Rnl - Revision history

Ardub23: NHW:Style guide#Capitalization – The game doesn't capitalize 'luck'

2026-04-12T22:13:54Z

NHW:Style guide#Capitalization – The game doesn't capitalize 'luck'

Furey: 37 references. 35 of them are to NetHack 3.4.3 source code. Article has no version tag. It is {{nethack-343}}.

2024-07-03T01:55:09Z

37 references. 35 of them are to NetHack 3.4.3 source code. Article has no version tag. It is {{nethack-343}}.

Cathartes: untrapping can specifically pacify non-@, not non-human

2022-04-02T00:57:16Z

untrapping can specifically pacify non-@, not non-human

Cathartes: "adjustment" is rounded toward nearest integer, not 0

2022-03-27T15:46:06Z

"adjustment" is rounded toward nearest integer, not 0

Darth l33t: /* Formula */ rewrite to clarify and remove redundancy

2022-03-08T20:17:21Z

‎Formula: rewrite to clarify and remove redundancy

Actual-nh: /* Events based on Luck and other stats */ Grammar/style

2021-06-27T01:29:24Z

‎Events based on Luck and other stats: Grammar/style

YakumoRising: /* Mathematical analysis */

2020-08-20T23:42:15Z

‎Mathematical analysis

RedFeather: /* Events based solely on Luck */ Corrected formula for wiz

2020-03-31T23:01:31Z

‎Events based solely on Luck: Corrected formula for wiz

Ardub23: {{distinguish}} for hatnote

2020-01-28T04:35:56Z

{{distinguish}} for hatnote

Ardub23: Formatting fixes and layout improvements (split the big table into three); more consistent wording

2020-01-23T23:31:05Z

Formatting fixes and layout improvements (split the big table into three); more consistent wording

