The Science of Slime-Splitting

Amoeba fission

Recently on Wandering DMs we had a neat conversation about slime-type monsters in classic D&D. Now, in Original D&D, a couple of those infamous monsters are said to split into smaller slimes if they're hit by any physical weapons (Vol-2, p. 19). For example, the Ochre Jelly: "hits by weaponry or lightning bolts will merely make them into several smaller Ochre Jellies". And likewise the Black Pudding: "It is spread into smaller ones by chops or lightning bolts..." But what should the exact result of that spreading be? Let's compute.

As a model, I'll assume that slimes are roughly spherical, and their hit dice are proportional to their volume, but their damage output is proportional to their surface area (being a bunch of acidic gastric vacuoles on the external membrane or something). A sphere's volume is given by V = 4/3πr³, while surface area is given by S = 4πr², r being the radius, of course.

Say we have a starting "unit slime" with radius r₁ = 1. The formulas above give V₁ = 4.2 and S₁ = 12.5. Now let's say we split it with the total mass being conserved; the volume of each of our split-slimes is half of what we started, that is V₂ = 2.1. Taking the equation 2.1 = 4/3πr³, we can solve in a couple steps of algebra to find r₂ = 0.8, and hence S₂ = 8.0. Now, the ratio of our starting and ending surface areas is 8.0 / 12.5 = 0.64, or 64%.

You can repeat this splitting calculation, but the whole process is proportional, so the surface-area ratio stays fixed at each step -- roughly speaking, the surface area, and hence our presumed damage output, always reduces to approximately two-thirds the value of the prior step.

Let's round off and suggest some parameters for split-up slimes of different types.

Ochre Jelly

  • Level 1 -- 5 HD, 1d6 damage
  • Level 2 -- 2 HD, 1d4 damage
  • Level 3 -- 1 HD, 1d3 damage

Black Pudding

  • Level 1 -- 10 HD, 3d6 damage
  • Level 2 -- 5 HD, 2d6 damage
  • Level 3 -- 2 HD, 1d6+2 damage
  • Level 4 -- 1 HD, 1d6 damage

Note that at any hit-die value, Black Puddings are twice as destructive as Ochre Jellies. I'll assume for mechanical simplicity that the splitting stops at the 1 HD level (hopefully PCs get the clue by then what they're doing isn't helping; maybe at 1 HD one half dies off while the other is at effectively full-strength).

What are the advantages of this scientific approach? Well, I like that splitting slimes is not advantageous to player-characters in terms of total damage output -- the total is actually increasing and making the PCs' situation more dire as they unwittingly chop up slimes. For example: level-1 black pudding does 3d6 damage; two half-puddings do a total of 4d6; four quarter-puddings do a total 4d6+8, and so forth. (Compare to the AD&D rule for ochre jellies where the damage is simply halved, keeping the total the same.)

On the other hand, the slimes will have a slightly harder time scoring hits with their reduced HD values. And for very advanced player behavior, move your fighters in to chop up the black pudding like so, and then withdraw, to make sure the wizard's fireball will be able to wipe out all the little pieces in one shot. If you dare?


Because-Dragons Is a Bad Argument

Dragon holding scales of justice
Is this a hot take?

In the D&D discourse, you'll see a common piece of rhetoric, and it goes like this. DM Alice says, "I don't want to allow X in my games; I think it's unreasonable". And DM Bob calls out Alice like this:

Alice says that she doesn't permit X in her games. But Alice accepts Dragons in her game! So that doesn't make any sense!

I call this the "because-dragons" argument. The next most common variant of this argument is, of course, "because-fireballs".

Here's the thing: The space where this argument usually plays out is in the field of features that a player character can opt to start out with. And, to put it briefly, there's lots of stuff in my fantasy world that I would not want players to have on their side at first level.

I'm not even essentially talking about power issues (although that can be a big factor). I'm talking about the background texture of the milieu where player-characters come from. The classic D&D that I fell in love with -- like the pulp fantasy and horror that inspired it -- is well-described by something like Joseph Campbell's theory of the hero's journey

The Hero's Journey

Note that there's a key separation in the structure between the "Known" world -- the place the hero starts at -- and the "Unknown" world -- the challenging region they travel into, before returning to their initial home.

