Oscillating Rotation to Order Dice

Diego Maza, et. al.,  Physical Review Letters: An experiment using oscillating rotation to order a container of 25,000 dice, which is seen to be greatly more efficient than tapping or shaking methods.

Hope you have a happy New Year!

APS Physics.



Have I not posted GamesByEmail's Dice-O-Matic before? Here it is. Merry Christmas.


Harpies Through the Ages

Hark! The herald angels sing!... Oh, no, wait, it's actually the gods-forsaken song of the damnable and murderous Harpies, seeking to lure men to their doom and destruction. Let's reflect on that.


D&D Harpies are, of course, a mashup of the mythological Harpies and Sirens. Both are destructive monsters with the lower bodies of birds and the upper bodies of ugly women. Harpies are mostly the personification of destructive wind spirits; they are "snatchers" and "swift robbers" (actually, that's what the name means), but do not exhibit dangerous music. Sirens are similar-looking creatures who lure coastal sailors to shipwreck and death by means of their enchanted singing (most famously for a few lines in Homer's Odyssey).

In D&D these features are combined into one type. Interestingly, there is a distinct difference in how their song/charming works in the Basic D&D line, versus the Advanced D&D line. Two major questions arise: Does the song charm victims directly? And, are saves made once for a whole flock, or separately per creature?

Original D&D (Greyhawk)

HARPIES: Harpies have the lower bodies of eagles and the upper bodies of human females. They are always opposed to mankind and its like, and  will  attempt to kill all they can. By means of their singing the Harpies lure men to them, then enchant them with powerful charms, and kill and devour them.  Any  creature not making its saving throw vs. magic will immediately proceed towards the Harpy. and if the Harpy touches it it will Charm the creature.
The above is from D&D Supplement I, Greyhawk. Note that there are two separate mechanisms; the song which can "lure" a victim, and a touch attack which can actually "charm" them. A save is necessary for the luring song; it is unclear whether the touch warrants another save or not. In addition, it is a bit unclear whether failing the "lure" is strictly required before the touching "charm" or not.

The magic song is among the first area-effect powers usable by a monster who routinely appears in numbers. Like many such abilities, an interpretation is necessary for the ambiguous question of whether each separate monster requires or saving throw, or only one for the whole group. In the strictest reading here, with "Harpy" in the singular, we might think each creature requires a separate saving throw. On the other hand, in the Greyhawk dungeon encounter tables, Harpies appear only on the 3rd-level table (out of 6); whereas, if each creature has its own effect, Harpies rank among the most dangerous of 6th-level monsters (per author's simulations).

Advanced D&D, 1st Ed.

Harpies have the bodies of vultures but the upper torsos and heads of women. They are voracious carnivores and foul creatures. Those that dwell along seacoasts are generally known as sirens. All harpies are able to emit sweet-sounding calls. Any creature hearing these calls will proceed towards the harpies unless they save versus magic. Similarly, the touch of a harpy charms those creatures which fail to make their saving throw versus magic. The harpies attack, torture, and devour their charmed prey. What they do not want they foul with excrement. A harpy attacks with her vulture claws and some form of weapon  -  often a bone club or some weapon left from one of her farmer victims. They speak their own language and none other.
In Gygax's AD&D, the powers of harpies are mostly the same. We see the same distinction between the luring song and the charming touch. In this case, it is clarified that each power requires a separate save versus magic. Also, with the two abilities in separate sentences and with separate saves, it is more clear that they are truly distinct, and the touch is not dependent on the luring song working first. The language is also modified to speak of "harpies" and "calls" in the plural, such that it's more likely only a single save for the whole group is intended, and more in line with the implied danger level, as above. In the DMG, harpies strangely do not seem to appear in the dungeon random monster tables; but based on experience points, they should be a 4th-level monster (out of 10).

Moldvay Basic D&D

A harpy has the lower body of a giant eagle and the upper body and head of a hideous-looking woman. By their singing, harpies lure creatures to them, to be killed and devoured. Any creature hearing the harpy's song must save vs. Spells or be charmed (see special attacks at the beginning of the MONSTERS section). Charmed indivuals [sic] will move toward the harpies, resisting any attempt to stop them, but not otherwise attacking. If a character saves against the songs of a group of harpies, the character will not be affected by any of their songs during the encounter. Harpies are resistant to magic and have a + 2 on all their saves.
In the basic line as of Moldvay, the separation of effects is eliminated. The song charms victims directly; no reference to a distinct touch effect is given. The effect is clearly attributed to "a group of harpies", implying just one save for the whole flock.

Note that the earlier Holmes Basic D&D keeps the same language as from OD&D; a separate song and touch effect to charm. Later Mentzer and Allston versions of the basic D&D game keep exactly the same text as laid down by Moldvay.

Advanced D&D, 2nd Ed.

Combat: The song of the harpies has the ability to charm all humans and demihumans who hear it (elves are resistant to the charm). Those who fail their saving throw versus spell will proceed towards the harpy with all possible speed, only to stand entranced while the harpy slays them at its leisure. This charm will last as long as the harpy continues to sing. Harpies can sing even while engaged in melee...