Show changes

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:rnl}}
 {{distinguish|rn1}}
-'''rnl(<var>x</var>)'''{{refsrc|src/rnd.c|116|nethack=3.6.6|name=main}} is a pseudo-random number function used in ''NetHack'' when a result should be weighted by [[Luck]].
+'''rnl(<var>x</var>)'''{{refsrc|src/rnd.c|116|nethack=3.6.6|name=main}} is a pseudo-random number function used in ''NetHack'' when a result should be weighted by the player character's [[luck]].
-rnl(<var>x</var>) has the same range as rn2(<var>x</var>) (that is, 0&nbsp;&le; rnl(<var>x</var>)&nbsp;&lt;&nbsp;<var>x</var>), but is weighted toward 0 if you have positive Luck, and toward <var>x</var>&nbsp;&minus;&nbsp;1 if you have negative Luck.
+rnl(<var>x</var>) has the same range as rn2(<var>x</var>) (that is, 0&nbsp;&le; rnl(<var>x</var>)&nbsp;&lt;&nbsp;<var>x</var>), but is weighted toward 0 if you have positive luck, and toward <var>x</var>&nbsp;&minus;&nbsp;1 if you have negative luck.
 == Formula ==
@@ Line 9: / Line 9: @@
 See source code in <ref name=main/>
-For rnl(<var>x</var>), let <var>L</var> equal your Luck, including the [[luck item]] bonus or penalty, whether positive, negative, or zero.
+For rnl(<var>x</var>), let <var>L</var> equal your luck, including the [[luck item]] bonus or penalty, whether positive, negative, or zero.
 If <var>x</var> &le; 15, <var>L</var> = {{frac|<var>L</var>|3}}, rounded toward the nearest integer.
@@ Line 19: / Line 19: @@
 Otherwise, return rn2(<var>x</var>) - <var>L</var>, but no less than 0 and no more than <var>x</var> - 1.
-This means that rnl(<var>x</var>) is almost always equivalent to rn2(<var>x</var>) - Luck when <var>x</var> > 15. The chance of Luck being ignored is less than 3% in any case, and even smaller for stronger (positive or negative) Luck. For smaller values of <var>x</var>, rn2(<var>x</var>) - {{sfrac|Luck|3}} is the most likely approximation.
+This means that rnl(<var>x</var>) is almost always equivalent to rn2(<var>x</var>) − luck when <var>x</var> > 15. The chance of luck being ignored is less than 3% in any case, and even smaller for stronger (positive or negative) luck. For smaller values of <var>x</var>, rn2(<var>x</var>) - {{sfrac|luck|3}} is the most likely approximation.
 == How it's used ==
@@ Line 25: / Line 25: @@
 In the tables below, some very high (99.8%) and very low (0.2%) values above are rounded to 100% or 0%. Nothing is completely 100% or 0% likely, except where spelled out as "certain" or "impossible".
-=== Events based solely on Luck ===
+=== Events based solely on luck ===
 {| class="wikitable"
@@ Line 117: / Line 117: @@
 |}
-=== Events based on Luck and other stats ===
+=== Events based on luck and other stats ===
 {| class="wikitable"
@@ Line 126: / Line 126: @@
 | Chance of kicking down a door
 | <code>rnl(35)<X</code>, where X = avg(str, dex, con) + (dex if [[Samurai]] or [[Monk]]){{refsrc|dokick.c|1046}}
-| colspan="9"| Approx {{sfrac|<var>Luck</var> + X|35}} chance<!-- computed numbers slightly incorrect -->
+| colspan="9"| Approx {{sfrac|luck + X|35}} chance<!-- computed numbers slightly incorrect -->
 |-
 | Chance of kicking down a door when avg(str, dex, con) is 10
@@ Line 140: / Line 140: @@
 |-
 | Chance of opening a door
-| <code>rnl(20)<X</code>, where X = avg(str, dex, con){{refsrc|lock.c|562}} || colspan="9"|Approx {{sfrac|<var>Luck</var> + X|20}} chance<ref>computed numbers slightly incorrect</ref>
+| <code>rnl(20)<X</code>, where X = avg(str, dex, con){{refsrc|lock.c|562}} || colspan="9"|Approx {{sfrac|luck + X|20}} chance<ref>computed numbers slightly incorrect</ref>
 |-
 | Chance of opening a door when avg(str, dex, con) is 10
@@ Line 220: / Line 220: @@
 == Mathematical analysis ==
-Basically, rnl(<var>x</var>) generates a number between 0 and <var>x</var>&nbsp;&minus;&nbsp;1, and adjusts it in proportion to the player's Luck, with a small chance (which is smaller when Luck tends toward the extremes) of leaving it alone. The net effect is that with positive or negative Luck, the highest or lowest numbers on the list become vanishingly unlikely, and the odds of getting the best and worst result increase, while the odds of getting every result in between stays the same.
