Monday, October 16, 2017

Here's 3 full days of play in Rappan Athuk from this past July, as logged on index-card records during play:

Monday, October 9, 2017

Classic Stat Block Formatting

I was writing some stuff recently, and started wrestling with myself over how to present monster statistical notations in the adventure text. Partly this is a result of the formatting in classic TSR modules and texts varying over the years; but of course I want something that satisfies my own intuitions regarding brevity, usability, etc.

The primary difference in styles that caught my attention as I write this is that the earliest adventures included statistics in parenthetical notes within narrative text paragraphs (the contents of course varied, sometimes as minimal as just hit points, but that's a not my main thrust here). Adventures at a later date removed the statistics from inside narrative text, placing them instead outside of each paragraph, in a specialized statistical block. Prominent examples of the early style included the GDQ modules, AD&D rulebooks, B/X rules and B1-2, etc.; examples of the later style would include module T1-4 and products of that era. So I started searching for where the switchover point was.

Now, here's the discovery that made me think this worth posting about: Gygax's AD&D Dungeon Module S4, The Lost Caverns of Tsojcanth, published in 1982, surprisingly constitutes the exact switchover point all by itself, because it actually includes both styles within the one product! Namely: The original dungeon-based adventure area, the "Lost Caverns" (used in Winter Con V, 1976), maintains the older parenthetical in-paragraph style. But the newly added wilderness encounter areas (which actually appear first in the module) instead use the newer isolated-stat-block style.

Example of the older style in the dungeon areas (S4, p. 14):

Example of the newer style in the wilderness areas (S4, p. 7):

The 1982-1983 era was clearly a time of great flux in the presentation of D&D rules and adventures. You'll notice in the S4 wilderness example above that the "new style" isolated stat blocks were given before the text, whereas later it would usually be after (a minor modification, I think). The Hickmans' modules I3-5 in 1983 had a very regimented structure of every single paragraph being labelled for either "Play", "Monster", "Treasure", "Character", etc. By 1985, T1-4 kept only the smallest part of that, with a specialized paragraph labelled "Treasure" for each encounter area.

While I'm not very fond of those experiments at hard regimentation (or even "boxed text" descriptions), on reflection I really do like the statistical elements being removed from the text paragraphs, and it's probably the only new formatting idea from that time that was "sticky" and still commonly used today (e.g.: see Bill Webb's Rappan Athuk). Among the advantages are: allowing the writer to stay in the descriptive "voice" and not get distracted by statistical elements (perhaps more of a problem for some of us than others); easier for the DM to read and parse sensory descriptions in play; better for finalizing paragraphs/orphans separate from stat edits; more attractive on the page; and, if desired, easier to convert a product to other game editions.

Which style do you prefer?

Saturday, October 7, 2017

Saturday Software: OED Monster Database v.2

Linked below is an updated version of the OED Monster Database (ODS open document spreadsheet). A few people observed trouble dealing with the first version a weeks ago, especially on systems different from mine, in terms of the formulas present in a few of the columns. So the rather minor changes are:
• Took out all of the formulas on the 1st sheet and replaced them with fixed values; and clarified column N with the label "Table" (it's meant to indicate the recommend Wandering Monster Level Table).
• On the 2nd sheet of stat blocks, converted the CONCAT function to the more traditional CONCATENATE.
• Added a 3rd sheet explication of the conversion in use of EHD to Monster Table (for use with VLOOKUP in any future additions).
While I personally created this in LibreOffice Calc 5, this version was tested and found to work in both Microsoft Excel 2010 and 2013 (in the former, after a file validation and repair operation), including the computed stat blocks on the 2nd sheet. Tell me if you still have notable problems with this version!

Monday, October 2, 2017

Tip-Offs in Tamoachan

So I was reading the "Collector's Edition" of the AD&D Lost Tamoachan module, published by TSR in 1979. This is the Mayan-themed adventure (in-game, "Olman") by Harold Johnson & Jeff Leason, later repackaged as AD&D Dungeon Module C1 in 1980/81. The cover (shown here) says:

This module was originally used for the Official Advanced Dungeon & Dragons tournament at Origins '79. This special numbered collectors edition (300 copies in print) contains background information, referee's notes, a large four-level map and reference matrices. Pre-rolled characters are included with brief histories for each. LOST TAMOACHAN: "The Hidden Shrine of Lubaantum", is the first in a new line of Collector's Edition modules from TSR. If you find this module intriguing, look for the TSR logo on future publications from The Game Wizards!