Whether you're playing this as modern mythology, fable-making, or horror (especially that: and recall that HPL is foremost among the Appendix N authors), the most compelling dynamic is that of player characters coming from a (mostly) completely mundane place, and adventuring into a space of unimaginable terrors. By having the "Known" world rooted in reality, we get to comment on things that might be connected to our own world. We get to explore transformations that may reflect possibilities for the players themselves. We can practice how a normal-person can best respond to scary challenges or setbacks. We can use the liminal space between normal and abnormal to test the boundaries of what it means to be people like us. And casual players can more easily interface with how our games start and begin playing with us, too. 

There's a pulp-fantasy gesture I'm very fond of in which the narrator, the normal-human population, and even the protagonists themselves, are essentially skeptical, and disbelieve that supernatural events are occurring around them. There's a nifty play there about whether that fantastic stuff is even real (and of course: it simultaneously is, in the fiction, and it is not, in the real world). The real magic is indeed "Unknown", maybe constitutionally incomprehensible, to the normal-folk from which PCs originate.

Simply put -- Dragons don't belong in the starting "Known" part of the story. This model of the monomyth only makes sense if they are cordoned off in the "Unknown" part of the world. Same goes for Fireballs. And a whole lot of other stuff in the game. The hero does not get to start with that stuff. It would dismantle the meaning of their hero's journey if they did.

I mean, obviously you can play a totally "wahoo" anything-goes-out-of-the-box game if you want. But that's not where the game originates, it's at odds with the most compelling model of the monomyth, and it's simply not for all (or I'd argue most) players.

So it's not inherently incoherent to say there's a "Known" world of mundane things where PCs are born, and an "Unknown" world of fantastic magic and terrors which is separate from that. In fact, it's arguably the strongest structure for fantastic storytelling.

And therefore the "because-dragons" argument (particularly in terms of the what-can-PCs-start-with-in-my-game question) is an epic failure.

(See also H.G. Wells: Nothing remains interesting if anything can happen.)

Thumbnail image courtesy of Craiyon.


On d6 Ability Checks

One of our Wandering DMs Patrons on our Discord server made a great observation: In AD&D Module WG4, The Forgotten Temple of Tharizdun, at one point Gygax calls for a roll-under-Dexterity-on-4d6 to avoid a net trap. More generally, it's been reported in play at tables run by Gygax and Kuntz that they would commonly call for checks in this fashion to roll 3d6 (you know, the same way you generate abilities in the first place for OD&D), 4d6, or 5d6 for tougher situations. 

Now most of us have probably at least heard of rolling d20 under an ability score as a classic check. Oddly, none of these ability-check methods were ever written into the core rulebooks for either OD&D or AD&D. (It does show up as one of the very last optional suggestions by Moldvay in his Basic D&D rules, 1981.) Was this one of those things that was so fundamental Gary overlooked ever writing it down? Or some other reason?

Anyway, the question was posed as to exactly what the success chances are with this method. Here's the result of a quick Monte Carlo program to estimate them (via C++ code on Github):

Chances to make a roll-under-ability-on-Nd6 check.

On the one hand, I personally like the theoretical elegance of a roll-under-ability-score (using some kind of dice) so very much that I often wish the entire system had been aligned to a roll-under methodology from the start, for every kind of check. 

On the other hand, a top complaint is that this makes ability scores too important in the game, whereas by the OD&D books you can legitimately play PCs with fairly unimpressive scores, because they make so little difference to the play of the game. Additionally, the chances for success are vanishingly small in many cases (less than 10% for scores 3-6 vs. 3d6; 3-8 vs. 4d6; and 3-12 vs. 5d6). As one of our top think-tankers wrote, "At which point why are you even rolling?".

A really short-and-sweet mechanic like this does whet my appetite occasionally. In this case the modifying number of d6s to adjust the difficulty seems neat and clean. Would you consider using a rule like this in your games? Or do you still use the classic roll-d20-under-ability idea?


