Monte-Carlo Measures of Monster Levels, Pt. 5

See Part 1 for the table of Monte-Carlo measured Equivalent Hit Dice (EHD) for most of the monsters from OD&D.

Higher Level Special Abilities: Special abilities for monsters at the upper end of the table become a little hazy in how well the Arena simulator can measure them, because they're even more dependent on DM adjudication, initiative and movement, player knowledge about how to counter them, area-effects against multiple characters, etc. (As of this writing, Arena is only 1-on-1; but the next version under development will have party-on-party action, so stay tuned for that.)

Note that the Arena simulator doesn't model any tactical movement; the combatants are presumed to come to melee range and start alternating blows. However, for monsters that are characterized particularly by some special ranged attack, an "Entry Attack" phase was introduced, where we assume the monster in question gets exactly one (1) opportunity to engage in its special attack form before melee is joined. Thus: Giants hurl a single rock before melee, Manticores get one volley of tail spikes, Basilisks and Medusae get one gaze attack before melee (and so, each fighter must always save or be turned to stone before even getting the first attack against these latter types). In a standard D&D game, these monsters may of course get none or more than one such attacks, depending on player knowledge and preparedness, etc.; but I think that the one free entry attack is a fairly good zero-level model.

Mummies: Mummies are surprisingly weak in this analysis; they are assessed at EHD 6 (one more than their HD of 5), which arguably should put them one monster table lower than in the book (all the other monsters at table level 5 have EHD 8 or above). Their long-term rotting disease is simply not a factor within a single melee. While it requires magic to hit them, I think we would agree that most fighters of this level should have at least one such weapon. While Vol-2 says of such weapons, "bonuses are at one-half value against them", that would be a totally negligible difference (maybe 1 pip in most cases), so instead I implemented the Monster Manual text that they do "one-half normal damage" (i.e., a straight 50% reduction in all damage). It turns out that even this defense is not a large factor, because at this level the fighter is reliably hitting, and the mummy does not have any truly threatening attack to stop them within the scope of the melee.

It sort of makes some sense, then, that later publications bolstered the mummy by adding to its abilities. At the end of Sup-II Blackmoor, Dave Arneson has a section on "Disease" in which he really lays it on, calling the mummy ability "Advanced Leprosy: ...  If  not cured within three days, there is a 95% chance of fatality, with a 2% decrease each successive day. Any character that  succumbs to this dread disease may NOT be raised from the dead; they are permanently dead" (as opposed to the Vol-2 rule which only slows down healing; although the table here instead specifies a 60% chance of irreversible death; but by item (f) causes a loss of 6 Strength points per day, maybe?). Gygax in the AD&D Monster Manual likewise makes the mummy rot potentially fatal (although in 1-6 months time; slowing natural healing as before, but negating all curative spells; and causing permanent Charisma damage), increases attack damage, gives fear and revulsion on sight (that causes paralysis), as well as standard undead immunities to sleep, charm, hold and cold. Another thing that I'm not modeling here is their extra-vulnerability to fire (which wouldn't make any difference anyway, because Arena fighters are not so equipped).

So in theory the mummy value might go up depending on your evaluation of the mummy rot risk (which might make a character potentially more vulnerable in some later encounter, or actually put them in the ground permanently), the implementation of fear and revulsion from AD&D, or possibly down because of the fire vulnerability (esp. when you have pyro-magicians as party members). Personally, the Arnesonian irreversible-death-gotcha has a certain roguish wit; but in my games with no Clerics, perhaps the divide-all-healing-by-10 rule originally in Vol-2 is sufficiently dreadful to be worth a significant EHD/XP bonus (e.g.: say results from a 1d6+1 healing potion get divided by 10 and rounded to the nearest integer; then you'd need a natural roll of at least 4+1, a 50% chance, to get even a single hit point back; so PCs in my games would be practically never able to heal again after an encounter with a Mummy, yowch!). Somehow I like that better than pulling strings to make sure a cure disease is always available before the clock runs out with the insta-death rule.

Giants: Only the Hill Giant is normally simulated in my program ("Hill Giants are the most common (60%)", per Vol-2). While they get a free stone-throwing attack in the Arena before melee, and 2 dice of damage in any attack, this doesn't make that much difference; their EHD is only 8, the same as their HD 8 (so: no XP bonus), in line with other humanoids. While they are on the top Level 6 table in OD&D, this analysis puts them one level lower that, equivalent to the weakest monsters on the Level 5 list. Perhaps if I had randomized among all the different Giant types, the average EHD would be a bit higher, but I don't think even that would legitimize their being on the Level 6 list. Without any save-or-die powers, they would be the odd man out there.

