Compleat Character Creation Catalog: OD&D

On the Wandering DMs a few weeks ago, we had a neat conversation about the history of generating ability scores for D&D across the various editions. This brought to mind a post I've wanted to make for a long time: in early D&D, what are the odds of qualifying for desired character classes, given the various methods presented for generating abilities? 

A few folks have worked on this problem previously. Probabilities for the 2E AD&D game rules were given by Ed Friedlander in Dragon Magazine #153, January 1990 (thanks to Dominic Brown for tracking down the reference!). One of our viewers pointed out that the Athenopolis.net blog had done basically the same thing for 1E a few years back. Actually, I think that was extremely helpful, because it gave me a nice opportunity to double-check my results -- we mostly agree on the major stuff for 1E. However, there are a few fine-print rules I think they overlooked there, and I've added more statistics, commentary, nearby editions, and so forth.

To avoid an overly long post, I've broken this up into separate articles: you'll see OD&D, AD&D 1E, and Unearthed Arcana (UA) 1E variant rules. Some opening ground rules: For simplicity, as others have done, we're basically only looking at the raw ability scores generated for single-classed human characters. We're not considering the after-the-fact racial adjustments from AD&D, the chances to qualify for multi-class combinations, dual classes, etc. All of the statistics you'll see were generated by Monte Carlo-type simulations from a C++ program, which you can see on my Github: ADnDClassAccess repository. Having noted that, let's begin:

Ability Generation Method

It probably bears without saying, Original D&D has only one way of generating ability scores, the classic 3d6-in-order procedure for all six ability scores. But some things that may be surprising about this: The rulebook says it is the referee that should be making these rolls (proto-pregens, perhaps?). There is a vague point-swapping method that allows you to trade a few points into your prime requisite, maybe (more on that in a bit). And despite many people's incorrect memory, this method was not supported in any way by the 1E AD&D books (although it was carried forward into the D&D Basic line).

The statistics for the standard 3d6 roll are fairly well known. (For example, it's the default sample roll for Torben Mogensen's excellent Troll dice roller and probability calculator). It has a symmetrical bell-shaped curve, with an average (mean, median, and mode) of 10.5, and a standard deviation close to 3 (2.958).

Okay, so about that point-swapping rule: Descriptions of the abilities say things like, "Strength is the prime requisite for fighters. Clerics can use strength on a 3 for 1 basis in their prime requisite area (wisdom)...", which would get me thinking this purely an additive bonus thing. But then the next page says, "Units so indicated above may be used to increase prime requisite total insofar as this does not bring that category below average, i.e., below a score of 9", so that makes it seem more like a points-swapping mechanism. But then the 5th printing of OD&D (at the same time as the Greyhawk supplement presented more advanced ability modifiers) added the clause "... for the purposes of gaining experience only", so maybe it's not meant to be a factor for class qualifications or combat bonuses? 

In short: the status of point-swapping rule is very unclear. As noted above, Holmes with his Basic D&D line took this as a key rule, and made the points-swapping explicitly permitted (and it was continued forward by Moldvay, Mentzer, etc.). But Gygax gave no hint of its presence in Advanced D&D. Recall that at best it's only for the very limited purpose of swapping a few points into one's prime requisite -- which as we'll see, is usually not really a requisite at all...

Classes and Requirements

Here's another thing that might be a tad surprising to longtime players of AD&D, say: in the Original D&D LBBs, there aren't any ability score minima to qualify for any of the classes. You can definitely enter any of the Fighter, Magic-User, Cleric, or Thief (from Sup-I) classes, regardless of what your ability scores are. In fact, the one example of a character being created highlights the player not picking the class according to their best ability. Moreover, the table of bonuses and penalties from ability scores includes the line, "Prime requisite 6 or less: Minus 20% from earned experience", so while that stings, it's clearly not prohibited -- and demonstrates my point that "requisite" isn't quite the right word for it (yet). 

Xylarthen: Example PC magic-user fo OD&D

Then, in the various OD&D supplements (I through IV) and The Strategic Review zine articles (issue #1 through #7), we sequentially start adding all of the various sub-classes that we ultimately see collected in AD&D. This is where ability-score minimum gateways come into existence, starting with Sup-I stating that lawful fighters with a Charisma of 17 or higher can gain "paladin status". Note one detail: even though Strength is their "prime requisite", there's still no actual minimum requirement for it -- under those rules you can roll all-3's but a 17 Charisma and still be a paladin. Some later sub-classes, like the Ranger (TSR #2, by Joe Fischer) and Illusionist (TSR #4, by Peter Aronson), continue to give no minima in their prime requisite, while other ones do add such a requirement.