There are many differences between this edition and the later, more mass-market publication of module C1 in 1980/81. For starters: The formatting is much more rudimentary; just run directly off a personal typewriter in a single mono font, from what I can tell. Areas are identified variously by letters or numbers (names of areas generally match C1, but the numbers do not). There is no separate illustration booklet, and generally just a few illustrations in the module itself. There is no tournament scoring system (which makes me suspect that the system in the later C2 was made just for that publication, and not used at Origins). As an aside: If you're curious, the only other "Collector's Edition" item was module C2. Anyway, here are the tidbits that I find the most interesting.

Table Scale of 1" = 5 Feet

Area N, "The Tomb of Pelota", features an aggressively animate rubber ball which challenges adventurers to a classic game of pelota, in a long hallway with goals on either end. This optional encounter includes 5 paragraphs of game rules for running the event. In part, it says:
The ball moves in increments of 5' or 1 inch on a scaled playing surface. Players must strike as if hitting with their major [sic] to hit AC 5 to connect and then drive the ball the resulting damage in inches along the corridor; in this case always roll for damage, don't use average rolls. To score the character must be within range of the goal and score +4 above the required roll "to hit". If players are within 6 inches, on scale, of the ball they may all swing to hit; if the nearest figures are 12 inches up to two may attempt to hit at -1; and if none are within range only 1 may attempt at -2... The ball moves itself 2-8 spaces each round, [sic] number is generated, but must always hit opposing walls in any round, +1 more wall if moving over 5 spaces...
Now, this tactical scene, with all distances given in inches, and the 1" = 5 feet scale is particularly interesting because it's written within the same year (1979) that Gygax is writing in the AD&D DMG, "Each ground scale inch can then be used to equal 3⅓ linear feet" (p. 10).

On the one hand, when ranges are specified in OD&D/AD&D, they are given in 1" units where officially 1" = 10' indoors, 30' outdoors, but (awkwardly) this should be a separate and distinct consideration (i.e., units-of-account only, not reflecting actual tabletop usage). But when the later module C1 was prepared, this pelota scene (now area #29) was edited to read, "The ball moves in increments of 5' (½")", and all the other references were converted to feet instead of inches, as though the editor wanted to mostly avoid the whole tactical issue (i.e., movement from a PC hit was no longer damage-as-inches, but instead a fixed "15' per blow").

Is this the earliest reference in an official D&D product to use of the 1" = 5 feet tactical scale? If we were wildly conspiracy-minded, we might be tempted to allege something outrageous, like that it took an ongoing and concerted cover-up to avoid the rather blatant fact that original D&D scale should have just been 1" = 5 feet all along, the most playable and mathematically direct conversion when playing with 25mm man-to-man figures.

Treasure in Silver Pieces

Most of the treasure in Lost Tamoachan is valued in units of silver pieces -- not gold, as is customary in official D&D. It seems like most of the treasure in areas #1-11 is valued in gold pieces, while the treasure in areas #12-25 is generally priced in silver pieces (there are exceptions to this assessment). Is it possible the Johnson/Leason originally played their games with a (more historically realistic) silver-standard economy, and partly but incompletely managed to convert that for their Origins tournament module?

When the later C1 module was prepared, all of these silver treasure valuations were converted by the rules-as-written in AD&D, in that 1 gp = 20 sp should be the base economic unit; that is, all of the silver treasure valuations were divided by 20 or thereabouts.

Here's an example from the original adventure, area #12, "The Tomb of Tlacaelel":
The chests hold large heaps of coin necklaces, silver coins pierced and threaded on gut, worth 360 s.p. each... In the first chest are: 10 coin necklaces, 6 pair of jade earplugs, worth 260 s.p. a set; an alabaster stature, worth 500 s.p.; and an agate ring, value 100 s.p....

