2009-12-05

The Problem with the Endgame

These rules are as simple and straightforward as I could devise for a game system which involves "magical" and fantastic factors. The FANTASY SUPPLEMENT written for CHAINMAIL assumed a man-for-man situation. While it is fine for such actions, it soon became obvious that something for large-scale battles was needed.

- Gary Gygax, "Swords & Spells" Introduction, 1976

As old-school D&D'ers, I think that many of us share the intuition that there is an "endgame" in which high-level PCs wind up managing castles, baronies, and leading fantasy armies in battle. It seems a little frustrating that the endgame seems to have been "lost" somehow over time.

For probably 30 years I've been trying to scratch this itch and find the proper solution to the reputed endgame. Once again I've been attacking the problem recently, having had an opportunity in the last year to become familiar with Chainmail, OD&D, re-reading Swords & Spells and Battlesystem, etc. Personally, I need my mass-war system to have the same statistical expectations as if you actually played the RPG rules out man-to-man (i.e., it's no good to have X beat Y in RPG rules, but Y beat X in mass-war rules; I'm looking at you, War Machine.)

Here's my new observation: The endgame never actually existed in original D&D. It was sort of an illusion all along, which caused a lot of personal frustration.

Let me be specific: In neither Chainmail nor OD&D is there any provision for handling fantasy battles between opposing armies of hundreds of men (or monsters). It looks like there is, but there really isn't. Consider the quote at the top of this post (emphasis mine). Indeed, the Chainmail fantasy rules were in their entirety only meant to work on a 1:1 scale, not a mass scale, i.e., they're a continuation of the "Man-to-Man Combat" section that immediately precedes them. In other words, OD&D is in some sense just a somewhat revised edition of the Chainmail Fantasy Man-to-Man rules, not a totally different game.

Let's think about this a little more, because you get conflicting signals/ advertising from Chainmail itself. Conflicts would include: (1) Chainmail in general is at a 1:20 mass scale, and the Fantasy section never says explicitly that anything has changed in that regard. (2) The opening to Chainmail Fantasy says that it can be used to "refight the epic struggles related by J.R.R. Tolkien, Robert E. Howard, and other fantasy writers," which is not truly the case at 1:1 scale. (3) The language for Super Heroes asserts that, "these fellows are one-man armies!", when in fact they are only able to counter 8 normal men, not a whole army. (4) Combat chances between fantasy creatures and men refer back to the standard (mass) Combat Tables, not the Mam-to-Man Melee Table.

So, these assertions in the past led me to think that Chainmail Fantasy was at 1:20 scale, which caused all kinds of collisions with the standard D&D rules. I would think, "How can Super Heroes be worth an army in Chainmail (8x20 = 160 men), but only 8 men in D&D?" (Or, "Is every individual catapult/ giant boulder/ fireball really killing 100-300 men per shot?") Furthermore, you would have all these situations in D&D indicating the action of hundreds of men or monsters (such as [a] monster number appearing stats, [b] guards in castles, [c] clerical faithful followers, [d] crew numbers on naval ships, etc.) And let's pile it on one more time with OD&D Vol. 3, p. 25, which has a very brief (as always) reference to "Land Combat" which says this:

The basic system is that from CHAINMAIL, with one figure representing one man or creature. Melee can be conducted with the combat table given in Volume I or by the CHAINMAIL system, with losses equalling a drive back or kill equal only to a hit. Battles involving large numbers of figures can be fought at a 20:1 ratio, with single fantastic types fighting at 1:1 or otherwise against but a single 20:1 figure.

Now, we can see that the first part of this is an honest description of the Chainmail rules (man-to-man). The second part is not so honest, making it sound like Chainmail has the capacity to handle a 1:20 fantasy scale, when the truth is it really doesn't. As much as we'd all like it to, Gygax included. The last sentence with its waffle-y "or otherwise" is really more of a thought-experiment or a proposal than an actual rules reference. The fact is, we really have no pre-planned way in either Chainmail or OD&D to deal with those hundreds of wandering orcs, castle guards, faithful soldiers, or ship crews. (Nor the hundreds of guards in the barracks of Sup-II's Temple of the Frog.)

The conjoined problem is that any single hero-type will, if we honestly look at the statistics in OD&D, get chewed to pieces by dozens or hundreds of 1st-level opponents. Even a D&D Superhero in plate & shield (HD8, AC2) will get hit by normal men 20% on each strike (req. 17+ on d20). Surrounded by just 5 normal men at a time -- ignoring flank/rear bonuses -- the Superhero can be expected to take 1 hit per round and go down in 8 standard rounds (or less). Even with their fearsome number of attacks and morale effects from Chainmail, the Superhero will be dead in just a few minutes of standard D&D combat. (In OD&D it requires AC -2 to become immune to the attacks of normal men; of course, this immunity is taken away by the AD&D combat tables with their repeating 20's.)

So, I find that for the first time in 30 years I fully understand Gygax's Introduction to Swords & Spells. It's a fascinating read. He knows that there's a problem with mass Land Combat in D&D and he's trying to provide a solution. He knows that the presented ruleset is only a partial solution at best (using all expected-value hit point calculations, with no dice or randomization of combat results whatsoever.) In fact, having recently drafted a forward for my own similar work, I find that Gygax anticipated most of my initial comments 33 years ago, working on an equivalent project.