This further highlights that swapping points into the prime requisite wouldn't make any difference in most cases for qualification purposes, while there's no allowance for swapping into the other abilities that do have requirements (like the Paladin's need for a 17 Charisma). So in conclusion, due to the great unclarity of the status of the rule, and the overall low impact on the question of qualifying for classes, we won't be considering that rule further here: it's just straight 3d6-in-order for us.

When all is said and done, here are the various classes indicated in OD&D and its supplements, with their ability score requirements, as best as I can read those rules (presented in order of publication of the classes):

Class Requirements: OD&D

Qualification Chances

At last, we can run our simulator with the straight-3d6 method against the OD&D class requirements, and derive the following chances for any new character to qualify for a desired class: 

Class Access Chances: OD&D
As noted above, we see the 100% values for the four primary classes, because there's no ability-score restriction on entering those classes in the LBBs. On the other hand, the sub-classes are all generally very hard to qualify for, usually in the range of 6% or less. There's less than a 2% chance to get the divine Charisma of 17+ that qualifies you for Paladin status (justifying many of our memories about the intense celebration that would erupt if anyone ever got to play a Paladin). And the Monk is even more insanely difficult, at just a third-of-a-percent chance (thanks, Dave). Although surprisingly for AD&D fans, the OD&D Bard has fairly gentle entry requirements, and so is actually the easiest subclass to enter, with 14% of any PCs qualifying (and you can do so immediately: no need to level up through other classes first). All of this will change when AD&D overhauls the rules, of course. 

I suppose, in review, given all the complicated methods that came later to give players more fine-tuned control over the starting abilities of their characters, there's some charm in the germ of the idea that's already in Original D&D -- allowing for limited points-swapping following the straight-3d6 rolls. Say we streamlined it and made it always at a 2:1 ratio (drop 2 points in one ability to gain 1 point in another), as we see in Moldvay, not to reduce any ability below 9. We could then pick from a few options for swapping allowances: (1) only from Str, Int, Wis, Dex into one's prime requisite, (2) from any ability into one's prime requisite, or (3) from anywhere to anywhere, at the player's discretion. A rule like this has the elegance that brand-new players can simply take their 3d6-in-order without further consideration, while expert players can dig into the customization possibilities.

Anything surprising to you in those results? Are there any OD&D rules that you interpret differently than I did? Would you consider using some form of the streamlined 3d6-with-point-swap rule outlined above? More fun with AD&D next time.


  1. P = 0.03 to qualify for the Monk seems ridiculously punishing to me (seriously, ~1:300 characters rolled up can play it? really?). It makes sense that Gygax switched to 4d6-drop-lowest for 1e. I'd absolutely try to find some way to adjust those numbers slightly for a 3d6-in-order OD&D game, either by allowing rearrangements or a point-allocation system.

    On the other end of the scale, Swords & Wizardry Complete, the OD&D-ish retroclone which incorporates classes from the Supplements and Strategic Review, modifies those ability requirements to simply be combined Prime Requisite scores, and lowers the XP bonus to +5% for having them. My impression is that this simply makes the Monk, Paladin, Ranger, etc. completely mundane and obvious choices (though it only gives the Strength bonus to-hit and damage to the pure Fighter).

    1. I totally agree, that was either completely not thought out, or was being used with some other ability generation from the start (I think I hear Arneson did 2d6 + 6 down the line)?

    2. Something else I noticed that I don't remember seeing brought up before:

      While Method-I technically makes for significantly higher scores in AD&D than 3d6 in OD&D, the changes between the Supp-I and AD&D PHB *bonuses* (particularly for Strength) mean it looks like it all might be a wash (I'm not going to write enough Fortran code to figure this out for sure, but by eye it seems like a +1 kicks in at roughly 1 sigma above the mean). So it sure seems like 4d6 was implemented to make qualifying for special classes more likely, but then the bonuses were moved around in order to keep the numbers roughly the same.

