflating dragon armor of speed, base d5, with the supercharging done for rings of speed. As pointed out by others, the base bonus for rings of speed is 4+M6, a value between 4 and 10 dependent on the generation level for the item. The base bonus is increased by the result of a sequence of coin flips: tails end the sequence and heads adds one to the bonus and continues the sequence. If one got the most likely base bonus, 8, for a ring of speed with a generation level of 94, the chance that it would be boosted to +19 is 1/2^12.

WRONG:
The base bonus is 1d5. Anything beyond that is set by a series of fair coin flips: tails ends the series; heads adds one to the bonus and continues the series. So once you get a ring of speed, the chance that it is +19 is 1/5 * (1/2^19 + 1/2^18 + 1/2^17 + 1/2^16 + 1/2^15) = 31 / (5 * 2^19) or roughly a 1.18 chance out of a hundred thousand. Roughly 3.70 out of ten million rings of speed would match the one PowerWyrm found.

[PowerDiver]

Surely creation depth has to figure in somehow. Speed rings sure seem to get better the deeper you go. Am I wrong yet again?

Also, 4.2.5 object.txt mentions SPEED 4+M6 which is better than 1d5 if I understood the comments at the top of the file. Have speed ring plusses changed much in recent versions?

[bboxman]

4+M6 is nearly always +10 base or almost, and then the M gives a series of coin flips for extra +1s.

A +19 ring is around a 1/512 occurrence (per RoS, maybe account for M 1/700-1/800) at depth.

Here's a char with a RoS +19 and a RoS +18 -

https://angband.live/ladder/ladder-show.php?id=26310

[backwardsEric]

Since I bungled the base bonus, I corrected my earlier post. The 4+M6 base gives a value between 4 and 10 dependent on the generation level for the item. For Carcharoth killed on level 94, the items should be generated at level 100, and the ring of speed's base value would most likely be 9. The coin flips are not specified because there is an 'M' in the dice: they are from a special case in obj-make.c's apply_magic().

[PowerDiver]

I thought that I remembered the M thing was level dependent, but the text file specifically says

# M4 uses the m_bonus function to generate a number between 0 and
# 4 according to a normal distribution.

That's highly misleading. Assuming it cannot be explained simply, how about changing it to something like

# M4 has a range from 0 to 4 that is strongly biased according to the generation depth. It is complicated. For details see m_bonus in z-rand.c

[Jay]

So it’s rare, but not nearly as rare as the current record holder of +24. Thanks for the replies.