Compleat Character Creation Catalog: Unearthed Arcana

This is Part 3 of our exploration of different ability-generation methods in O/AD&D, and the chances for creating characters of different desired classes. The last installment was all about 1E AD&D according to the core books (PHB 1978 and DMG 1979). Today we'll be inspecting the Unearthed Arcana supplement that came out six years later (1985), the last year of Gary Gyax's tenure at TSR, as the initial D&D boom faded and the company was in dire need of a boost to income. As many AD&D players agree, that book overturned a bunch of apple carts. 

Boilerplate reminder on ground rules: We're looking only at entry possibilities for single-classed humans, not considering demi-humans with racial adjustments, multi-class combinations, etc. Statistics were generated from Monte Carlo-type simulations from my C++ program (and spot-hand-checked in a few cases and against other resources). You know the drill.

Ability Generation Methods

As an expansion on 1E AD&D, the Unearthed Arcana enhanced game obviously relies on the same stat-generation methods presented in the core rules. Recall the notable oddities there: (a) stat generation is not given in PHB, being locked away in the DM's book, (b) 3d6-in-order was disavowed as a generation method, and (c) the four methods that did appear were explicitly intended to make it easier for PCs to qualify for various classes of interest. You can see specifics on those 4 methods in the last post.

Even though Unearthed Arcana is just one volume, it's still split into separate sections for the player vs. the DM, with separate tables of contents, indexes for tables and charts, and everything. Presumably the player should not read the DM's section.

But if you do read that DM's section, you'll see that it starts with a proposal for a new Method 5 for ability score generation. They key point of this method is this: It guarantees access to any class that the player desires. ("subject to DM's approval", of course).

Specifically: The player chooses a class for their human character -- the rule explicitly says it can only be used for humans, thereby, I think, dodging the complications from multi-classing for the same reason we do in these articles. The DM gives consent, then turns to a table that specifies how many dice to roll for each ability score. For example, a Paladin will roll 3d6 for Dexterity, 7d6 for Strength, and 9d6 for Charisma (the maximum in the table). In each case you keep the best 3 dice for your ability -- and if you still don't have the minimum for the class, then it's automatically mulliganed up to that minimum. Pretty neat.

Two things about this new method occur to me. One is that Gygax here, precisely at the moment his official leadership of the game ends, completes a journey from OD&D being extremely strict about player entry to subclasses (e.g., less than a 2% chance to qualify for a Paladin initially), to making more-generous-allowances with the methods in AD&D (e.g., 24% to get a Paladin with Method 1), to completely expunging the randomness of that choice, and letting players take any class by fiat. That's obviously been the idiom of the game in later years, and was likely inevitable -- but there's at least a little tension in that generosity, which at the same time makes formerly-exotic options somewhat less special, and less worthy of the frenzied celebrations we once enjoyed.

The second thing is that, of course, Method 5 short-circuits the whole point of this series -- to analyze the chances of qualifying for various classes in O/AD&D with the different methods available. Using Method 5 the answer to that is, of course, 100% in every case ("subject to DM's approval"), and it basically time-stamps the moment when the whole topic became merely an academic issue. So I actually won't consider it further, and assume you're still only using one of Methods 1 to 4 for your AD&D character generation.

Classes and Requirements

What we do need to analyze are the additions and changes to the various character classes in Unearthed Arcana. While Method 5 is pretty clearly an optional variant (it's in the DM's section, it's one more in an array of method possibilities), the character class changes are all in the front-facing Player's section, and are presented in a way that they look like core changes for the play of AD&D (assuming you use Unearthed Arcana at all, obviously). Some of these are frankly hard to look at. Here's how the list of AD&D classes is now presented in Unearthed Arcana:

AD&D Unearthed Arcana Classes

So the first thing that jumps out is that whereas since 1975 we've had 4 primary classes (fighter, magic-user, cleric, thief) with their various subclasses, here Gygax brazenly sets forth the "Cavalier" as a new 5th primary class, and moves the Paladin subclass from the Fighter branch to Cavalier, with several class modifications flowing downstream as a result. Ugh. Gygax writes (p. 16):

The paladin is no longer considered to be a sub-class of the fighter, but is a sub-class of the cavalier. A paladin must have all the requisite ability scores of the cavalier, plus a wisdom score of at least 13 and a charisma of 17 or higher...

