you must be this lucky to play, part 2

“I’ll work up how to do the math for 4d6 drop lowest arranged, but not today.”  Well, that was more than a year ago, and I can’t say I’ve really devoted myself to the project.  Frankly, I have failed you, dear trio of readers: it was much easier to re-learn Java to solve this problem by brute programming force rather than to re-learn probability.  The University of Illinois Math Department will probably come ’round demanding that I return my diploma…

Anyhow, I worked up a crappy little program to handle 4d6 arranged to taste for one million characters.  Surprisingly, even with that many data points there’s a lot of random noise in the second decimal place and a moderate amount of wobble in the first decimal place.  But I ain’t running this beyond a million characters.

Here are PDF’s of the charts below, in case, like me, you have trouble reading the way WordPress formatted the diagrams below.

advanced dungeons & dragons, 1979

As was pointed out in comments to the earlier blog post, 1e apparently uses 4d6 Drop Lowest Arranged to Taste as its default method of creating a character.

Several of these stat requirements are not specifically identified in the class description, but rather called out in the ability score charts. For example, if you have a Strength of 3-5, you can only play a Magic-User. Thanks to Olivier Fanton for pointing this out.

 

Class	Min Stats	3d6 Straight	4d6 Dr. Low, Arr.
Cleric	Str 6, Int 6, Wis 9, Con 6, Cha 6	61.28%	99.80%
Druid	Str 6, Int 6, Wis 12, Dex 6, Con 6, Cha 15	2.87%	73.51%
Fighter	Str 9, Wis 6, Dex 6, Con 7, Cha 6	58.30%	99.80%
Paladin	Str 12, Int 9, Wis 13, Dex 6, Con 9, Cha 17	0.10%	24.19%
Ranger	Str 13, Int 13, Wis 14, Dex 6, Con 14, Cha 6	0.16%	29.46%
Magic-User	Int 9, Wis 6, Dex 6, Con 6, Cha 6	61.28%	99.80%
Illusionist	Str 6, Int 15, Wis 6, Dex 16, Cha 6	0.37%	35.82%
Thief	Str 6, Int 6, Dex 9, Con 6, Cha 6	61.28%	99.80%
Assassin	Str 12, Int 11, Wis 6, Dex 12, Con 6	6.39%	93.51%
Monk	Str 15, Int 6, Wis 15, Dex 15, Con 11, Cha 6	0.04%	13.15%
Bard	Str 15, Int 12, Wis 15, Dex 15, Con 10, Cha 15; Fighter 5, Thief 5*	0.00%**	1.59%

 

* = Before becoming a Bard, characters would have to survive through 5 levels of Fighter and then 5 levels of Thief, totalling around 28,000 XP, before beginning Bard training. From our five years of weekly play, that would require about three years, assuming the character didn’t get killed or super-killed in the meantime.

 

** = The odds of the 1e Appendix II: Bard is actually 0.0017%. That is, if you rolled 1 million AD&D 1e characters using 3d6, you could expect to see 17 Bards occurring in nature using 3d6 in order.  

unearthed arcana, 1985

Unearthed Arcana has a lot of alternate ways to generate character stats. I have ignored these alternate methods, as I have ignored everything else in this book. I leave rolling 9d6 or whatever as an exercise for severely bored readers.

 

Class	Min Stats	3d6 Straight	4d6 Drop Low, Arr.
Barbarian	Str 15, (Wis 16), Dex 14, Con 15	0.14%	28.23%
Cavalier	Str 15, Int 10, Wis 10, Dex 15, Con 15	0.03%	12.52%
UA Paladin	Str 15, Int 10, Wis 13, Dex 15, Con 15, Cha 17	0.00%*	0.89%
Thief-Acrobat	Str 15, Dex 16; Thief 5**	0.43%	35.74%

 

* = The actual number is 0.0002%, which means out of 1 million characters rolled up using 3d6 in order, a full 2 of them might expect to qualify for Paladin status in Unearthed Arcana rules.

 

** = Thief-Acrobat has to accumulate 10,000 XP as a Thief first. I don’t know how to assess how hard that is, but several players in the Glantri campaign have hit similar numbers after three years of play (and leaving many corpses of less-fortunate PC’s in their wake). 

 

dragonlance adventures, 1985

 

Class	Min Stats	3d6 Straight	4d6 Drop Low, Arr.
Knight of the Crown	Str 10, Int 7, Wis 10, Dex 8, Con 10	18.56%	97.94%
Knight of the Sword	Str 12, Int 9, Wis 13, Dex 9, Con 10; Crown Knight 2	3.33%	84.90%
Knight of the Rose	Str 15, Int 10, Wis 13, Dex 12, Con 15; Sword Knight 4	0.05%	27.60%
Tinker Gnome	Gnome only*; Int 10, Dex 12	23.12%	99.90%

 

Note that, like the 1e Bard and the Thief-Acrobat, the Knights of the Sword or the Rose require you to advance in level to qualify.

