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.



13 Responses to “you must be this lucky to play, part 2”

  1. 1 finbikkifin
    June 5, 2013 at 7:44 am

    I can’t remember if AD&D 1e had stat-increasing manuals, but 2e did, which would effectively lower the Bard’s requirements by one point each if you spent your first ten levels questing for one of each and train for six months before switching. What are the numbers for Str 14, Int 11, Wis 14, Dex 14, Con 9, Cha 14?

    I’d try to work it out myself, but you said it was hard and you already have a program for it, and I’m feeling lazy this morning.

  2. June 5, 2013 at 12:16 pm

    Fin, about 8.3% on stats alone, using 4d6 drop lowest, arranged to taste. A quick search before heading out to work reveals that 1e apparently only has three of those books, for Str, Dex, and Con. (Maybe there are others, but I didn’t see ’em.) Trouble is that your odds to find a specific book is 0.03% in any randomly stocked treasure pile, assuming it’s a treasure type that allows miscellaneous magic items.

    You found a clever work-around for those stat requirements, but it basically amounts to having the GM (and your fellow party members) specifically design a six-part quest just for you. It’s not a bad idea for a campaign–“Prince Demanding wants to matriculate to Bard College and keeps flunking the entrance requirements, go fetch him some books!” But if I were a player I think the better approach would be, “Yo, can I just be a Bard? Nobody’s ever seen one in play ’cause it’s pretty rare, so we would basically be the first people playtesting these rules in 30 years.”

  3. June 5, 2013 at 12:33 pm

    …And then someone uses that exact same argument to play 1e Psionics, and your game is ruined. So, y’know, tread cautiously.

  4. June 5, 2013 at 1:24 pm

    Thank you for rising to the occasion and presenting a good blog post (for a change). (Giggle).

    This post is all the more interesting after having discovered that the OSR has no clothes, D&D is an unplayable mess, etc.. It reflects the proper morbid curiousity of a post fandom autopsy. Unfortunately, that post is past due on the blog. Someone needs to leak the 8 page PDF!

  5. 5 James N.
    June 5, 2013 at 1:29 pm

    Yes, I plan to post it later today.

  6. June 5, 2013 at 3:38 pm

    Nice. Two quick refinements:

    1. Don’t forget that class is mandated if ever you roll a stat of 6 or less. This will create situations where a character is completely nonviable due to two or more bad rolls (competing mandates) or rolls the trigger score but still technically fails to qualify for the mandated class. I don’t think Gary was darwinian enough to suggest that these people don’t survive to adulthood. I think he’d just say they can’t class.

    2. Speaking of class, under full UA, 55% of the potential adventurer population is excluded from cavalier or paladin status because they’re only middle class or lower. So cut those numbers in half! Otherwise the social class rules only really exclude magic-users and illusionists — 20% of the smart people are still too poor to “hope to make their way in the profession.” And those too poor to be anything but a thief or assassin but fail the class minima will be completely non-viable.

    I wonder how big the “unclassable” population is, taking all combinations of characteristic generation and social class into account.

  7. June 5, 2013 at 3:46 pm

    Oops, I see you already refined “refinement 1” into your numbers. Carry on!

  8. 8 James N.
    June 5, 2013 at 4:04 pm

    Bombasticus, the “unclassable” population was actually my original reason for working on this project. I think I can adjust the program to handle it, but not today (apparent translation: within the next year or so!)

  9. June 13, 2013 at 12:46 pm

    Strangely, I grew up using the crazy 9d6 (descending) rolls from Unearthed Arcana–I started playing 1e with my dad and never bothered to question why you had to roll so many stupid dice until I bought 2e for myself, the 4d6 arranged standard for 2e seemed so streamlined and *gasp* introduced some risk of not playing the character you wanted–which appealed to me a lot. With 3e+, since there were no longer stat requirements for classes, I moved to 3d6 in order and have stuck with it ever since (even when going back to older editions).

    If nothing else, I miss the 7th ability score (Comeliness) from UA. Somehow Charisma made a lot more sense as a thing a character would want when it was strictly decoupled from appearance.

  10. June 21, 2014 at 3:02 pm

    Instead of a million random characters, why not just use one of the 7772 possible characters? 6 * 6 * 6 * 6 * 6 = 7772. Just nest five loops from 1 to 6, one for each die and then the last one is for the six stats. Probably easier for the computer to deal with while also being more correct.
    Thanks for doing this though. Great work digging through all those modules.

  11. June 21, 2014 at 3:20 pm

    Whoops, it’s (6 * 6 * 6 * 6)^6, not (6 * 6 * 6 * 6)*6. You’re right, a million sounds pretty good. Proceed. :)

  12. July 23, 2015 at 1:45 am

    Did you ever get around to figuring the % of the population that is unclassable? I’d still love to see those numbers. :D

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Past Adventures of the Mule

June 2013

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