Rne - Revision history

99.239.146.253: cat

2011-05-29T21:09:29Z

cat

Ray Chason: Categories

2011-02-01T23:54:46Z

Ray Chason: Details of use; mention rings

2008-06-12T20:07:19Z

Details of use; mention rings

Ray Chason: Provide standard deviation; relation to the Wikpedia article

2008-06-12T11:49:05Z

Provide standard deviation; relation to the Wikpedia article

Ray Chason: Approximate mean

2008-06-11T02:17:24Z

Approximate mean

Ray Chason: A quick summary of this function; 343; punt on the mean and stddev for now

2008-06-11T01:59:56Z

A quick summary of this function; 343; punt on the mean and stddev for now

Ray Chason: Tweak of lame-looking whitespace

2008-01-10T01:46:32Z

Tweak of lame-looking whitespace

Ray Chason: Give this a DISPLAYTITLE tag

2008-01-10T01:45:41Z

Give this a DISPLAYTITLE tag

Ray Chason: Initial revision

2007-05-06T19:06:40Z

Initial revision

New page

[[image:rne3.svg|thumb|Probability graph of a call of rne(3) with [[experience level]] less than 18.]]

''The correct title of this article is '''rne'''. The title is capitalized due to technical limitations.

'''rne''' returns a random number with a bounded [[wikipedia:geometric distribution|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 [[weapon]]s 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:

{| class="wikitable"
!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
|}

[[Category:Game mechanics]]

@@ Line 38: / Line 38: @@
 For the formulae in the [[wikipedia:geometric distribution|Wikipedia article on the geometric distribution]], the value of <tt>p</tt> for a call of <tt>rne(x)</tt> is the probability that the returned value will be 1; this value is <math>1-1/x</math>.  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 <tt>rne</tt> is bounded.
 [[Category:Random number functions]]
 {{nethack-343}}

← Older revision		Revision as of 23:54, 1 February 2011
Line 39:		Line 39:

	[[Category:Game mechanics]]		[[Category:Game mechanics]]
		+	[[Category:Annotations]]
		+	[[Category:Random number functions]]
	{{nethack-343}}		{{nethack-343}}

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:rne}}
-{{randomvariable|name=rne(x)|graph=rne3.svg|caption=[[wikipedia:Probability mass function|Probability mass function]] of a call of rne(3) with [[experience level]] less than 18.|distribution=bounded [[wikipedia:geometric distribution|geometric]]|mean=approx. <math>x/(x-1)</math>|stddev=approx. <math>\sqrt{x}/(x-1)</math>}}
+{{randomvariable|name=rne(x)|graph=rne3.svg|caption=[[wikipedia:Probability mass function|Probability mass function]] of a call of <tt>rne(3)</tt> with [[experience level]] less than 18.|distribution=bounded [[wikipedia:geometric distribution|geometric]]|mean=approx. <math>x/(x-1)</math>|stddev=approx. <math>\sqrt{x}/(x-1)</math>}}
-'''rne''' returns a random number with a bounded [[wikipedia:geometric distribution|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.
+'''rne''' returns a random number with a bounded [[wikipedia:geometric distribution|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 <tt>rne(3)</tt> 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 [[weapon]]s and [[armor]].  It is also a component of [[rnz]].
+A call of <tt>rne(3)</tt> is used to determine the [[enchantment]] of randomly generated [[weapon]]s, [[armor]], and [[ring]]s.  A call of <tt>rne(4)</tt> is a component of [[rnz]].
 == Mathematical analysis ==
@@ Line 10: / Line 10: @@
 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:
+Here are the probabilities of each return from <tt>rne(3)</tt> for experience levels 1 and 30:
 {| class="wikitable"

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:rne}}
-{{randomvariable|name=rne(x)|graph=rne3.svg|caption=[[wikipedia:Probability mass function|Probability mass function]] of a call of rne(3) with [[experience level]] less than 18.|distribution=bounded [[wikipedia:geometric distribution|geometric]]|mean=approx. <math>x/(x-1)</math>|stddev=''TBD''}}
+{{randomvariable|name=rne(x)|graph=rne3.svg|caption=[[wikipedia:Probability mass function|Probability mass function]] of a call of rne(3) with [[experience level]] less than 18.|distribution=bounded [[wikipedia:geometric distribution|geometric]]|mean=approx. <math>x/(x-1)</math>|stddev=approx. <math>\sqrt{x}/(x-1)</math>}}
 '''rne''' returns a random number with a bounded [[wikipedia:geometric distribution|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.
@@ Line 35: / Line 35: @@
 |10||0||1/19683
 |}
 [[Category:Game mechanics]]
 {{nethack-343}}

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:rne}}
-{{randomvariable|name=rne(x)|graph=rne3.svg|caption=[[wikipedia:Probability mass function|Probability mass function]] of a call of rne(3) with [[experience level]] less than 18.|distribution=bounded [[wikipedia:geometric distribution|geometric]]|mean=''TBD''|stddev=''TBD''}}
+{{randomvariable|name=rne(x)|graph=rne3.svg|caption=[[wikipedia:Probability mass function|Probability mass function]] of a call of rne(3) with [[experience level]] less than 18.|distribution=bounded [[wikipedia:geometric distribution|geometric]]|mean=approx. <math>x/(x-1)</math>|stddev=''TBD''}}
 '''rne''' returns a random number with a bounded [[wikipedia:geometric distribution|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.