Basilisks: Here's another type that sits on the Level 6 list in OD&D, which the simulator would put on Level 5 (HD 6, EHD 8) -- perhaps a bit surprising. Now, here's the assumption I made for Gaze attacks in the Arena: the monster (such as a Basilisk) automatically gets one such gaze as an entry attack; so the fighter must save-or-be-petrified (thus instantly hors de combat) before joining melee. Afterward, we assume that the fighter is crafty enough to "avert their gaze", taking a −4 penalty hit from then on, but not being subject to any more gaze attacks. Granted that the Basilisk bite attack does only 1 normal die of damage in any ruleset, it's then hard for them counter the abilities of a high-level fighter.

But what this discounts, as we noted at the top of this post, is the game situation where a whole party of PCs turns into a cave and the gaze attack instantly wipes out, say, half of them before the fight even gets started. That area-attack-style capability certainly warrants adding some more EHD (and XP) to their rating. But even if we roughly double their HD from 6 to 12, that still argues for their being a Level 5 monster, not Level 6. (We'll see a more specific result for that in the upcoming Arena v.108.)

Edit: Looking more closely at the OD&D Basilisk description, I see that I've missed a key trait: "it has the power of turning to stone those whom it touches and those who meet its glance". The "touch" ability was removed by Gygax as of the AD&D line (1E, 2E, 3E, etc.), although it still appears in the Basic D&D line (Holmes Basic, Cook Expert, Allston Rules Cyclopedia). My memory of AD&D made me overlook this touch power and it wasn't simulated here; I should do that for the next cycle. It's pretty easy to guess that this will safely justify it being in the 6th level monster list.

Medusa: Now, the other petrifying-gaze monster, the Medusa, has a few less hit dice than the Basilisk, but a much more potent secondary attack: save-or-die Poison by virtue of its venomous snaky tresses. So an opposing fighter must save-or-die before combat even begins, and then again every time a hit is made. The Monte Carlo method tells us that this is a much more potent combination; from a HD 4 base, the Medusa is measured at EHD 12; a jump of +8 points, that is, triple the base HD (and so quite sensibly, triple XP), the highest such ratio among all the monsters measured (excepting a few questionable cases at the very end). This puts the Medusae at the top-end of Level 5 (where OD&D put them) in our analysis; arguably they should go in Level 6 instead. Perhaps an elegant adjustment is to just switch the entries of the Basilisk and Medusae in our tables.

How do you run your mummy rot -- as in Vol-2 with slowed healing only, or with Arnesonian creeping-death-in-3-days, or later Gygaxian death-in-d6-months? And are you prone to forget that Basilisks have petrify-on-touch in OD&D, like I did?


A Game of d6's and d20's

A delightful tidbit from D&D Classics Product Historian Shannon Appelcline on the recently re-released digital version of OD&D -- regarding the very early days when the game was in development but not yet released:
At some point, someone (perhaps Dave Wesely, perhaps Gary Gygax) found a twenty-sided dice supplier in the US: Creative Publications of California. However they sold their dice in packs of five, including a d4, a d6, a d8, a d12, and a d20. Notably missing was the d10, which didn't appear until Gen Con XIII (1980). There was one problem with Creative Publications' dice: D&D only needed the d6 and the d20. TSR decided to use the full sets to avoid having to sort out the other polyhedrons when they sold them. As a result, OD&D added some rules for using the other dice — particularly in the number appearing charts for monsters. Nonetheless, they were pretty scant.

This makes so much sense: OD&D definitely has the flavor of a game that is barely a few inches away from just needing d6's and d20's. And frankly: I want that game. So incredibly elegant! (Recall: My monster hit dice and damage are still all d6's; to date players have never noticed any difference, and its so much easier to manage as the DM).


Monte-Carlo Measures of Monster Levels, Pt. 4

The devil is in the details. More discoveries on running OD&D monsters through a computer simulator a few million times each, here focused on some giant versions of real-world creepy-crawly animals:

Giant Ants: OD&D situates these creatures on the 3rd level table. This monster doesn't have any statistics specified in Vol-2, or even a suggestion for damage in Sup-I (like most giant animals do), so we necessarily turn to the Monster Manual. The basic type of giant ant is AC 3, HD 2, Atk 1 for the canonical 1d6 damage; the text indicates that this is a worker ant ("90% likely") -- and the simulator measures this simple creature at only EHD 1, which would suggest that we move it one table lower in OD&D. But the text also indicates another option (presumably 10% of ants): the warrior ant with HD 3 and a poison sting (save or die, of course) -- and this type the simulator assesses at EHD 5, which would put it one table higher than shown in OD&D. So here we have a dilemma: the worker ant is too weak, and the warrior ant too strong, for the given location in the OD&D random monster tables. I've left it as the warrior type in my charts, just because the poison sting makes it a little more interesting; perhaps that's a mistake thematically.