In the later module C1, this becomes area #33:
These chests hold large heaps of coin necklaces, 360 silver coins pierced and threaded on gut worth a total of 18 g.p., and other assorted valuables... Chest #1: This chest is jammed shut and must be broken open. It holds 10 coin necklaces, 6 pairs of jade earplugs, worth 15 g.p. a set, an alabaster statuette, worth 50 g.p., and an agate ring valued at 5 g.p...
Note that standard jewelry treasure in any version of D&D is valued in units of hundreds (ostensibly gold pieces). The original adventure text has treasure on this same order-of-magnitude; but the converted module C1, with jewelry valuation through in the single-digits and teens (as seen above), is an anomaly. The physically biggest treasure caches become effectively worthless garbage in the AD&D economy and XP system. The only thing that makes sense is that someone was originally running their economy and XP awards in silver-standard units. Again, this echoes the prior section: there is an "obviously correct" scale to D&D pricing values, and it's not really in gold piece units. It took a lot of labor over time to try and continually align the publications with Gygax's early and fundamental errors.

This is somewhat further confused by the fact that, despite the amount of adventure text dedicated to treasure descriptions (the passage quoted above is just the start of a 10-paragraph presentation of treasure in one room!), treasure is not a factor in the C1 tournament scoring system. Perhaps the most obvious deduction, granted that the the original Lost Tamoachan had no such system included, is that originally the tournament was judged simply on value of treasure taken, and silver units were initially the basis on which that was scored.

Other Curiosities

Languages -- The pre-generated characters in Lost Tamoachan are given extensive language lists, and these are important at many points of the adventure. Included among them are Latin, Hebrew, "Tolemy (astronomer's script)", "Harney (Hillfolk tongue)", and "Melange (merchant business tongue)". In the later publication these seem to be respectively replaced by the World of Greyhawk setting elements of Suloise, Elven, Old Oeridian, Orcish, and Flan.

The Mouther -- Lost Tamoachan features (in area #21) the first appearance of the infamous gibbering mouther monster, before it actually was assigned that name. Here, it is simply called the "Mother" throughout -- "'Mother' was once worshipped as the goddess of the earth...". When turned into a more generic monster in C1 (and Monster Manual II), the "mother" became the "mouther".

Hopefully you all are using 1" = 5 feet scaling and silver-standard currency at this point. And salutations to you for being so sagacious and tasteful.

Monday, September 25, 2017

Castle Construction Costs

One of my Top 5 major adjustments to D&D is in using a "silver standard" for the economy (see the sidebar). That is: I simply read all the costs, nominally in gold pieces, as silver pieces instead. This is particularly easy to do in OD&D where all costs are just in a single unit.

One major reason for this is that it generates a more realistic set of prices that given in D&D in terms of gold pieces. We get a better simulation. When we want to expand our gear selection, we can just look up real-world historical information, and use that with some confidence. It avoids the awkward rationale in AD&D that all of the campaign area is suffering a hyperinflation economy. Plus, it effectively increases the coin-value that adventurers can haul out of a dungeon. At some point they can level-up to gold and carry out increased density in value and XP. So it's also good gaming design.

As related previously, I usually think of the D&D copper, silver, and gold pieces as equating to English pence, groats, and nobles, respectively (link1, link2). Note that groats are one-third of a shilling, and nobles are one-third of a pound in worth (recall that shillings and pounds were not ever medieval coins). So this means that if I do find a real-world price list in shillings, then I need to multiply the shillings by 3 to get actual silver pieces (i.e., groat coins). In other words, 1 noble = 20 groats, and 1 groat = 4 pence (note that copper pieces still have reasonably legitimate worth by using the real-world coins, much as in OD&D; they are not entirely rubbish as in AD&D).