Now, the Cavalier's own stiff ability requirements are: Strength 15, Dexterity 15, Constitution 15, Intelligence 10, Wisdom 10 (resembling the Monk requirements quite a bit, actually; the only thing they don't have an explicit requirement for is Charisma). And then you combine this with the other Paladin requirements (Charisma foremost of all), and you see the Paladin now needs: Str 15, Int 10, Wis 13, Dex 15, Con 15, Cha 17. Yikes!

In addition to that, of course, Gygax has also added the new classes of Barbarian and Acrobat. Being held out as super-special options to spice up the AD&D game (and book sales), they too have very high ability requirements. The Barbarian (largely based on Gygax's earlier writeup of Conan for AD&D in Dragon #36) needs Str 15, Con 15, and Dex 14. They also uniquely have a maximum on Wisdom, in that it can't be over 16 -- which I've ignored here, as it wont make any visible different in the acceptance statistics. The Acrobat needs Str 15 and Dex 16. Note they're presented as a "split-class" (another early iteration on the "prestige-class" idea, like the Bard), in that you have to start as a normal Thief and then switch into the class after reaching 5th level. All of these new classes will be very hard to qualify for via standard dice-rolling methods.

Here are the combined requirements for all of the AD&D classes as given in Unearthed Arcana:

Class Requisites: Unearthed Arcana

Qualification Chances

Presented below are the results of our simulator program to find qualification probabilities for the various methods and classes in Unearthed Arcana. Recall the "No Class" row at the bottom is for the case of a PC have more than one ability in the 3-5 range, and thereby barred from picking any class due to a fluke in the AD&D fine-print rules (although that's basically negligible for any of the official Methods 1 to 4). Classes are presented in the same order as the book:

Class Access Chances: Unarthed Arcana
Recall that the instances of 0's and 100's in the table are the result of rounding -- e.g., the 4 original primary classes are 99.8% to be available to any Method 1 character.

Note that the Cavalier doesn't look at all like those other primary classes, does it? The chances to qualify for a Cavalier are, as expected, very close to those of the Monk -- at one time the hardest-to-qualify-for class in the game. Both are about 12% likely by Method 1, about 9% by Methods 2 or 3, and about a third of a percent chance by Method 4.

The new Barbarians and Acrobats are at about the same tier as the earlier Rangers and Illusionists -- about one-chance-in-three to qualify with Method 1, and less for other methods. 

But the standout result from Unearthed Arcana is that the Paladin (remember, it was the first-ever subclass introduced to D&D), with its sky-high stacking of various ability requirements, has once again returned to being the most extremely rare class in the game -- even harder to qualify for than the Appendix-quarantined Bard! It's approximately 0.9%, 1.0%, 0.8% likely by Methods 1, 2, and 3 (respectively), and less than 0.01% by Method 4. Rounding off, we can say it's pretty close to impossible to make a Paladin in 1E Unearthed Arcana -- unless you use the new Method 5, at which point you're guaranteed of your preference.

And that's where we'll end this series. It runs exactly parallel to the decade of Gary Gygax's direct involvement with the D&D game design, from 1974 to 1985. We've seen a progression from high rarity for subclasses from random ability generation, to open-access by player fiat, if you use the possibility of Method 5 generation mechanics. On the other hand, if you don't use that, we've seen the Paladin cycle from high-rarity to more-accepted, and back to maximal-rarity at the end.

What's you overall take on our compleat catalog? What bits and pieces would you actually want to use from Unearthed Arcana, if any? And what further topics should we discuss live at Wandering DMs?


Compleat Character Creation Catalog: AD&D

This is Part 2 of looking at statistics for how likely various start-generation methods are to qualify you for desired classes in early D&D (partly inspired by our recent chat on Wandering DMs). Last time we looked at stat-generation in OD&D (3d6-in-order, maybe with a few point-swaps allowed) and the various sub-classes presented in supplemental material (ultimately resulting in the same list of classes that appear in AD&D). Here we'll look at the AD&D game and its very different matrix of possibilities for generating ability scores, and the ways it overhauled those classes and requirements.