Giant Beetles: The type is shown on OD&D random table level 4. Sup-I (p. 18) suggests that Giant Beetles be given 3-30 (3d10) damage per bite; that seems highly excessive in our context of non-revised OD&D combat, because even Giants are originally given only 2 dice of damage (d6's). Looking at the Monster Manual with its half-dozen options for Giant Beetles, the one that seems the most appropriate is the giant Boring Beetle, with AC 3, HD 5, and Atk 1, now reduced on average to 5-20 points (5d4). If I lower this to simply 2d6 damage, to match it with Giants (and the only type on my list below Giants to get more than 1 die of damage), then the assessed EHD is 5, the same as its Hit Dice -- so no bonus to XP, but nicely situating it in the middle of the Level 4 table where OD&D says it belongs.

Giant Snakes: OD&D places these creatures on the Level 3 table; and there are so many issues to juggle with this one (again, we can only guess at it assumed Hit Dice, Attacks, etc.). Sup-I suggests that the Giant Snake should have both a poison bite and a constriction attack (if I read it correctly); a combination that doesn't actually occur on Earth for any type of snake. The Monster Manual thereafter takes a more naturalist stance, splitting up the types of snakes into either a giant Constrictor HD 6+1 or Poisonous HD 4+2 types (among others: Amphisbaena, Sea, and Spitting snakes, not considered here). So we have a number of different options to consider for our OD&D serpent.

Let's take a step back and consider the pulp literature for the type. Conan is known to deal with monstrous snakes in many of his stories (including famous cover artworks), so let's look there. Fortunately, I found a post compiling those giant-snake encounters on the Official Robert E. Howard Forum precisely one day before it's scheduled to be shut down (currently at www.conan.com; I'll be copying the content in comments below when I get a chance). Poster blanor notes that Conan fought giant snakes in 4 stories (Hour of the Dragon, Queen of the Black Coast, Beyond the Black River, and The Devil in Iron). As I look up the scenes in the various stories myself, I note that in each case they are described as a tremendous python, a constrictor type that tries to crush Conan or someone else in its coiling mass (the word "python" is directly used in all of the stories except for Devil in Iron; although tellingly the description of a "wedge-shaped head" is used uniformly in all of those stories). The serpents are each described as being variously 20 or 40 feet long (and The Scarlet Citadel has a whopping 80-foot snake that chases Conan for a while, but he never actually comes to blows with it). But the creature in Beyond the Black River is given an additional terrifying aspect:
That was the reptile that the ancients called Ghost Snake, the pale, abominable terror that of old glided into huts by night to devour whole families. Like the python it crushed its victim, but unlike other constrictors its fangs bore venom that carried madness and death. It too had long been considered extinct. But Valannus had spoken truly. No white man knew what shapes haunted the great forests beyond Black River.

Taking the Conan stories as a cue for the basic type, my list features the MM Giant Constrictor as the basic Giant Snake: AC 5, HD 6+1, can bite and constrict at the same time for 1d6 damage each (this requires an initial successful bite; thereafter it gets 1d6 constriction every round automatically, and can still bite normally as well; the victim can act normally meanwhile); this gets assessed as EHD 6, the same as its HD (so no XP bonus), but placing it one level higher than in the OD&D tables (and on the tail end of that table, in fact, almost into Level 5).

So perhaps we should consider some other options to rectify that. Take the MM Giant Poisonous type (HD 4+2). Unfortunately, the save-or-die poison makes this even more dangerous, at EHD 8 -- clearly into the Level 5 table, then. Or we could simulate the infamous "Ghost Snake" at HD 6 with both constriction and poison -- of course, that's even more deadly, at EHD 11 (pretty deep into the Level 5 monster table at this point). We could consider a mini-Ghost snake, 3 HD with both constrict & poison, as per Sup-I -- that's EHD 5, still one level too high.

If we decide to dial things down to a simple snake of 3 HD and constriction as its only ability, then in this case, we get EHD 3, properly placing it on the Level 3 table as OD&D is printed. (The constriction ability by itself always generates EHD = HD.) Of course, as DM you can create a snake of whatever hit dice and abilities your heart desires. For example, the Holmes Basic D&D Sample Dungeon has a 2 HD snake in room "S" (no special abilities noted; are we meant to assume this is a constrictor, poisonous, both, or neither?).