On to the main point here: Let's see what kind of estimated conversions we can male, based on what we see in the OD&D books (Vol-3, p. 20, 5th print), versus some real-world data on castle construction costs. Fortunately Wikipedia has some information and links under its Castle: Construction article on different types of castles. I always count Wikipedia as good enough for gaming inspiration; although you can follow up on the citations to these data there if you wish, of course.
Even a very small tower, such as Peveril Castle, would have cost around £200. In the middle were castles such as Orford, which was built in the late 12th century for £1,400, and at the upper end were those such as Dover, which cost about £7,000 between 1181 and 1191.[131] Spending on the scale of the vast castles such as Château Gaillard (an estimated £15,000 to £20,000 between 1196 and 1198) was easily supported by The Crown, but for lords of smaller areas, castle building was a very serious and costly undertaking. It was usual for a stone castle to take the best part of a decade to finish.

I followed up on the links to articles on each of those castles, documents sizes and construction details, did some Googling for extra maps of the castles, roughly estimated measurements for wall lengths where I could, etc., then tallied up costs as indicated in OD&D Vol-3. For example: Peveril Castle is simply a single keep, 40' square, and 50' tall (or at least that's the only part that we have construction costs data for). Looking in Vol-3, I compared this to the 40' round tower, 40' tall; as per the adjustment note, to add 10' height costs +20%, giving a D&D cost of: 10,000 × 1.2 = 12,000. And so on for the other, more complicated castles.

Of course: In D&D this is officially in gold pieces and vastly different from the 200 real pounds indicated in the article. So as an experiment, let's see what happens when we convert the real price in pounds to silver groats (i.e., multiply by 60):

Conclusion: I'd say it's completely uncanny how well the D&D costs correlate to real-world costs, assuming we express them in silver groat coinage. For example, the cost for Peveril castle is exactly the same as our estimate from the D&D rulebook above. The cost for Orford castle is off by only about 1%. My estimated cost for the enormous Dover castle is at least on the correct order of magnitude. Initially, I did expect such a close correlation!

What can account for this? Are the castle prices in OD&D invented from whole cloth, and just accidentally match the real-world cost in silver (and so too all the other prices for almost everything)? Is there some prior work based on historical research that expressed prices in silver, and was converted by fiat to "gold pieces" for D&D? At any rate, it rather stunningly gives added confidence to the very handy idea of reading prices in D&D in silver (groats) instead of gold.

A few other points: Note that time (in years) does not scale linearly with cost. Based on the three data points here, it's actually more exponential in nature (R² = 0.95). The other thing is that I left out the reference to Château Gaillard in France; while described as "vast" and supposedly costing between 15,000  and 20,000 pounds, by my eye it is actually smaller than Dover Castle (although in a more precarious location), and took a lightning-fast 2 years to build (perhaps due to personal, eager oversight by Richard the Lionheart). So that doesn't correlate in any way with the prior data points.

In summary: Feel free to use the Original D&D prices as pretty good estimates for real-world costs, as long you read them in units of silver pieces (groats). Thoughts?

Monday, September 18, 2017

Turnbull's MonsterMark System

Following on from the discussion of systematized EHD (equivalent hit dice) last week, let's look at a much earlier attempt at the same idea. In the first three issues of White Dwarf magazine, Don Turnbull presented a measurement he called "The Monstermark System". This would be through the summer and fall of 1977, that is, exactly 40 years ago as I write this. (Thanks to Stephen Lewis for the tip-off to these articles!)

In the third article in the series, Turnbull writes:
Although it has been said by quite a few D&D addicts that the Greyhawk system of experience points, which is based on monsters' hit dice, is too stingy I don't think this is something which can be considered in isolation...  So, circuitously, back to experience points. In my view they are intended to reflect risk. A character gets experience for meleeing with a monster because there is a finite, non-zero, risk that he will be killed or at least suffer wounds which could contribute to his eventual death. He gets experience for gold because he has taken risks to grab it... He should not, however, get experience for finding a magic sword or that seven-spell scroll since these things will assist him in getting experience by other means... Since the whole point of the Monstermark is to measure the risk inherent in tackling a particular monster, experience points should bear a linear relationship to M...
I fully agree with those observations, and my motivation for EHD is exactly the same: to provide a measure of risk, from of which we can support a simple, linear calculation for experience points. We both assume a protagonist fighter with a fixed armor type, shield, and a sword; we both give the fighter one attack per round. Now, the basis of his system is this: for the default fighter, compute the expected amount of damage he would expect to take fighting the monster (assuming the combat never ended from the fighter's death). In this case, the calculation is done by first computing the number of rounds the monster would expect to live (D); and then multiplying that by the expected damage per round (analogous to the DPS -- damage-per-second -- statistics in MOORPGs) for an overall aggression level (A). In the first article, Turnbull presents it like this:

