Radius or Diameter?

I've been working on refining spell descriptions (again) lately -- for hopefully upcoming expanded releases of the OED Book of Spells and Book of War rules. (E.g., we started testing top-level spells in mass battle play in the BOW livestream sessions the other week.) A couple of recent testbeds brought to mind the question: what's better for expressing the area of a circular spell effect, the radius, or the diameter?

For many years I've been strongly biased towards using the radius, because that's the used in mathematical definition of a circle. Arguably, however, it's easier and more common to measure real-world existing circles via the diameter (given the center is not actually part of the circle or necessarily distinguished; think tires, pizzas, wells, etc.)

Funny observation: Gygax's writing for O/AD&D was amazingly inconsistent on the matter, often flip-flopping for various spells in opposite directions. Starting with the first few spells in the Chainmail list, I see:

• Chainmail: Catapults/fireballs given by diameter, light by radius, protection from evil by diameter, etc.
• Original D&D: Fireballs by radius, light by diameter, protection from evil by radius (so, each of example toggles)
• Swords & Spells: Everything by diameter.
• Advanced D&D: Everything by radius (as far as I can tell).

I think the Swords & Spells case is interesting, because it gives a big list with all the stats (range, area, duration) for every spell in OD&D in a master list. When I did the same thing for my simulator, I found that things got confusing for a specific reason -- every other shape was being expressed by overall width (squares, lines, cubes, rectangles, etc.), but circles were listed by half-width. So I was getting a bit scrambled comparing entries of "circle-2-in." next to "square-3-in." and remembering that the former is actually bigger (wider). Note this is the case where Gygax gave diameters for everything, and I think this explains why.

The other (and related) case is trying to build templates for area spells in a VTT, specifically Roll20. There's a single pipeline for importing a token image and specifying how big it should be in map-square-units, and that interface asks for the total width (whether the image is of a square, rectangle, circle, etc.). So for my circle areas I was having to do an extra mental step and remember to double the indicated rule dimension for each token. In addition, I'd note that hand-drawing circles, ellipses, etc. in Roll20 and most drawing software I'm familiar with involves drawing and reporting on the bounding box for the shape in question; they don't draw from center to circumference.

Based on these experiences, for consistency with other shapes, I had an urge to switch all the circular specifications from radius over to diameter. But I also thought to ask opinions online, and got feedback like this on the ODD74 forums:

Similarly, folks on Twitter were almost unanimously in favor of using the radius. Voting on the Wandering DMs Discord server also went for the radius (with some votes switching from diameter back to radius based on discussion there: esp., targeting and determining casualties for a blasting spell). I didn't bother to ask on an AD&D forum, since those rules do uniformly use radius, so I assume everyone will be habituated to that.

Therefore, I'm taking that as an overwhelming preference among the classic D&D community, and not indulge my momentary instinct to switch things to a Swords & Spells type presentation, but instead keep giving radius like everyone expects.

We're all lucky I didn't find some way to argue for the circumference.

Dragon's Lair

I've gotten a chance to play the Dragon's Lair arcade game on my PC (finally in the last week or so).

I can't emphasize how ground-breaking this game was when it showed up in arcades back in 1983 (40 years ago as I write this). Up to that point, we'd only seen 8-bit sprite-based games with digital audio blips. Consider the top games from 1982 (per Wikipedia, "the peak year for the golden age of arcade video games") -- Dig Dug, Pole Position, Zaxxon, Q*bert, Time Pilot, etc. Rendered 3D games were about a decade away at that point.

And then all of a sudden the Dragon's Lair cabinet shows up with Laserdisc technology, and you're playing through a full-on Disney-quality animated movie by Don Bluth & co., experiencing booming professional voice acting, etc. My brain still hasn't recovered from what a leap it was.

For years I've tried to get a PC version working and never succeeded. I think I bought at least two CD versions and each time they were broken beyond usability. This past week I decided to do another search and, amazingly, managed to get a version that actually works. Plus the sequels: Dragon's Lair 2, Space Ace, etc.

So I'm playing through and actually learning how to play and decoding the terrifying puzzles for the first time. An amazing trip.

Here's a point: I'm finding that I don't like the sequels nearly so much. This is not remotely a nostalgia thing because, for budget reasons, I really never played any of them back in the day more than once or twice. So, why this preference?

