rne(x)
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Distribution | bounded geometric |

Mean | approx. $ x/(x-1) $ |

Standard deviation | approx. $ \sqrt{x}/(x-1) $ |

**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 Edit

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 articleEdit

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 $ 1-1/x $. 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.