Here's a D&D math puzzle. Consider a 4HD creature versus a 1HD creature -- say, an OD&D Hero versus a Veteran. (For this discussion we assume that all hit dice and damage are uniformly d6's.) On average, will the 4HD creature take 4 times as many hits to kill as the 1HD creature?

You might assume so -- I know I did, and that assumption is more-or-less built into the bridge that connects *Chainmail* to *D&D*. But somewhat surprisingly, that turns out not to be the case. Consider the following table (PDF): www.superdan.net/download/CompareHD1.pdf

What you'll see is that on average, any creature takes about HD + 0.5 successful hits before being eliminated. That is, we expect about half of the last hit to be "wasted" damage, perhaps as the creature is reduced to 1 or 2 hp, and still requires another full hit before being struck down. And what this means is that, as a proportion of overall HD and hit points, the 1-HD creature types will be "wasting" more of the attacker's hits and damage than higher-HD types.

In the second and third columns of the table, you'll see things like this: Whereas a 1HD creature takes an average 1.5 hits per HD, a 4HD creatures only takes 1.1 hits per HD. In short, a 4HD creatures actually only takes 3 times as many hits as a 1HD creature (on average). And this grows progressively more severe: an 8HD creature only takes 6 times the hits of a 1HD creature, and a 15HD creature really only takes 10 times more total hits than a 1HD creature!

This might be merely a mathematical curiosity. Or, it might be something we have to make decision about if (to pick a random example) we wish to construct a set of mass-warfare rules which replicate D&D results with high statistical fidelity. Should we honor the *actual* hits-to-kill-over-1HD (as in D&D above), or should we more simply use the HD as hits-to-kill (as in *Chainmail*)?

I've come to call this the "Packing Problem" in regards to hit values in a classic RPG or wargame -- the fact that very weak targets are wasting more of the enemy's damage on overkill hits, while those with higher hit-point scores are suffering full damage from most attacks, effectively reducing the true value of those higher hit points.

Follow up -- More Hit Dice Stats (checked by closed probability formulas).

Spreadsheet version of table (ODS).

C++ code to generate the table (GitHub).