This seems like a solid, undeniably valid base measure of monster risk level. As long as the monster has no special abilities. Which is, as you know, almost none of them. As soon as a monster has special abilities, then Turnbull is forced to step out of the methodical expected-value analysis and revert back to a purely discretionary set of multipliers, hoping to estimate the power of various abilities, to get the final MonsterMark score (M). As he writes, "All this is very subjective and I would be surprised not to meet with different views, but the following bonus relationships seem to give results which instinctively 'feel' right:"

Now, if you take nothing at all but one thing away from this blog, I hope that it's this: these kinds of a la carte scoring systems for game entities are always a lost cause.The inter-relationships of different abilities and powers are too complicated to be encapsulated in such a system; the true acid test can only be made by systematic playtesting (which is very hard).

Consider a few short counterexamples -- A giant rat given magic-to-hit defense is effectively unbeatable by the PCs it normally fights; but a very old red dragon, given the same ability, would have little effect against its high-level opponents (surely wielding magic weapons already). If ghouls have possibly paralyzing attacks, then it makes a huge difference if they have one attack for 1d6 damage, versus three attacks for 1d2 damage (even with nearly the same expected damage). Centipedes and carrion crawlers, with a base damage of zero, even with poison or paralysis, would generate a product that is still zero by this multiplicative system. And so on and so forth.

Nevertheless, Turnbull pushes forward with the tools he has, first presenting a table of basic humanoids without special abilities (of which there's really only a half-dozen), and then separate tables for various other categories of monsters from OD&D, the Greyhawk supplement, and a few magazine articles current at the time. For a few examples of his M scores: orcs get 2.2, ogres 29.9, trolls 158.4, and red dragons 675.5 (by comparison, I give those creatures EHD values, respectively, of 1, 4, 9, and 32; and no, I don't think that going into decimals here is a great idea). Ultimately he recommends giving XP of 10 times his M score, which is generally about double the low Greyhawk XP awards for these sample creatures (whereas I still prefer 100 times the EHD level, in the spirit of Vol-1).

There are 73 monsters for which Turnbull & I both are willing to give measurements. Consider the correlation between our assessments:

That's not very close at all. The data points are scattered all over the place, not close to any regular relationship; knowing one measure only allows you to predict about 50% of the variation in the other measure. On average, Turnbull's Monstermarks are about 20 times what I find for EHD levels, but that doesn't tell us much. He assumes plate armor for fighters whereas I assume chain (for reasons given last week), but that can't explain the low correlation either. Let's look at some specific cases for why this is.

The most obvious problem for Turnbull is this: The Monstermark system cannot handle area effect abilities at all. His model tries to do accounting on the hit points from breath weapons (in the 2nd article), but he steadfastly assumes just a single deathless fighter in melee against a given monster; so, if a red dragon breathes fire, then only damage to that one fighter is accounted. But that doesn't reflect the true risk or utility of area-effect weapons like that; our PCs don't adventure in solitude but in groups of some size. The examples of dragon combat in both OD&D and AD&D show three PCs being incinerated at once from a single breath attack; so the damage/risk multiplier should really be at least several times higher than Turnbull counts. Likewise, petrification weapons get no distinction for delivery by touch or wide-area gaze -- the cockatrice (touch), medusa (gaze), and basilisk (both!) each get an identical 2.5 multiplier for their abilities. This alone probably accounts for a massive skewing in many of his scores, downward from the true risk level. In contrast, my Monster Metrics program runs up to 64 opposition fighters simultaneously against any given monster, and they suffer appropriately from area or gaze weapons.

