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?