What do you use for baseline giant ants, beetles, and snakes in your OD&D game? Bigger, badder, and more fantastical stuff considered in the next post.


Devil's Advocate

Lest we forget our history, let's remember that there was a freer time for the publisher of D&D, when it was not yet taboo to probe possibly darker themes and subject-matter touching on real-world belief systems. The high-water mark was likely in August, 1979, in Dragon magazine #28, with Alexander von Thorn's article "The Politics of Hell". It's the featured article of that issue, running some 5 pages (or 20+ paragraphs). It opens with this unusual (and perhaps questionable) disclaimer by the author:
(Author’s note: The following article cannot be considered the official doctrine of either  Advanced Dungeons and Dragons  or the Roman Catholic Church. However, it is compatible with  AD&D,  and except for the parts about Asmodeus it is not in conflict with works on demonology as generally accepted by Catholic exorcists, thus enjoying tacit approval by the Church. However, this article does not have a nihil obstat; much of it is original, and it approaches the subject from a different angle than a religious tract would and should not be considered as such. The rise of Asmodeus is not documented in any major text on demonology, but very little original work on the subject has been done since the Middle Ages, so it is possible that the situation has changed. Perhaps Mr. Gygax has more accurate sources of information...)

The first half of the article is a mythology, to my eye a pastiche of Biblical and Dantean ideas, and twice referencing the Lesser Key of Solomon. This presents a historical tale explaining the overthrow of Satan by Beelzebub/Baalzebul, and then likewise by Asmodeus, in such a way as to explain why it is that latter figure who leads the Hells in official AD&D rules. It identifies the first coup with the real-world Renaissance period, and the second with the period of World War II. Von Thorn writes:
In fact, most people including the majority of the clergy, were not aware of the change in the leadership of Hell. To this day, when people think of “The Devil,” they think of Satan, and if the name of any devil is mentioned in a Catholic sacramental ritual, it is his (e.g. when the celebrant asks, “Do you reject Satan?,” etc.).

The latter half of the article presents information on three now-fugitive figures: Satan, Belial, and Astoroth (i.e., famous devils who had not previously appeared in works of AD&D). Here is the stat block and the first part of that ten-paragraph section:

A few details are given that would certainly be proscribed later on, such as: a suggestion that an actual paper contract between Satan and an interested PC be drawn up for clarity; special status for clerics of mainstream Abrahamic religions, etc.:

It is best to have the contract actually written out, with identical copies for the player character and the DM (which the player should study carefully before signing), because Satan is extremely literal, and he’ takes sadistic pleasure in twisting the intent of a contract by fulfilling its letter...
Naturally, a person cannot take any positive action to get out of a contract without first deciding to do so. Any Jewish, Christian or Muslim cleric of at least Patriarch level (such as a Cardinal, Primate, Metropolitan, Chief Rabbi, Ayatollah, Caliph or equivalent) can invoke the name of the Deity to save the person’s soul. However, they usually require some token of one’s devotion to the cause of good, such as the performance of some appropriate Quest, as the price of redemption...

It's likely that articles like this one by von Thorn -- including those by Ed Greenwood in Dragon #75, 76, and 91 -- touched a little bit too close to home in some circles, and were among the catalysts for the witch-hunts regarding D&D in the 1980's. You can see some of those cultural warriors of the period (notably Pat Robertson) still making the same warnings about D&D today. In order to survive as a business, TSR made references like the above completely prohibited from their publications, a taboo that survives to this day for owner of the official D&D license.


Armor of the Gods: Dots and Dashes

Quick observation regarding OD&D Sup-IV: Gods, Demi-Gods and Heroes (Kuntz & Ward, 1976): In some stat blocks the key "Armor Class" is followed by a colon, while in other places it is a long dash. This makes it very easy to mistakenly read many ACs as negative when they're really not. As one example, these Egyptian deities on p. 6 both have the same AC:

If you consistently misread the ACs followed by dashes, you'd have a lot of very weak creatures (like, otherwise playable low-level monsters) with ridiculously hard ACs: for example, in its first appearance in this work, the 6th-level Naga would be given AC −5, whereas in the later Monster Manual it more clearly appears with AC 5.

The majority of entities, even greater gods, tend have ACs capped at 2 (plate), the same as for monsters in the original rules. The only creatures I see listed in Sup-IV with truly negative ACs are: the Fenris Wolf (AC −2), the Midgard Serpent (body AC −4), and the Earth Queen (AC −3). For more of the rare monsters who have negative ACs in OD&D, see: Sup-I (elder dragons and will-o-wisps), and Sup-III (demons and ki-rin).