+Basically, rnl(<var>x</var>) generates a number between 0 and <var>x</var>&nbsp;&minus;&nbsp;1, and adjusts it in proportion to the player's luck, with a small chance (which is smaller when luck tends toward the extremes) of leaving it alone. The net effect is that with positive or negative luck, the highest or lowest numbers on the list become vanishingly unlikely, and the odds of getting the best and worst result increase, while the odds of getting every result in between stays the same.
 Further complicating the matter is that, when <var>x</var> is 15 or less, the adjustment is divided by 3, which means that for those calls there is a stepwise distribution where the odds of everything are almost completely the same within blocks of 3 numbers (&minus;13 to &minus;11, &minus;10 to &minus;8, &minus;7 to &minus;5, &minus;4 to &minus;2, &minus;1 to 1, 2 to 4, 5 to 7, 8 to 10, 11 to 13). Larger parameters have smoother distributions.
@@ Line 226: / Line 226: @@
 In addition, the function often being called in unusual manners, such as comparing it to a non-zero constant, which results in a "slice" being taken from the distribution graph at a less easily explainable point.  This is evidenced in the distrubtions for rnl(A)&lt;B or rnl(A)&gt;B above.
-Since many of the comparisons are made against 0, having even &minus;2 Luck can cause many results to swing against the player's favor with near certainty. &minus;1 Luck is not as bad as most of these calls also have a small parameter, although it does negatively affect many things that do not call rnl (like [[prayer]] or [[wish]]ing). On the flip side, positive Luck's effect tends to be much less dramatic, and +2 Luck still has a lot of room for improvement. +1 Luck changes almost nothing significantly; the only pronounced effect it has is to cause jousting to be much safer.
+Since many of the comparisons are made against 0, having even &minus;2 luck can cause many results to swing against the player's favor with near certainty. &minus;1 luck is not as bad as most of these calls also have a small parameter, although it does negatively affect many things that do not call rnl (like [[prayer]] or [[wish]]ing). On the flip side, positive luck's effect tends to be much less dramatic, and +2 luck still has a lot of room for improvement. +1 luck changes almost nothing significantly; the only pronounced effect it has is to cause jousting to be much safer.
 == Sample distribution ==
-This table is the computed odds of rnl(10) at each possible Luck for each possible result. The "0%" values are actually around 0.24–0.26% depending on the magnitude of the Luck.
+This table is the computed odds of rnl(10) at each possible luck for each possible result. The "0%" values are actually around 0.24–0.26% depending on the magnitude of the luck.
 {| class="wikitable"
@@ Line 299: / Line 299: @@
 Let <var>R</var> be a random integer number from 0 to <var>x</var>&nbsp;&minus;&nbsp;1 (inclusive).
-If Luck&nbsp;=&nbsp;0, <var>R</var> is returned.
+If luck equals 0, <var>R</var> is returned.
-Otherwise, with {{sfrac|1|50 &minus; Luck}} chance (since Luck ranges from &minus;13 to 13, the chance should be between {{sfrac|37}} and {{sfrac|63}}), <var>R</var> is returned.
+Otherwise, with {{sfrac|1|50 &minus; luck}} chance (since luck ranges from &minus;13 to 13, the chance should be between {{sfrac|37}} and {{sfrac|63}}), <var>R</var> is returned.
-Otherwise, if <var>x</var>&nbsp;&le;&nbsp; 15 and Luck&nbsp;&ge;&nbsp;&minus;5 (that is, <var>x</var> is not too big and the player is not too unlucky), {{sfrac|Luck|3}} (truncated towards zero) is subtracted from <var>R</var>, then <var>R</var> is forced into the interval [0, <var>x</var>&nbsp;&minus;&nbsp;1] and returned.
+Otherwise, if <var>x</var>&nbsp;&le;&nbsp; 15 and luck&nbsp;&ge;&nbsp;&minus;5 (that is, <var>x</var> is not too big and the player is not too unlucky), {{sfrac|luck|3}} (truncated towards zero) is subtracted from <var>R</var>, then <var>R</var> is forced into the interval [0, <var>x</var>&nbsp;&minus;&nbsp;1] and returned.
-Otherwise, Luck is subtracted from <var>R</var>, then <var>R</var> is forced into the interval [0, <var>x</var>&nbsp;&minus;&nbsp;1] and returned.
+Otherwise, luck is subtracted from <var>R</var>, then <var>R</var> is forced into the interval [0, <var>x</var>&nbsp;&minus;&nbsp;1] and returned.
 == References ==

