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?


  1. He he! I like it. Your point that each splitting should become worse is the correct one I believe. Just think what happened to Mickey Mouse/the sorcerer's apprentice in Fantasia.

    As fun as this analysis is though, just think how odd trying to justify (or generate verisimilitude) this looks to people outside our niche.

    Keep up the good work!

  2. I will be covering area and volume in a Math class I will be teaching next semester. I'm tempted to use this as an example😁

  3. What do you mean by "at 1 HD one half dies off while the other is at effectively full-strength" ?

    1. It's basically just a hand-wavy justification for, "You hit a 1 HD slime in melee and nothing changes", so as to avoid fractional-HD slimes.

  4. Another entry for the appendix.
    I do wonder if the "at 1 HD one half dies off ", may give the players the false impression that they are making some sort of progress?

    Maybe just describe that at the smallest size, the slime just sort of "sploots" out from under the weapon blow.....

  5. 64%! Maybe these slimes depend on adventurers splitting them as part of their lifecycle.

  6. Professor, did you ever make up a wilderness travel rule set? I remember feeling like I owed a lot to you when it came to hexcrawling.

    1. Thanks for asking! Have been tuning that for a while, nothing really released yet. Hopefully back to that soon. Our friend Baquies suggested some rules in our expanded OED appendix

  7. https://youtu.be/k_GTIL7AECQ possibly apropos

    1. Love that channel, so glad you found that link! Moreover... describing DNA as scrolls of magic spells is actually one of the most brilliant things ever.