Friday, November 27, 2009

More Hit Dice Stats

In the prior post, I presented some numbers for the average hits required to take down different HD creatures. Of course, that was done by random simulation, so it will have some small amount of sampling error in the numbers. I wanted to double-check these numbers with a closed-formula, direct probability calculation. Even that takes some heavy-duty processing power (with permutations, combinations, convolutions, and such). Fortunately, it turns out that the numbers do in fact check out very nicely. Exact statistics and code below if you're interested. 

Hit Die Equivalence TableAgain, this illustrates what I call the "Packing Problem" for classic RPG and wargame hit values: low-hit types more frequently waste overkill hits and damage from attackers, while high-hit types are taking full damage, effectively reducing the value of their manifest high hit points.

Spreadsheet version of table (ODS).

Tuesday, November 24, 2009

Are All Hit Dice Created Equal?

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):

Hit Die Equivalence Table 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).

Saturday, November 7, 2009

OED: Book of Spells

We just published a volume on Lulu, entitled Original Edition Delta: Book of Spells. It's a concise, comprehensive collection of magic spells for use with the "original edition" fantasy game rules (as published by Gygax & Arneson, 1974-1975).

Personally, I always wished that the magic spells were set aside in their own booklet (instead of filling up the basic player's book), and now we have that. It uses the OGL to extract the bare-bones original rules back out of current, freely available source material.

Myself, I plan to print one of these out for each of the wizard players in my games (or whatever subsection they need: for example, the 1st-level spells all fit on one page again, so I just hand new players that and tell them it's their entire spellbook). I also made some minor edits to particular spells after playing with them for 30 years, which may or may not outrage you personally. :-)

It's 18 pages, with interior art on about 1/4 of the text pages where it fit. Available on Lulu as a download for $3.50 or printed with extra cover art for $7. Tell us what you think!