A few reminders of ground rules: We're just looking at entry possibilities for single-classed humans, not considering demi-humans with racial adjustments, multi-class combinations, etc. Statistics were generated by Monte Carlo-type simulations from a C++ program (and spot-hand-checked in a few cases and against other resources). Today's entry is only dealing with rules as presented in the 1E AD&D PHB/DMG -- rules changes from 1E Unearthed Arcana (6 years later), will be considered in a follow-up post.

Ability Generation Methods

A wrinkle in the publication history of AD&D is that PHB came out in 1978, and it gave no rule for how players should generate ability scores -- it's one of several things locked away in the DMG ("The referee has several methods of how this random number generation should be accomplished to him or her in the DUNGEON MASTERS GUIDE"; PHB p. 9). And the DMG didn't come out until a year later, in 1979. So I'm assuming in the intervening year players were still using the OD&D 3d6-in-order method by default?

When the AD&D DMG did finally appear, Gygax specifically calls out using straight-3d6 as a bad idea in these rules (p. 11):

While it is possible to generate some fairly playable characters by rolling 3d6, there is often an extended period of attempts at finding a suitable one due to quirks of the dice. Furthermore, these rather marginal characters tend to have short life expectancy -- which tends to discourage new players, as does having to make do with some character of a race and/or class which he or she really can't or won't identify with.

He then offers four alternative methods that can be used for the AD&D game, as shown below:

AD&D DMG 4 Methods for ability score generation

I'll rephrase those slightly. For comparison sake, I'll also include the OD&D method as "Method 0" to see how it stacks up against the AD&D methods. And note that while the book identifies them with Roman numerals, I'll use Arabic identifiers here, to more easily synch with my C++ code and its customary output:

  • Method 0: Roll 3d6 in order for the six abilities. (The OD&D rule, of course, not actually in AD&D for player characters.)
  • Method 1: Roll 4d6 and drop the lowest die, six times, and order to taste. (This is the default rule from 1E all the way to 5E -- and most likely 6E as well, which won't be changing that element, according to a draft Character Origins document released by WOTC the other week.)
  • Method 2: Roll 3d6 twelve times, take the best six, and order to taste.
  • Method 3: Roll 3d6 six times for each ability, and take the best of the six in each case. 
  • Method 4: Roll up twelve separate characters using 3d6 in order (i.e., as per the OD&D Method 0). Pick your favorite of the twelve characters.

(Yes, Virginia, there is a "Method 5" variant from the later Unearthed Arcana, but we'll address that next time.)

One thing to note is that the AD&D methods require exponentially more dice-rolling as one proceeds to the later methods:

Dice Rolls per Method

And, here are the base-level descriptive statistics differentiating the various methods:

Ability Method Descriptive Statistics

We see that Method 3 produces notably higher scores than the other methods -- it has an average of 14, while the other AD&D methods all hover around 12 to 13. Method 3 is also the most reliable in that it has the lowest standard deviation (e.g., the gold-standard for modern portfolio theory). Yet, we'll see later that, due to its lack of re-ordering to taste, Method 3 is not necessarily the best method in regards to the question of qualifying for certain classes.

I'll also note that for Method 4, I assumed that from the dozen characters generated, you pick the one with the highest sum (or average) of abilities -- although that too may not be the way it actually gets played, depending on the which character class one most desires. Again, we'll see the results of that further below.

Classes and Requirements

Recall that OD&D had no ability score requirements for the core classes in the LBBs, but did start using that as a mechanic to gatekeep the various sub-classes added in supplemental works. AD&D generally raised all of the requirements, in particular, instituting that any class had to have a score of at least 9 in their prime requisite (explicitly counter to the OD&D table of ability modifiers). Higher scores were required for sub-classes and even nonhuman racial choices.

And there's a further wrinkle in the fine print of the ability score rules that's easy to overlook: each of the character ability tables has a note for the 3-5 score range that restricts a character to only one particular class. For example, in the Strength table (PHB p. 9), it says, "Here or lower the character can only be a magic-user". Low Intelligence restricts you to Fighter; low Wisdom to Thief; and low Dexterity to Cleric -- while low Constitution mandates the Illusionist subclass, and terminally low Charisma restricts the character to being an Assassin.

