rne
| rne(x) | |
|---|---|
 | |
| Distribution | bounded geometric |
| Mean | approx. 
|
| Standard deviation | approx. 
|
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.
A call of rne(3) is used to determine the enchantment of randomly generated weapons, armor, and rings. A call of rne(4) is 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 |
Description in terms of the Wikipedia article
For the formulae in the Wikipedia article on the geometric distribution, the value of p for a call of rne(x) is the probability that the returned value will be 1; this value is 
. The mean and standard deviation for the above infobox are calculated accordingly; but they are approximate, as for the sake of simplicity they give the values for the unbounded geometric distribution, and the return value from rne is bounded.
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