Rne
The correct title of this article is rne. The title is capitalized due to technical limitations.
rne returns a random number with a bounded geometric distribution. That is, each possible return greater than 1 has a probability that is a fixed fraction of the next lower return, up to a given limit. The fraction is 1 divided by the parameter of rne; thus rne(3) returns 2 one third as often as it returns 1, 3 one third as often as 2, and so on.
The maximum return is 5 while the hero's experience level is less than 18; from that point, it is the experience level divided by 3 and rounded down. As experience level cannot exceed 30, the upper bound of rne can never be greater than 10.
rne is used to determine the enchantment of randomly generated weapons and armor. It is also a component of rnz.
Mathematical analysis
The effect of experience level on the return from rne is often overstated. Only possible returns greater than 5 are affected, and these are improbable events in any case. Thus, while a level 30 hero could in principle find a random weapon with +10 enchantment, this is a rare event indeed.
Here are the probabilities of each return from rne(3) for experience levels 1 and 30:
| Return | Level 1 | Level 30 |
|---|---|---|
| 1 | 2/3 | 2/3 |
| 2 | 2/9 | 2/9 |
| 3 | 2/27 | 2/27 |
| 4 | 2/81 | 2/81 |
| 5 | 1/81 | 2/243 |
| 6 | 0 | 2/729 |
| 7 | 0 | 2/2187 |
| 8 | 0 | 2/6561 |
| 9 | 0 | 2/19683 |
| 10 | 0 | 1/19683 |