Monte-Carlo Measures of Monster Levels, Pt. 3

More observations and discoveries from coding and simulating the OD&D monster special abilities. See Part 1 for the table of Monte-Carlo measured monster levels (Equivalent Hit Dice, or EHD).

Undead and Energy Drain: One possible weakness of the simulated-combat model here is that it can't objectively weigh the value of long-term disabilities like energy drain, disease, and/or lycanthropy. In the scope of a single fight-to-the-death, these abilities make little difference. Of course, if a fighter of middle level can be assumed to have a magic weapon, then this cuts through all the undead defenses. So I was somewhat surprised to see wights measured at 1 EHD under their actual HD, and wraiths at just parity (arguing for no XP bonus, although higher types do start outstripping their base HD as a level of danger).

A few adjudications are necessary regarding OD&D energy drain, which might change your results: Does the target get a save? Does the drain reduce current hit points? To what XP level does the victim get reduced?

Personally, for some time I've been orbiting the zone of giving characters hit by undead a save to avoid the level-drain; however, the simulation here did not include that, and the EHD's for wights and wraiths still didn't evidence any boost for XP value. And yet I still like the texture of a saving throw; in the window where the player reaches for the die, rolls it, and watches for the result, it would seem like they get to "feel" the existential horror of the unknown in their gut, as opposed to the DM just announcing the loss as a done-deal-by-fiat. And it's consistent with giving a save for about every negative effect (like poison, paralysis, etc.) One remaining concern would be exactly what save to call for? I've been using the "Death" column (powers of undeath and all that), but it's the most generous save category, which feels a bit too soft, actually (almost 50% to save even at 1st level in the OD&D text).

Other decisions that seemed the most elegant while writing this in code: I had the energy-drain reduce maximum hit points, but not necessarily current hit points. Example: A 3rd-level fighter starts out at 15 hit points and gets hit by a wight; say the base 1d6 damage comes up "6", reducing current hit points to 9; and then the energy-drain kicks in, reducing level to 2, and maximum hit points proportionally to 10. So in many cases like this, the energy-drain may have no practical effect on current hit points or increased risk of actual death. This would be very different, and more dangerous, if the mechanic was to actually keep a record of damage taken and dynamically compute current hit points as maximum - damage when checked (but that doesn't resemble what I see most players doing at the table, so I didn't implement it that way).

Also, it seemed most elegant to just drop XP to 1 under the current level -- that is, the same mechanic used in the limit on gaining more than one level at once. That constitutes maximum generosity to the PC in question, and a single level loss is sure to be regained at the end of the given adventure when new XP is awarded (although still might be a lot of XP over the bridge, or multiple level losses a more lasting penalty). In the past I've used proportionally-rated XP drops (same relative location in XP as in the starting level), but I kind of like not having to pull out a calculator for that anymore. Alternatively, I think some rulesets specify dropping to the start of the prior level; the most punishing interpretation you could make.

Giant Hogs: Giant hogs are listed on the 3rd-level table for OD&D random monsters, and apparently in Gygax's Castle Greyhawk, the 6th level was nothing but a maze with "dozens" of giant hogs and lycanthropic leaders (link; and see below). Now, even the Monster Manual doesn't have an entry for "giant hog", but it does have "boar, wild", at 3+3 Hit Dice (same as the "3 dice" mentioned by Gygax regarding the Greyhawk level). This is a fairly weak opponent, only assessed at EHD 2 in the simulator (but at least it marginally belongs in the indicated table); note that the MM ability of fighting for a few rounds while in negative hit points is not something I could implement easily in the Arena code (in breaks the standard mechanic for hit points, and also breaks the Arena expectation that every fighter has an identifiable survivor/winner). On the other hand, if we were to use the 7 HD "giant boar" from the MM, this type would be much stronger, assessed at EHD 6, and so would belong at the upper end of the next table higher. So of the two, the Monster Manual's "boar, wild" has more evidence of being the better fit.

Lycanthropes: I only implemented the base type of lycanthrope, the Werewolf (you'll see that the same thing happened for Giants and Dragons, say). I was kind of surprised to see how underwhelming it is in practice. It's the only monster in the system assessed at two pips lower in EHD than its actual HD (i.e., EHD is only half HD). Assuming a fighter with a magic sword by this level, its defense is not relevant, and neither is the lycanthropy effect an increased risk to lose a given fight. If we assume no magic weapon for our fighters, then the EHD jumps from 2 to 4, the same as its HD (the Arena simulator does assume that fighters have a silver dagger to draw out in any case, but in that case their damage is halved from d8 to d4). Perhaps if we randomized from among the 4 types of lycanthropes in the book, this overall result would be a bit different (although even then HD are in a narrow range from 4 to 6, so likely not a huge difference).