← Older revision		Revision as of 01:55, 3 July 2024
Line 312:		Line 312:

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

@@ Line 96: / Line 96: @@
 | 99.5% || 99.5% || 99.5% || 99.5% || 80.0% || 60.5% || 41.0% || 21.5% || 2.0%
 |-
-| Chance of a hostile, awake, unfrozen, mindful, nonhuman monster becoming peaceful when you free it from a trap not set by you
+| Chance of a hostile, awake, unfrozen, mindful, non-{{monclasssym|@}} monster becoming peaceful when you free it from a trap not set by you
 | <code>rnl(10)<8</code>{{refsrc|trap.c|3166}}
 | 40.1% || 50.8% || 60.5% || 70.3% || 80.0% || 89.7% || 99.5% || 99.5% || 99.5%

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:rnl}}
 {{distinguish|rn1}}
-'''rnl(<var>x</var>)'''<ref name=main>{{function|rnd.c|rnl}}</ref> is a pseudo-random number function used in ''NetHack'' when a result should be weighted by [[Luck]].
+'''rnl(<var>x</var>)'''{{refsrc|src/rnd.c|116|nethack=3.6.6|name=main}} is a pseudo-random number function used in ''NetHack'' when a result should be weighted by [[Luck]].
 rnl(<var>x</var>) has the same range as rn2(<var>x</var>) (that is, 0&nbsp;&le; rnl(<var>x</var>)&nbsp;&lt;&nbsp;<var>x</var>), but is weighted toward 0 if you have positive Luck, and toward <var>x</var>&nbsp;&minus;&nbsp;1 if you have negative Luck.
@@ Line 11: / Line 11: @@
 For rnl(<var>x</var>), let <var>L</var> equal your Luck, including the [[luck item]] bonus or penalty, whether positive, negative, or zero.
-If <var>x</var> &le; 15, <var>L</var> = {{frac|<var>L</var>|3}}, rounded toward zero.
+If <var>x</var> &le; 15, <var>L</var> = {{frac|<var>L</var>|3}}, rounded toward the nearest integer.
 If <var>L</var> = 0, return [[rn2]](<var>x</var>).

@@ Line 9: / Line 9: @@
 See source code in <ref name=main/>
-Let <var>R</var> be a random integer number from 0 to x&nbsp;&minus;&nbsp;1 (inclusive).
+For rnl(<var>x</var>), let <var>L</var> equal your Luck, including the [[luck item]] bonus or penalty, whether positive, negative, or zero.
-If <var>Luck</var>&nbsp;=&nbsp;0, <var>R</var> is returned.
+If <var>x</var> &le; 15, <var>L</var> = {{frac|<var>L</var>|3}}, rounded toward zero.
-Otherwise, let <var>A</var> be
+If <var>L</var> = 0, return [[rn2]](<var>x</var>).
-If <var>A</var>&nbsp;=&nbsp;0, <var>R</var> is returned.
+With chance {{sfrac|1|37 + {{!}}<var>L</var>{{!}}}}, return rn2(<var>x</var>).
-Otherwise, with chance {{sfrac|1|37+{{!}}A{{!}}}}, <var>R</var> is still returned (the chance is always between {{sfrac|38}} and {{sfrac|50}}).
+Otherwise, return rn2(<var>x</var>) - <var>L</var>, but no less than 0 and no more than <var>x</var> - 1.
-Otherwise, <var>R</var>&nbsp;&minus;&nbsp;<var>A</var> is forced into the interval [0, <var>x</var>&nbsp;&minus;&nbsp;1] and returned.
+This means that rnl(<var>x</var>) is almost always equivalent to rn2(<var>x</var>) - Luck when <var>x</var> > 15. The chance of Luck being ignored is less than 3% in any case, and even smaller for stronger (positive or negative) Luck. For smaller values of <var>x</var>, rn2(<var>x</var>) - {{sfrac|Luck|3}} is the most likely approximation.
 == How it's used ==

@@ Line 45: / Line 45: @@
 |-
 | Chance of [[Magic marker|writing]] a scroll you have not seen, as a [[Wizard]]
-| <code>rnl(3)==0</code>{{refsrc|write.c|201}}
+| <code>rnl(5)==0</code>{{refsrc|write.c|201}}
-| 0.8% || 0.8% || 0.9% || 0.9% || 33.3% || 65.8% || 98.3% || 98.3% || 98.3%
+| 0.5% || 0.5% || 0.5% || 0.5% || 20.0% || 39.5% || 59.0% || 78.5% || 98.0%
 |-
 | Chance of failing to set a [[land mine]] (in which case it blows up) or [[beartrap]] (nothing happens) while [[riding]] and [[Skill|unskilled]] at riding