 

* = The Tinker Gnome must first qualify to play a Gnome: Strength 6, Constitution 8, and a Wisdom no higher than 12; they also get a +2 to their Dexterity. These stat requirements and adjustments have been factored into the “Odds to Qualify” columns.

oriental adventures, 1985

Oriental Adventures explicitly says to roll 4d6 Drop Lowest Arranged to Taste as the way to create characters.

 

Class	Min Stats	3d6 Straight	4d6 Drop Low, Arr.
Barbarian	Str 15, (Wis 16), Dex 14, Con 15	0.14%	28.28%
Bushi	Str 9, Dex 8, Con 8	52.02%	99.98%
Kensai	Str 12, Wis 12, Dex 14	2.28%	80.91%
Monk	Str 15, Wis 15, Dex 15, Con 11	0.04%	13.63%
Ninja-Bushi	Str 9, Int 15, Dex 14, Con 8, Cha 14	0.15%	34.54%
Ninja-Sohei	Str 13, Int 15, Wis 12, Dex 14, Con 10, Cha 14	0.01%	10.07%
Ninja-Wu Jen	Int 15, Dex 14, Cha 14	0.24%	35.16%
Ninja-Yakuza	Str 11, Int 15, Dex 15, Cha 16	0.02%	12.63%
Samurai	Str 13, Int 14, Wis 13, Con 13	0.28%	31.98%
Shukenja	Str 9, Wis 12, Con 9	20.57%	99.54%
Sohei	Str 13, Wis 12, Con 10	6.08%	95.23%
Wu Jen	Int 13	25.93%	35.16%
Yakuza	Str 11, Int 15, Dex 15, Cha 16	0.02%	12.63%

 

 advanced dungeons & dragons, second edition, 1989

Advanced Dungeons & Dragons Second Edition uses 3d6 in order as its default method to roll character attributes, but 4d6 Drop Lowest, Arranged to Taste, was listed as an alternate method that a lot of people seem to have used.

 

Class	Min Stats	3d6 Straight	4d6 Drop Low, Arr.
Fighter	Str 9	74.07%	100.00%
Paladin	Str 12, Con 9, Wis 13, Cha 17	0.13%	27.05%
Ranger	Str 13, Dex 13, Con 14, Wis 14	0.18%	30.55%
Mage	Int 9	74.07%	100.00%
Hard Specialist	Stat 16 *, Int 9	4.63%	56.76%
Easy Specialist	Stat 15 **, Int 9	9.26%	79.43%
Cleric	Wis 9	74.07%	100.00%
Druid	Wis 12, Cha 15	3.47%	78.28%
Thief	Dex 9	74.07%	100.00%
Bard	Dex 12, Int 13, Cha 15	0.90%	68.90%

 

* = The “Hard Specialists” are the Diviner, Enchanter, Illusionist, Invoker, and Necromancer.

 

** = The “Easy Specialists” are the Abjurer, Summoner, and Transmuter.

 

what have we learned?

First: that knowledge of calculus does not survive fifteen years of total disuse.

Second: wow, no wonder people like 4d6 Drop Lowest, Arranged!  The odds of playing a 2e Paladin jump from barely one-in-a-thousand to about one-in-four.

Third: 4d6 Drop Lowest, Arranged works on a “generosity curve,” for lack of a better term.  Slightly less than 60% of characters using 3d6 in order qualify to play a Fighter in 1e, but using 4d6 Drop Lowest, Arranged this basically hits 100%.  That’s a 66% improvement in the odds to qualify.  But the 2e Bard, who occurs just under 1% of the time using 3d6 straight, is about 7000% more likely using 4d6 Drop Lowest, Arranged.  And the freakish Unearthed Arcana Paladin, who occurs in 2 out of a million characters using 3d6 straight, occurs roughly 8900 times in a million using 4d6 Drop Lowest, Arranged–becoming 445,000% more likely.  There’s a reason for this!  But I am now too dumb about math to understand why!

Fourth: the UA Paladin is still the hardest class to qualify for in terms of straight-up stats, but the 1e Bard is only twice as likely, and requires you to earn 28,000 XP before you can even show up for Bard College.  I think that’s got to be a huge filter, easily making the class 10 to 20 times harder to qualify for than stats alone would suggest.

Fifth: in the earlier blog post, it really looked like people back in the day had to cheat like crazy to qualify for some of those hard-to-reach classes.  That’s much less likely using 4d6 Drop Lowest, Arranged.  Whether people still cheated on stat rolls or not, who can say. I sure did as a  kid, but we were using 3d6 in order.

 

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