# rne

rne(x)

 Probability mass function of a call of rne(3) with experience level less than 18.

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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