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?