It's because the later iterations made that classic misstep (to me) of inserting more story into the games. The first Dragon's Lair is essentially a picaresque: the action sequences come in basically a random order, and you never know what's coming next. Part of the play is keeping on your toes and identifying each scene quickly as it starts, so as to engage the right move series. This randomness keeps replayability high, and keep the focus tightly on the player skill in each puzzle as you learn and gain expertise with it.

But then each of the games afterward make the Hickman-esque movement of "this game would be better if it was more like a story you'd see in a book or movie". There are more narrative sequences of people talking when you don't have anything to interact with. More importantly, the sequence of scenes is always exactly the same for every play-through, because it needs to keep on a tightly railroaded plot. I find this has three effects: One, replays get boring faster because of the predictability. Two, it's more likely that you replay parts of the same scene back-to-back because the scene needs to get completed before you can continue. Three, when it mulligans you and just pushes you forward after a failure (death), I find that weirdly more jarring, because the Kenny-like death in the middle of the narrative story seems more lampshaded-incoherent.

This sense is of course consistent with my discomfort with the historical progression of inserting more "story" elements into games. For me, something is lost when the tilty-trap swings more in that direction away from the focus on technical player skill. My partner & I have always rolled our eyes at the narrative cut-scenes in real-time strategy games, as another example. But I think we're in the minority, as it's something I've been fairly well exhausted at debating with people over the years -- and probably more than one guest we've had on Wandering DMs has said things like "RPGs aren't about the gameplay, it's about the stories we make with our friends", which I guess I have to respect, but feel completely different about.

Advancement in Classic D&D

We frequently marvel at how sketchy the advice was in Original D&D (and other early editions) was for the number of monsters, amount of treasure, and expected rate of PC advancement in the dungeons.

There are a few semi-secondary sources that give estimates for advancement rates -- and it's rather remarkable how widely they differ. This is even though they all date from a time post-OD&D-Supplement-I, so they're all using basically the same monster XP chart and treasure tables.

Gygax in The Strategic Review Vol. 2, #2, p. 23 (1976)

It is reasonable to calculate that if a fair player takes part in 50 to 75 games in the course of a year he should acquire sufficient experience points to make him about 9th to 11th level, assuming that he manages to survive all that play. The acquisition of successively higher levels will be proportionate to enhanced power and the number of experience points necessary to attain them, so another year of play will by no means mean a doubling of levels but rather the addition of perhaps two or three levels. Using this gauge, it should take four or five years to see 20th level. As BLACKMOOR is the only campaign with a life of five years, and GREYHAWK with a life of four is the second longest running campaign, the most able adventurers should not yet have attained 20th level except in the two named campaigns. To my certain knowledge no player in either BLACKMOOR or GREYHAWK has risen above 14th level.

Note that on average this suggests about 60 games in the first year of play to achieve 10th level (i.e., an average of 6 games/level; but there's no reason to think this is a uniform rate over the ten levels). The data points afterward suggest a subsequent rate of about 2.5 levels gained per year of play. Obviously: that's an enormous number of games by modern standards!

Holmes in Basic D&D, p. 22 (1977)

As a guideline, it should take a group of players from 6 to 12 adventures before any of their characters are able to gain sufficient experience to attain second level. This guidelining will hold true for successive levels. Note that it is assumed that the 6 to 12 adventures are ones in which a fair amount of treasure was brought back — some 10% to 20% of adventures will likely prove relatively profitless for one reason or another.

On average, this works out to 9 adventures per level -- 50% slower than Gygax's general estimate (prior to name level).

Moldvay in B/X, p. B61 (1981)

If no one has reached the 2nd level of experience in three or four adventures, the DM should consider giving more treasure. If most of the players have reached the 3rd level of experience in this time, the DM should consider cutting down the amount of treasure, or increasing the "toughness" of the monsters.

On average, this suggests around 2.5 adventures to gain the first level-up -- over 50% faster than Gygax's general estimate.

Is it surprising how much those estimates vary? The one thing I might point to as a difference is that Gygax's play in OD&D/AD&D awards (some) XP for acquisition of magic items, whereas that's never suggested in the Basic D&D lines. Hypothetically that might explain why the Holmes rate is slower, but certainly not why the Moldvay rate is faster.

Can you think of any other obvious mechanical differences in those rules that would explain that? Which rate best matches your experience at the table? Which best matches your desire as a DM at the table?

The Science of Slime-Splitting

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

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: 

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.)

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):

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:

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:

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:

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?