    3. That's maybe a good point, although those boosted bonuses are basically all in OD&D Sup-I (Greyhawk), when clearly 3d6 in order was in play. Of course, in the LBBs there's no explicit mechanical benefit to Strength at all, and the Con threshold is kept the same. The one place where it gets harder to achieve a bonus is for Dex (which I hadn't noticed before).

  2. Good on the interpretations I think.

    Happy to have left point swapping behind.

    I’m still partial to the "3d6 in order, swap two" that was in your house rules for so long; then, if needing to fill out a party with a specific class, can use your newer 12+1d6. (Tried to do that the other day but brain-farted and used 6+2d6 instead—worked out fine though, got 13 strength which fit the bill, and then, yes, an 18 on the charisma roll.)

    1. Yeah, it's actually the 2d6 + 6 that's been in my rules for a while now, I'm glad that worked to taste!

    2. It's tempting to offer players two options per character: one with a higher minimum and average but lower maximum. Such as:


      Thus preventing the latter from getting the coveted 18, and making a 17 slightly less likely.

      What are your thoughts on something like that? Is it too diabolical?

    3. I don't see why not, sounds fair to me!

  3. I thought (and I may be mistaken) that in 1e racial modifiers were included prior to eligibility checks and age modifiers applied after. So that (for instance) a halfling rolling a natural 9 str was ineligible for fighter but an elderly dwarf could fall below 9 via age penalties and remain a (quite weak) fighter.

    1. That certainly makes sense. The DMG aging rule is not explicit about about the ordering, but it does say, "any adjustments cannot lower any ability score below racial or class minimums". Largely the permutations of different race modifiers, multiclassing, and aging would be so enormous I didn't want to bloat the (next) article with so much stuff.

  4. This sort of thing interests me. I have done basically the same thing with the classes in the AD&D Players Handbook (Demon Idol edition, natch).

    First, the chances of each class using 3d6 in order:
    cleric: 61%
    druid: 1 in 35
    fighter: 58%
    paladin: 1 in 1,062
    ranger: 1 in 623
    magic-user: 61%
    illusionist: 1 in 269
    thief: 61%
    assassin: 1 in 16
    monk: 1 in 2,769
    bard: 1 in 58,029

    Or, if using my favorite of the DMG's methods of rolling ability scores (method IV: roll 12 characters using 3d6 in order, and pick your favorite of the 12), we get:
    cleric: 100%
    druid: 1 in 2.9
    fighter: 100%
    paladin: 1 in 88.5
    ranger: 1 in 51.9
    magic-user: 100%
    illusionist: 1 in 22.4
    thief: 100%
    assassin: 1 in 1.3
    monk: 1 in 230.8
    bard: 1 in 4,835.7

    I like my AD&D to include the sub-classes (along with monks and bards), but I like them quite rare, which the above methods deliver.

    1. Great, I agree with all that. I've got that queued up here for next week along with the other methods. It's interesting that you use the most restrictive DMG method, I like it!

  5. We've had a lot of fun with 3 sets of 3d6 in order, take the best set (the rest to the DM for henchmen/ rival parties), 2 for 1 trade to add to prime requisite ( not below 9) and minimum prime requisite of 9.

    For non standard class (e.g. assassin, bard, elven spell sword, etc) there are 2 prime requisites. This makes it good (can increase 2 stats) and bad (need exceptional scores in both for xp bonus).

    I also house ruled that you can add one to one prime requisite when you choose a class. Generally everyone can roll up a PC to play and make it fit a class they like.

    It is amazing how a little change, like how ability scores are generated, can affect play. In our campaign there are several pcs that started with a 5 or 6 in one of their ability scores. That forced the low CON assassin to focus on taking out foes quickly, while the thief with low CON and STR relying more on henchmen, etc.

    It also drives a search for ways to increase those scores, mostly through magic items. Also it fights against the modern trend that what makes the PCs special is their talent, rather then their will and drive to suceed.

    1. I really like all of that! E.g., the roll-3-characters -- I've always been attracted to the roll-12-PCs idea (see Geoffrey above), but wow 12 PCs is a lot of rolling. And I agree that I've been fond of the action in my games of players being driven to get rule-breaking magic to boost scores (and esp. get the 15 score that lets you double-class). Likewise, magic to break the racial level limits. Excellent stuff.

    2. I really like the roll-3 idea. Is this using 1e or OD&D ability score minimums? IIRC they're different.

    3. Yeah, they're definitely different. Sounds to me like Jojodogboy may be using custom limits, too.

    4. The minimum score for the prime requisite (9) is the base for the bx clone I run. The house rule part is the +1 to a prime stat for each character.