Gargoyles: Similar to lycanthropes, and more critically, their main special ability is their defense in not being hit by normal weapons; and therefore the key to their measurement is at what level do we assume fighters will usually have a magic weapon? In my model that all fighters in the arena have the +1 sword, you see that the EHD turns up at 4, the same as its actual HD (and so: argues for no XP bonus). Of course, if your model/assumption is that fighters only get magic at some higher level, then the Gargoyle EHD will follow suit (at exactly the same number; the simple proof is left to the reader).

That's it for this week. Open questions: At what level would you assume that a fighter has a magic weapon (and so gets to hit high-level Undead, Lycanthropes, Gargoyles, etc.)? And how do you adjudicate the details of  Energy drain -- Saving throw? Hit points effect in combat? XP reduced to what level?


Link: OD&D Print Comparisons Video

More great stuff from Jon Peterson of Playing at the World:


Monte-Carlo Measures of Monster Levels, Pt. 2

See last week's post of the output of the Arena monster-measuring program (link). Some more observations and discoveries as I thought through implementing all the monster special abilities in code:

Position in Monster Tables: In OD&D the random monster tables were organized in (of course) six different "monster levels". In the table in the prior post, I've shaded in six alternating groupings that follow those six levels as closely as I could tell. Generally speaking, the relative rankings are about the same; the monsters the gained or lost their position on a particular table are noted in the TC column, with a "<" or ">" as appropriate. There are 4 that want to go up a level, and 6 that suggest going down, in this analysis.

You can see in this model that Monster Table 1 would be composed of all EHD 0 monsters; Table 2 would be about EHD 1-2; Table 3 approximately EHD 2-3; Table 4 EHD 4-6; Table 5 EHD 8-12; and Table 6 EHD 13 and up, roughly speaking.

On Points for Special Abilities: At the end of the day, the main theme of this blog might be: "Creating new elements for a game is easy, but evaluating those elements is very hard; and a table of summed points is almost surely broken." Speaking of XP, pretty much every edition assumes that a special ability of a certain type will be worth the same relative boost for any monster that possesses it. But consider a monster who, say, has poison, paralysis, and petrification attacks, but can only use one at a given time; then the effect is about the same as having only one of them (there is a marginal added value for having the different options, but the value will be pretty small). Or, as we will see: save-or-die hits might be more useful against a high-level PC with many hit points, but negligible against a low-level PC who would die from the one hit anyway (and hence: more valuable for high-HD monsters, and less valuable for low-HD monsters). Actual examples include the Gold Dragon with its two different options for breath attacks, or the Demons of Sup-III with their multitudinous spell lists.

Missing Monsters: Almost all the monsters in the OD&D random dungeon monster lists were included in this analysis. But: no NPC spell-casters were included (magic-users or clerics), because implementing the entire D&D spell list, and AI to choose from the different options, was outside the scope of this project (and secondarily, it also seemed a bit outside the theme of a gladiatorial arena). Also: the Ochre Jelly could not be included, because it's entirely unkillable by weapon blows (and so invulnerable to the attacks of our comparative fighters).

Zero-Level Monsters: All of the monsters on the OD&D "Level 1" table (Kobolds through Spiders) were evaluated as Equivalent Hit Dice zero (EHD 0). This is something of an artifact that the Arena best-level process can't output fractional values; after all, it only has integer-valued levels of fighters to choose from as opponents. In other words, these monsters are a fair fight, or less, for a single 0-level man with 1d6 hit points bearing chain, shield, and a sword. I wouldn't plan on reducing any XP awards from the base Hit Dice; I would still award a full 1 HD or appropriate fraction based on actual HD. So I blanked out the "Diff" and "Mult" columns here to avoid suggesting the reduction in XP in this range.

Centipedes and Spiders are basically as seen in the Monster Manual. (Centipedes get 1-2 hp [1/3 HD here], no damage, but poison at a +4 save bonus; Spiders are of the "large" variety, HD 1+1, 1 damage, and poison at +2 save.) Related to the point on special abilities above, it's interesting that even this save-or-die poison doesn't actually boost their threat level past level 0 in this analysis. We might observe that for a fighter with a single hit die, whether you're hit for 1d6 damage or poison, the effect is indistinguishable; you're probably dead. However: this value may be different if you team a lot of the monster type against a higher-level fighter (like say: consider 10 goblins vs. a Lord, against 10 spiders vs. a Lord; then one hit in the latter case is more worrisome), but this is not visible in the current model. In the past I considered doubling the save bonus indicated for centipedes and spiders; now I'm pretty convinced that they're reasonable as written, and may not even be worth any XP adjustment at all.