Some extra-curricular way must be added to allow our D&D heroes to survive on the battlefield, when they really shouldn't according to the stock rules of D&D. Gygax writes in Swords & Spells, "The admonition regarding single creatures is important: If they meet, or are simply near each other, they should seek combat with each other rather than inferior opponents, and this combat should be fought at 1:1 in the normal D&D manner". Yep, that's one way to keep them alive (i.e., force them to avoid masses of normal men whenever possible).

Likewise, Doug Niles writes in the Battlesystem 2E book p. 106: "From a mathematical perspective, the attributes of heroes in a BATTLESYSTEM scenario are inflated beyond those of the creatures in the units surrounding them. However, the conversion is based on the assumption that there is an intangible quality to heroism that exceeds in importance the hero's worth as a fighting machine." Yep, that's another way -- just arbitrarily boost the hero's stats on the battlefield to keep them alive.

An interesting problem, and some highly interesting reads when you lay out the entire sequence of mass-land combat in D&D. The truth is, there were no rules even intended for mass combat in fantasy D&D until Swords & Spells, and later Battlesystem, and these were only limited successes at best. OD&D hinted at an endgame that wasn't really ever there in the first place.

(Special thanks to James & Jervis for recently getting the 1972 Gygax letter on fantasy wargaming posted on Grognardia, which jogged my thought process a bit more on this subject.)

2009-11-27

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).

2009-11-24

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): www.superdan.net/download/CompareHD1.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).

2009-11-07

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!

http://www.lulu.com/content/paperback-book/original-edition-delta-book-of-spells/7871266

2009-09-29

Death Statistics in D&D: 1978

Character dies from spear

This is an excerpt from a short article by Lyle Fitzgerald in Dragon #20 (November 1978, p. 26). I find myself mentally returning to this glimpse of the past rather frequently.

Our campaign is primarily a wilderness one (as the statistics reflect), although huge dungeons do exist. The 600 deaths listed include deaths of playing characters and their advanceable hirelings, not mercenaries or other non-playing characters. We started compiling these statistics 2 to 3 years ago...
  • Goblin races (61) 10.1%
  • Dragons (45) 7.5%
  • Giants (34) 5.7%
  • General Combat (26) 4.3%
  • Lycanthropes (24) 4.0%
  • Execution/ torture, sacrifice (23) 3.8%
  • Undead (21) 3.5%
  • Bandits/ pirates/etc. (20) 3.3%
  • Giant insects (20) 3.3%
  • Assasination/ treachery (18) 3.0%
  • Giant rocs (18) 3.0%
  • Fireballs/ lightning (17) 2.8%
  • Trolls (16) 2.7%
  • Turned to stone (14) 2.3%
  • Guards, military patrols (13) 2.2%
  • Evil high priests (13) 2.2%
  • Man-eating vegetation (13) 2.2%
  • Related dragon species (13) 2.2%
  • Cursed items/ booby traps (12) 2.0%
  • Giant animals (12) 2.0%
  • Falls (12) 2.0%
  • Gnolls (11) 1.8%
  • Gargoyles (9) 1.4%
  • Hell Hounds (8) 1.3%
  • Demons (8) 1.3%
  • Elementals (8) 1.3%
  • Griffins (8) 1.3%
  • Kindred races (elves/dwarves)(6) 1.0%
  • Misc. spells (6) 1.0%
  • War (6) 1.0%
  • Misc. causes (85) 14.6%

2009-09-27

A Trite Expression

From a column this week by Jim Rossignol at Offworld.com:
Games don't necessarily have to be fun to be engaging. Indeed "fun" seems like a trite expression in the face of some contemporary projects: games can provoke more than simple enjoyment. Look at the terrifying crypts of Stalker, or the strange sadness of Shadow of the Colossus. To realise that games ride on more than fun only takes a quick glance at the bigger picture.

Sing it, brother! Of course, this is just prelude to an interesting article about other new developments, highly recommended. Plus, discussion at Slashdot.

2009-09-26

Solo Thief Adventures

A recent post on Grognardia features a player reminiscing about playing in Gygax's Lake Geneva campaign in a solo expedition to Castle Greyhawk (as a 1st-level magic-user, no less). It brought to mind what I've long considered a potentially really great untapped market -- solo adventures, specifically for Thieves.

It's always seemed like there's a bit of awkwardness around having "thieves" working with adventuring parties, when they're presented as likely to cheat and steal from the very party they're working for. On the other hand, I've had lots of occasions in my life where I it would be great to run a game with the one single player I had available. It seems like "solo thief" scenarios would be an ideal solution (ostensibly two problems cancelling each other out).

I actually had a lot of fun once running module "O1: Gem and the Staff", which is the one dedicated solo-thief module I can think of. It also offered a really nice opportunity to run a "mini-tournament" game where I ran each person in my regular gaming group through it individually, and then compared scores at the end -- among other things, this got a little "quality time" with each player to see their personal reactions and preferences.

As much as I'd like to see scenarios like that, I know I'm not the one to make them -- I think you need someone a little more steeped in noir, crime drama, Lankhmar and Thieves' World traditions than I am (which is to say, practically none whatsoever).