      As an aside, I have sets of colored d6 (my dad used them in his statistics classes). A pc will roll 3d6 black, 3d6 white, and 3d6 red at the same time, creating 3 STR scores for each set, the process repeats giving you a red, white, and black set of scores. It allows for quick generation. ( I actually have 3 sets of 5 different color d6s so you can roll up an entire replacement party after a team wipe in like 15 minutes)

  6. Another interesting post. Thanks Dan! I do know what Gary Gygax had to say about the M&M "3 for 1" rule:

    1. Thanks! And nice find. Although they manage to overlook the "not below 9" rule in that short convo, and I wonder if the fairly late date of "for experience only" represented a clarification or an actual rule change. (?)

  7. I'm not a big fan of the trading points; it seems like a step along the path towards the twin scourges of dump stats and needing to optimize stats. The notion that you could adjust your XP bonus if you were good at something else (per that enworld comment of Gary's) is maybe more interesting... except that as, you've pointed out in the past, for practical purposes the XP bonus rarely amount to anything.

  8. I like this sort of deep dive post into the rules - it's almost reverse engineering. I suspect that the creators didn't have any design methodology in mind when they set the minimums, just that it had to be difficult to qualify for some of the classes.

    While back in the day I was a 4d6 drop the lowest guy, these days I'm a 3d6 in order person. Like Jojodogboy says it creates reasons for playing the character differently, allows the DM to introduce specials such as pools to add or subtract from stats and thereby enhances the roleplaying and quality of the game in my view.

    In an only tangentially related topic, I'd like to see you tackle the idea of which character creation rolls (characteristics, hit points or gold) have the most influence on survivability. For BX I think that the order is gold, DEX and HP and I'd rather have a fighter with 9 STR and 18 DEX than a fighter with 18 STR and 9 DEX.

    1. We were just recently chatting about this on our Discord server (thanks to a question by Joshua Macy above), and the stats I've seen agree with you. Avoiding a hit at low level seems more important than a few extra hit points, so survival for fighters in my Arena simulator shows Str & Dex biased more than Con, say, and maybe only one hp above what you'd expect from average rolls. Now, gold, I never thought to measure (depends a lot on whether you go by the book with low price for plate). Check the ability-score chart in this post here.

  9. Why do a Monte Carlo simulation instead of a straight calculation? Your results are close, but not exact. For example, the paladin minima are achieved in 1 out of 54 of the possible dice rolls (that is out of the 1,296 possible ways to roll 3d6 six times, 24 of them have a 17 or 18 in the final 3d6). That's 1.85% rather than 1.86%. Not a big deal, and it doesn't change your conclusions, just seems like going the long way around to get results that test your random number generation instead of making the straight calculation.

    1. Well, that's a good point. I'm personally in the habit of simulating stuff like this b/c it's more how I naturally/statistically think of stuff, and I find it more generally useful for complicated cases where direct calculations may be infeasible (or just hard). E.g., next time when AD&D allows re-ordering, then combinations of the possible re-ordering get really hairy, whereas this method just naturally works the same (and AD&D was what I was really coding up in the first place).

  10. I'm actually a little surprised the Monk has such a high chance of occurring. By my half-remembered napkin math from years ago, I only recall the Monk as being "absolutely impossible" to qualify for. :P

    Like others, I think it's charming to have classes that players only have a small chance to qualify for. It adds an extra wrinkle of exciting possibility to rolling up a new character, and perhaps makes character death less galling as a result.

    But I think the odds are much too low to actually create that positive effect. I figure there ought to be closer to a 30% chance that a newly created character will qualify for at least one unusual class.

    1. I agree that there ought to be about a third of characters rolled qualify for at least one of the unusual classes. Totting up the percentages I get about 35%. The minimums shouldn't be any higher than 12 in my view.

    2. Well, the chance for a Monk certainly rounds off to 0% as the closest integer percentage. :-) I agree that probably if I were designing something like that intentionally, I might set the chance for a given "special" character at around 20%, or 1-in-6, say.

  11. >Although surprisingly for AD&D fans, the OD&D Bard has fairly gentle entry requirements, and so is actually the easiest subclass to enter

    Also not technically a subclass in OD&D. Monks are a subclass of cleric, but bards are the fifth base class.