Some examples where the Monstermarks seem clearly too low:
• Basilisk (EHD 25, MM 128), with its combined touch-and-gaze petrification, which only gets the same multiplier as a cockatrice does.
• Medusa (EHD 13, MM 56), likewise with her area-effect gaze petrification.
• Carrion Crawler (EHD 14, MM 120); as noted above, the multiplication system from zero damage should come out to zero, so I think he just made this up from whole cloth (note the round number).
• Harpy (EHD 9, MM 22), with her mass charm song ability, shouldn't be weaker than an ogre.
Another rather egregious issue is this, although it affects only two creatures: Summoning abilities are entirely left out of the accounting. As noted before, we find these abilities to be among the most potent in the game! But the Monstermark system actually overlooks them entirely, giving no bonus at all for them.
• Vampire (EHD 39, MM 440), given no summoning abilities.
• Treant (EHD 33, MM 420), which actually appears in Turnbull's first table of "simple human-type monsters" without any special abilities, and yet its tree-controlling ability allows it to effectively triple its own brute strength. (As an aside, consider a vampires-vs-treants scenario, in which we find two of the most powerful opposition monsters in the game due to their parallel summoning abilities.)
Meanwhile, there are some other monsters with nothing but brute strength that appear too highly scored -- like the Fire Lizard (EHD 14, MM 758), and Hydra with 10 heads (EHD 18, MM 707) -- but I think that this is only an artifact of the special ability monsters being relatively too low. Also, the Mind Flayer's score seems ridiculous (EHD 20, MM 700), granted that he doesn't even note its mind blast power, and was probably again just a raw guess (another suspiciously round number).

Now, there are two other cases that literally jumped off the chart above, such that I felt compelled to remove them as outliers -- and on inspection they are rather obviously in error. These were:
• Roper (EHD 16, MM 3,750). This is clearly a mistake. Turnbull notes the creature in part 2, p. 15: "These calculations make the Ropers the most fearsome beasts we have met so far; I don't recall ever meeting them down a dungeon, and I devoutly hope I never will." The problem, if I'm reading his attack notation correctly, is that he's applied the Roper's 5d4 damage factor -- which should be just for its mouth -- to every single one of its 6 ranged tentacle attacks. That really would be horrifying! While the Roper is a tough customer, it obviously shouldn't be worth the same as 5 or 6 Red Dragons; that doesn't pass any kind of sanity check.
• Flesh Golem (EHD 21, MM 1,920). In this case, the problem is that Turnbull shows a radically different AC for the monster than I see in the books: My copy of Sup-I (with correction sheet) gives it AC 9, as does the AD&D Monster Manual. Turnbull shows it has having an AC of -1, which is obviously the diametrical opposite. I'm not sure where he got that from, maybe from a wild guess before the Sup-I correction sheet was available to fill in that statistic?
There were some other things I had to leave out of the analysis, such as those other golems and elementals that are hit by only +2 or better magic weapons, which have undefined EHD in my model. Turnbull gives medium and large elementals a score of 1,000-2,000, stone golems nearly 13,000, and iron golems just shy of 33,000 (but again their ACs are treated as much harder than in the rulebooks, namely AC -3 and -5, so there are multiple reasons to leave them out of our comparison).

In conclusion, while the motivations are exactly the same, the scores that Turnbull & I come up with a radically different, effectively incommensurable. (If you want the full data, my Monster Database from last week has Turnbull's MonsterMarks entered in hidden column Q.) Of course: while Turnbull's instinct was noble, he didn't have the immense computing power all around us to simulate playtests the way we can today. Now, maybe someone will come back to critique my work in another 40 years -- someone who has access to a complete game engine with all the special abilities, full wizard spell selection, mixed-class PC party simulator, and hard Artificial Intelligence to optimize the best tactical choices on each side -- and in that light my suggestions might look totally naive. We can only hope for such continuity and progress.

Saturday, September 16, 2017

Saturday Software: Monster Metrics v.103

Previously, we've looked at the output of my "Monster Metrics" program (a branch off the "Arena" codebase), which simulates thousands of fighters in combat against specified monsters, so as to gauge their physical power level in terms of Equivalent Hit Dice (EHD). Last Monday, I presented the OED Monster Database, including pretty much every monster in OD&D and the first few supplements, which served as a platform to comprehensively assess every monster's EHD. Of course, the program needs to get updated every time a monster with a new special ability is added, so here is the current codebase with a few comments.