As an aside, if we take out the +1 sword given to our nominal fighter opponents, then it makes no difference in the assessed EHD level for these 0-level monsters. Among higher-level monsters, the trend would be to adjust +1 or +2 EHD higher, although the magic-to-hit monsters would of course turn unbeatable (immeasurable) in this case.

Toads, not Thouls: Many of us know that "Thouls" were listed in OD&D monster Table 2, without any statistics or description given for them in those rules. Tom Moldvay's later Basic D&D detailed a Thoul with 3 HD, two attacks, paralysis like a ghoul, and regeneration of 1 hp/round. Gygax separately communicated his take on the Thoul as 4+2 HD with the same abilities.

What was news to me recently is that the entry for Thouls did not appear in the 1st printing of OD&D; what appeared originally in that slot were "Toads". Now, this makes a lot more sense to me. First, giant frogs and toads seem like an intrinsic theme of early D&D, and with all the other giant-animal types, it seems weird for these amphibians to be entirely missing. Second, evaluating the Gygaxian Thoul would put them at either EHD 8 or 12 depending on the attacks permitted, and so would be misplaced on the random tables by fully 3 levels (out of the 6 total). Instead, by returning the Giant Toad to its rightful place (using MM stats), their power level fits right into Table 2 where they originally squatted.

Why were Giant Toads taken out of the later printings? Partly this has the smell of erasing the thumbprints of Dave Arneson, who is perhaps chiefly remembered in official D&D publishing for his "Temple of the Frog" complex in OD&D Sup-II. (Link to discussion of toads and thouls at Dragonsfoot.)

NPC Fighters: NPC fighters, as they are shown in the table, conveniently get assessed at an EHD equal to their actual level (i.e., true HD) in each case. Like the protagonist fighter, they get abilities of 3d6-in-order, and normally-rolled hit points. But they also get plate mail and a 5% chance/level for a boost in magic to armor, shield, and weapon. This is partly offset by the guaranteed +1 sword for the baseline fighter, so on average the difference is only 1 pip to hit (at least until we get into very high levels, in theory).

As an aside, here's how the simulator generates magic arms: for each NPC fighter level, we make a separate 5% roll to see if that fighter's armor, shield, and/or weapon should be boosted by a +1 magic bonus. Then we roll again at the next level, and so forth. This may produce up to a +5 magic bonus if several rolls succeed. Note that this is a hairs-breadth difference in probability from the straight 5%/level indicated in Vol-2, but it smoothly generates magic items of higher values, so it's very close and I actually like the elegance of this method a lot better.

In fact, I like this so much I may start doing it when I manually create NPC fighters. Say: Take 3 d20's of different colors. Roll this group once for each level of the NPC. Each time a "20" shows up, tally another magic pip on the associated armor, shield, or weapon. This might take a minute longer than just a single percentage roll, but the results are a smoother distribution. It doesn't directly generate any of the exotic weapon types (flaming, +3 vs. trolls, etc.), but even that I kind of prefer; normal NPCs won't have them, and only adventuring the underworld can dig up those special types. Personally I'm always aggravated when some 4th-level sergeant winds up with a sword of wishes and I have to spend time thinking about how to adjudicate that.

That's it for this week; more next time.


Link: Precursor to Chainmail Fantasy

Jon Peterson of Playing at the World has another ground-breaking, possibly bombshell piece of research that he's dug up about the origins of D&D. Namely: a set of fantasy miniature rules for Tolkien's orcs, wizards, dragons, etc., written by one Leonard Patt, and published by the New England Wargamers Association in 1970 (and recipient of "Best of Show" award at the Miniature Figure Collectors of America convention that year).

Notably, much of the rules and rules language is shared by the later Chainmail Fantasy supplement by Gygax and Perren (and hence incorporated into D&D after that). I find these observations by Peterson to be fascinating and compelling. I, for one, am very happy to have a better understanding of the origins of the game from this work. Thanks once again to Mr. Peterson for bringing this to light, and also to Mr. Patt for his initial ideas!


MadMath: When Dice Fail

If you're interested in the dice-testing procedures that we've considered on this blog, hop on over to my math blog to see the first case of dice that actually failed the chi-square test that I've found to date. Before you do: Can you spot anything wrong with the dice below?


