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?
2016-02-12
2016-02-08
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.
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.
2016-02-05
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!
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!
2016-02-03
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?
2016-02-01
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.
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.
2016-01-29
OD&D is Back at D&D Classics
Great news! The Original D&D little brown books (LBBs) are once again officially available in PDF form on RPGNow's D&D Classics site. Nicely timed to celebrate the 42nd birthday of their release (link).
It's been a frustrating number of years since OD&D was available for legal purchase. I got my digital copy on RPGNow back in 2007 -- shortly before I fell in love with it as my favorite, purest and most playable edition, and starting this blog dedicated to it. (To my amazement the RPGNow system still remembers that purchase and provides me with re-download access for the current work, bravo.) Hopefully it will remain available for the foreseeable future, so that we can refer fellow players back to the classic if that's the ruleset we're using for our games -- and I recommend that we do.
Of course, a number of OSR publications in the intervening years had as their raison d'être the need to fill in for the original game being out-of-print in any form. Notably, my own Book of Spells was partly motivated by this fact -- I could run everything in the game as DM, with players basically responding with real-world intuition, except for players of wizard characters who at a minimum did need rules text for the magic spells. Of course, that's fine, and I think the "missing rules" generated a lot of creativity -- in particular, I really do think that having spells removed to their own book is a better organizing principle, and the Original D&D spells were very sketchy indeed, so it pays to have the necessary interpretations written down in an official form. (As D&D Classics Product Historian Shannon Appelcline writes: "Clerics and magic-users cast spells, but the rules for doing so are quite terse, which caused some confusion about how the rules worked in the early days...".)
Bonus content: Check out Zenopus Archives' blog for a handout re-presenting the top-level Balrog monster, which was in the 1st printing of OD&D, but struck out from later editions (such as the version available at D&D Classics). Fight on!
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