So this results in an implicit "hopeless character" rule that requires re-rolling an AD&D character in some cases -- if you get more than one ability score in the 3-5 range, then the conflicting class mandates are not mutually satisfiable, and the character cannot pick any class at all. This gets echoed years later in the rules for D&D Basic; for example, Mentzer writes (Basic D&D Players Manual, p. 48), "If two or more Ability Scores are less than 6, the character may have problems later on. This type of character should also be discarded, unless the DM says otherwise." This is just a rephrasing of the same implied criteria in the AD&D PHB. (Also, I'm guessing that the 5E "no hidden rules!" dogma was motivated precisely in response to Gygaxian mechanics like this.)

This is a place where the otherwise excellent analysis of AD&D class access at Athenopolis.net made a misstep, I think -- they show the default ability minima to be 3 unless otherwise stated, when it's actually 6 by the AD&D ability tables (excepting precisely one 3 allowed for any given class). Fortunately, we'll see that in most practical cases this makes for only a small difference in our results.

A further interpretive assumption I'll make is that these very-low-score restrictions permit entry into an associated sub-class, unless otherwise stated. For example, if you have a 3 in Strength, such that the table explicitly says you can only be a Magic-User, then I'll assume you could alternatively be an Illusionist (if your other scores qualify). But that won't make a detectable difference either way you read this corner-case issue.

In summary, here are the requirements for the various classes in the 1E AD&D PHB as I see them:

Class Requisites: AD&D

Qualification Chances

So here's what our simulator reports for qualification probabilities across the various AD&D stat-generation methods. Numbers are all percentages, rounded to the nearest whole number. At the bottom there's an extra row denoted "No Class" for those unfortunates trapped by having more than one very low ability score, as described above. Classes are presented here in the same order as tables in the AD&D PHB:

Class Access Chances: AD&D
Note that the 0's and 100's in this table are all the result of rounding; nothing is guaranteed, but you get very close in many cases. In light of the inflated AD&D requirements, we see that we really had to progress to something other than the OD&D Method 0; many of the classes would be effectively impossible by that method (less than a half-percent chance to be accepted), our primary four classes now only have about 60% pass rate, and 13% of all characters are "hopeless" and can't enter any class.

Note that those primary classes, rolled under the OD&D method but with AD&D requirements, are really the only places where our numbers notably differ from those of Athenopolis.net (they show acceptance values about 10% higher than what we have here). These are the classes where the 6-not-3 default requirement affects the most abilities. Of course, this whole column is purely theoretical, because Method 0 is nowhere officially supported by AD&D -- unless we consider the one-year window between PHB and DMG when that may have been still practiced? All the other entries are usually less than a 1% difference in our mutual results.

By using any of the official AD&D methods, we see that the primary classes return back to near certainties (for example, you're 99.8% likely to qualify for a cleric, fighter, magic-user, or thief, using Method 1). It's actually Method 1 that generally has the best chances to qualify for a given subclass, with Method 2 generally a close runner-up -- these are the two methods that allow re-ordering abilities to the player's taste. If you're stuck with abilities in a predetermined order, as in Methods 3 and 4, regardless of how much they otherwise boost the numbers -- remember, it's Method 3 that generates the highest scores on average -- it's fairly unlikely you'll have the exact profile you need, and qualification rates are a lot lower as a result. Method 4 in particular, using a stack of a dozen Method 0-OD&D characters, is very bad in this regard (showing 0, 1, or 2 percent for a number of classes).

Let's focus mostly on that prominent Method 1 (there's a reason it was carried forward as the starting point for all later editions, while the other methods were mostly abandoned). It boosts previously very rare subclasses to more common occurrences: for example, about one-quarter of all characters qualify to be a Paladin or Ranger (compare to less than 2% in OD&D). Druids go from 6% to 78%. Illusionist was 9%, now it's 36%. Assassins scaled up from 5% to 94% (and, again, are even required in the case of very low Charisma).

One thing that jumps out at many of us when we first see this is that the Monk is actually even harder to qualify for than the much-treasured Paladin class -- it's about half the rate of Paladin success in both Methods 1 and 2. But the truth is that getting 3 scores of 15+ is harder than getting a single score of 17+, which are the critical requirements in both OD&D and AD&D. It's probability, kids!