Monte-Carlo Measures of Monster Levels, Pt. 1

Abstract: Recently I've been expanding my "Arena" simulator program for OD&D combat analysis (current version 1.07). In particular, I implemented special abilities for all of the monsters in the OD&D dungeon wandering monster lists (with a few exceptions). As I did, this, it became possible to run simulations against all of those monster types to get a measure of the "true" power level for all of those monsters. This, in turn, then gives some confidence for exactly how much XP should be handed out for each monster in the OD&D Vol-1 context (recalling that at that time, there was no awareness of the need to modify XP for monster special abilities). See the chart below for the output, and then I may spend some number of blog posts discussing this model, it limitations, and the results. The second column, "Equivalent Hit Dice", indicates overall power level, and is what I would generally expect to use for monster XP awards (specifically: this number × 100). Spreadsheet version here: ODS file.

The Model: The Arena program simulates one-on-one gladiatorial fights between single fighters and some other opponent in original D&D (which could be either men or monsters). The rules implemented are essentially OD&D with 5%-step smoothing applied to attacks and saves.

After trying a few different models for assessing monster power levels, here's what seemed to work the best. NPC fighters are faced off against each monster in sequence: these fighters are assumed to be in chain mail & shield (base AC 4), with a +1 magic sword (to allow attacks on gargoyles, etc.), and ability scores rolled straight-3d6 (no bonus on average, except the 1 pip from the magic sword); but they may be of any level. No other improvements for equipment, improved magic, or higher ability scores are made for advanced levels. Fighters do not ever get multiple attacks (as they did not in OD&D; even for under-1-HD types, they are likely only being compared to 1st level fighters anyway, and we want a consistent basis for comparisons here in any event). This choice seems to allow for a fair measurement of the "raw" power of each monster, gauged against an opponent of fixed AC and damage output (i.e., the fighters only vary in HD alone, so "Equivalent Hit Dice" is in fact the output).

For each monster and any suggested fighter level, we can generate a random monster and fighter of that type, and have them battle to the death in the Arena. This is repeated 10,000 times for a given suggested level, and a proportion of times that the fighter wins produced (a Monte-Carlo method). Then we run a binary search on all possible levels from 0 to 50 to find the fighter level that gives the win percent closest to 50%; and we call this the "Equivalent Hit Dice" (EHD) of the monster.

Some of the confidence that this model gives us are that the EHD's generated for all the NPC fighters in the monster list are in fact identical to their actual HD (level). Also, the brute humanoid types like orcs, gnolls, ogres, and giants, have EHD in approximate linear progression to the Hit Dice, with trolls specially being valued at about double-HD -- the same as shown in our prior analysis of monster values in Chainmail, Vol-3 Mercenary costs, and Book of War (link).

Note that these results in EHD are not the same as the level of PC fighter that would be fairly matched against a given monster. If a PC is assumed to have better equipment, more magical arms and armor, and also receives a survival benefit (filtering effect) to ability scores, then those fighters will be much more proficient in battling monsters than shown here (like, say, able to contend with a monster of EHD +50% over their own level, as a zeroth-order estimate).

The Monsters: I implemented almost all the monsters in the OD&D random dungeon monster tables, and almost all of their special abilities. Sticking with OD&D rules, Hit Dice and damage dice are still d6's in almost all cases (damage 1d6 for all attacks by default, with exceptions noted in the Vol-2 text: e.g., ogres 1d6+2, giants 2d6, earth elementals 3d6, and a maximum 4d6 suggested for the largest of sea monsters or a Tyrannosaurus).

By necessity, many interpretations must be made regarding the monster statistics. In particular, OD&D included no statistics for any of the giant animal types referenced in the random tables (giant spiders, centipedes, ants, snakes, scorpions, etc.) In some cases we can look to Sup-I which included alternate attacks and damage for some of these types, although translating back to d6-based dice was done. In other cases I looked to the AD&D Monster Manual for the intention behind giant animal Hit Dice, armor class, attacks, and special abilities (the AD&D MM is compatible with OD&D in almost every way, and was chiefly a compilation of prior material).

I'll leave that as the end of Part 1 of this analysis. Next time: Commentary on individual monsters and special ability effects. Below, two downloads: First, a data file of the exact monsters and statistics used in this simulation, if you want to inspect that. Second, the current Arena code (Java) if you want to audit or compile that yourself.

P.S.: Tell me if you would desire the Arena program being packaged up so you could run it from a command-line with needing to compile it yourself (say: to input and measure your own unique monsters, or monsters with adjusted stats, or experiments with totally different assumptions)? If more than a couple people express interest in that, I could do it.