First, I added a couple command-line options which you see below if you want to play around with them.

 Usage: MonsterMetrics [monster] [options] By default, measures all monsters in MonsterDatabase file. Skips any monsters marked as having undefinable EHD (*) If monster is named, measures that monster at increased fidelity. Options include: -a armor worn by opposing fighters: =l, c, or p (default Chain) -b chance for magic weapon bonus per level (default =15) -f number of fights per point in search space (default =100) -r display only monsters with revised EHD from database -u display any unknown special abilities in database 

For each monster, the program runs through fighters of level 1 to 12 and does a binary search at each level for the number of such fighters which provide the closest to a fair fight (i.e., 50/50 chance of either side winning). Each step in the search runs 100 fights by default to determine the winning percentage (which you can adjust with the -f switch above for greater fidelity and slower running time, if you wish). Then a total EHD is assessed across all levels by computing the weighted total $$EHD = (\sum_{n = 1}^N n \cdot f(n))/N$$, where $$f(n)$$ is the fair number of fighters at level $$n$$ in the table above, and $$N$$ is the maximum level considered (in this case, $$N = 12$$). Note that this is likely different from "best fighter level to provide a fair fight", in that special abilities that can wipe out an army of of 1st-level fighters, but are impotent against high-level fighters, do get accounted here.

Every fighter in the simulated combat gets a sword, shield, and chain mail. One might ask, "Why chain mail by default, when most fighters after 1st level will be wearing plate?". But the thing is, I wanted the EHD ratings to actually be scaled to units of monster hit dice, e.g., the number of orcs that a monster is really worth, and those low-monster like humanoids all have chain-like armor (goblins/orcs AC 6, gnolls/ogres AC 5, trolls/giants AC 4), so we want to keep the simulation in that scale without adjusting other factors. Doing it this way, the EHD for those low-level types (lacking any special abilities) does in fact match their normal HD (orcs 1, gnolls 2, bugbears 3, ogres 4, etc.). If we switched the default fighter armor to plate, then that would devalue the monster risk, and even the simple monsters would see their EHD fail to synch up with their HD (in that case: gnolls 1, bugbears 2, ogres 3, etc.).

The next important consideration is: what level of magic weapon to give each fighter? Previously, I just assumed a +1 magic sword for every fighter, so as to not make creatures hit by magic totally invulnerable. But we will really don't want fixed bonuses like that (or fixed bonuses by level), because it creates singularity dropoffs between level or steps of bonus (e.g., makes the protection of lycanthropes and gargoyles totally useless, even to 1st-level fighters). So in this version I switched that to a probabilistic factor of 15% per level to get an extra magic boost, and also a silver dagger as a backup weapon. Having tried several levels between 5% (as seen in Vol-2) and 25% (as suggested by some comments online), I found that 15% overall gave the best match to the prior version, while giving a reasonable boost to lycanthropes, etc. And that's also what I do in my OED house rules, giving a 1-in-6 chance per level for a magic boost to characters created at higher levels.

Now, that leaves another problem, namely that any monster hit only by +2 magic or better weapons (e.g., golems or elementals in Sup-I) is totally invulnerable to 1st-level fighters, who can theoretically only have at best a +1 bonus. This means that the number of 1st-level fighters, and thus our EHD clculation, becomes technically infinite. That is: in these cases our model simply fails.

It's for reasons like this that the OED Monster Database shows an asterisk (*) under EHD for some very exotic monsters, to note that the EHD is effectively undefined in our current model. More generally, this is done for any creatures with wizard-like spell capability that isn't implemented in the program (triton, titan, lich, lammasu, gold dragon, beholder), creatures hit only by +2 or better magic weapons (golems, elementals), and creatures totally immune to blows from weapons (various oozes).

So that's the skinny on what the program is now doing under the hood, and why the Monster Database appears the way it does. Note that the included data file MonsterDatabase.csv is an exact duplicate of the Monster Database from Monday (just in CSV format so it can be read in by the software). Hopefully this makes it easy to investigate or add other monster in the future when we need them.