Then you have the totally overhauled Bard class (also removed to PHB Appendix II), which is the only class in the book with explicit minimum requirements for all 6 ability scores (needing at least four 15's, one 12, and a 10). This is an overwhelmingly challenging prospect, with success rates of only 2% for Methods 1 and 2 (but oddly 4% with Method 3, making Bards the only class that Method 3 is better for). Contrast this with the gentle requirements in the OD&D version which gave it the highest acceptance rates for any subclass there.

Forgive me for a rabbit-hole on further weirdness with the Bard regarding the topic at hand: As any AD&D player knows, you can't start as a Bard (unlike the OD&D version); you have to starts as a Fighter, get to at least 5th level, switch to a Thief, progress to at least 6th level, and then switch to the actual Bard super-class (in the direction of what 3E would later identify as "prestige classes" in immense profusion). Note that among the several 15's the text says a Bard needs for their abilities, one of those is Dexterity. But: the core rule for humans switching classes ("The Character With Two Classes", PHB p. 33) dictates that one needs a 17 or 18 in the prime requisite of the class you're switching into -- in this case, Dexterity, when you make your first switch to Thief. So how do those rules interact? I can see arguments for (1) the core switch-class mechanic still apples, so you have a "hidden rule" that a Bard really needs Dexterity of 17+, or (2) the specific description of the Bard class overrides that, and Bards-to-be have a special allowance in their class switching. With that latter rule I can imagine a case where some rules-lawyer says they're aiming for Bard, double-classes as Fighter and Thief with only Dex 15, but then later reneges (a very niche case, to be sure). Nonetheless, for this analysis I've gone with option (2) and assumed the Bard truly needs only Dex 15. (If you instead rule that they really require Dex 17, then the chance to create one drops to approximately 1% for Methods 1 to 3, and less than 0.01% for Method 4.)

Finally, as we see in the last row, the "hopeless" no-class possibility that we outlined above is really a nonissue using any of the AD&D generation methods. With Method I the chance of this happening is only 0.06% (6 times in every 10,000 characters rolled), and with other methods it's even lower (less than 0.01% each).

What surprising things do you see in those results? Would this analysis make you re-think what method(s) you'd want to use in a new AD&D game? Next time: in what ways Unearthed Arcana stirred stuff up a few years later.


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.


OED Expanded Edition

Original Edition Delta: Verbose edition

It's been over 10 years that I've been maintaining, testing, and refining my OED House Rules for Original D&D, which you can find at OEDGames.com. Over that time, I've gotten lots of great feedback from readers & players via this blog and other sites. One of the guiding principles of that work, based on my own proclivities of course, is for it to be exceedingly minimalist -- just the barest of facts polishing up OD&D in some ways, taking up the smallest amount of page space it possibly can. Maybe sometimes it's even too minimalist.

Recently our chief aide-de-camp over at Wandering DMs, Baquies -- supporter, archivist, live-chat moderator, clip artist, etc., etc. -- created something I think is pretty amazing. For those people or places where my OED work was too sketchy or ambiguous or possibly fraught with confusion, he's written a completely expanded, "verbose" edition that lays out everything greater clarity than I had inclination to write. My few pages for Players and Judges rules have blossomed into an almost 50 page comprehensive ruleset  -- complete core rules, racial and class information in table form, equipment lists, spell rosters (from the OED Book of Spells), treasure tables, encounter tables, complete monster rosters, traps lists, and so much more. He's even added a Forbidden Appendix of his personal design that includes (gasp!) an option for Clerics and other stuff.

It's clearly your one-stop shop for all things OED. At prices like this (totally free), we've got to be crazy!

Baquies & I thought it best to host this document over at Github, in a completely open format (Open Document Text), so players can download it and modify it to taste. And make public edits, too? If you have a Github account (and know how to use it), feel free to make edits & pull requests and see if they become part of our OED campaign going forward. We're excited to see what happens next!

To view the OED Expanded rules, click the following link, then OED-Expanded.odt > Download:

OED Expanded at Github