The touch of a harpy upon a charmed individual has a similar, though somewhat less potent, effect. Those who are touched and miss their saving throw versus spell will stand mesmerized for 20+1d10 hours.
In Dave Cook's revision to AD&D, he somewhat changes the effect of harpies' powers from 1E, moving it closer to the B/X edition that he worked on earlier with Moldvay. Here the song charms its victims directly. The touch has a separate and slightly reduced effect, stunning the victim for a limited time, but is not required for the destructive charm.

D&D, 3rd Ed.

Captivating Song (Su): The most insidious ability of the harpy is its song. When a harpy sings, all creatures (other than harpies) within a 300-foot spread must succeed at a Will save (DC 15) or become utterly captivated. This is a sonic, mind-affecting charm. If the save is successful, that creature cannot be affected again by that harpy’s song for one day. A captivated victim walks toward the harpy, taking the most direct route available. If the path leads into a dangerous area, that creature gets a second saving throw. Captivated creatures can take no actions other than to defend themselves. A victim within 5 feet of the harpy stands there and offers no resistance to the monster’s attacks. The effect continues for as long as the harpy sings. A bard’s countersong ability allows the captivated creature to attempt a new Will save.
In 3rd edition, all reference to the harpy's touch attack, as in the Basic D&D line, is gone. The song directly "captivates" its victims, who march forward to their destruction (but are allowed possibly other saves and the ability to defend themselves from other dangers along the way). Interestingly, the language here again refers to a "harpy" in the singular, implying in a strict reading that each creature forces a separate save vs. the magic (which would be completely devastating in large numbers to parties of almost any level).


Gygax's editions of OD&D and AD&D were consistent in laying down separate effects for a luring song and a charming touch. All other editions moved away from that towards a single charming song; first by fiat in Moldvay's Basic D&D game, and meanwhile via a more gradual evolution through the mainline 2nd and 3rd Editions.

What is your preference: Gygax's separate lure-and-charm effects, or the single charming song? Should the save (for this and other similar group area effects) be one per separate harpy, or only one for a whole group of same?


D&D in the New Yorker

You may have seen this already: a rather glowing writeup in The New Yorker (by a fan and DM) of the modern resurgence of tabletop D&D.
Dungeons & Dragons seems to have been waiting for us somewhere under the particular psyche of this generation, a psyche that may have been coaxed into fantasy mania by the media that surrounded it. Many were seeded with “Harry Potter” books as children, raised with the “Lord of the Rings” movies (and more “Harry Potter” in cinematic splendor), and brought to blossom in adulthood by “Game of Thrones” on television. Let us not forget the imminent return of “Stranger Things,” a show in which something akin to Dungeons & Dragons not only literally lurks in the wings but is also played by the central characters.


Anniversary of William Tell's Shot

710 years ago today: under threat of execution by the Lord of Altdorf, William Tell shoots an apple off he son's head with a crossbow. (A second quarrel was on hand for the Lord if the first didn't work.)


Testing Crescent-Headed Arrows

Mark Stretton posts test results of using a crescent-headed arrow to hunt game, slice sails, and cut ropes holding heavy weights in the field. Interesting stuff! Warning: Includes photos from shooting the carcass of a goose for testing purposes.


Staff Sergeant Reckless

For Veteran's/Armistice Day: Remembering Staff Sergeant Reckless, the highest-ranking war horse in the U.S. Military, earning two Purple Hearts in the Korean War.


Please Stand By

So us professor-types are hip-deep in a rising tide of work for the academic semester. In my case, I've burned through my backlog of articles to present on the blog and upcoming posts will be irregular at best from now through the holidays (as well as comment replies, emails, these papers on my desk, etc.). I wish I had more time! Hope you have a successful back end to 2017 and hopefully we'll get some interesting stuff coming up soon thereafter.


Mummies Through the Ages

Halloween is this week -- time for a spooky undead-themed reflection. Let's mind-wipe ourselves of the movie that came out this year. Think that energy level drain is horrifying? You ain't read up on old-school mummies lately!

Popular Culture

The golden era for mummy mythology seems to be at the start of the 20th century, coincident with the golden age of Egyptology, especially after the tomb of Tutankhamen was opened in 1922. Within the next two years, a half-dozen members of the archaeology team (out of a group of about 60) had died from various weird causes, and this fueled the popular imagination that there was some "curse" from disturbing the tomb. In particular, Lord Carnavon, the financial backer of the effort, died about 4 months after from a confounding combination of mosquito bite/ shaving accident/ blood poisoning. Others died from fever, malaria, more blood poisoning, assassinations, and being shot by one's angry wife.

Now, apparently real-life curse-inscription texts in Egyptian tombs are pretty rare; but at least one was found that actually reads, "Cursed be those who disturb the rest of a Pharaoh. They that shall break the seal of this tomb shall meet death by a disease that no doctor can diagnose." Read more at the Wikipdia article on Curse of the pharaohs.

A decade later in 1932, Universal Studios made The Mummy starring Boris Karloff (and then a bunch of sequels). Almost 30 years after that, Hammer Film Productions did a revival of The Mummy starring Peter Cushing and Christopher Lee (and then a bunch of sequels). This latter film was often shown in a double-feature with the vampire/Western film Curse of the Undead. In each of these films, the titular character is brought back to life by a magic scroll, and then dark deeds ensue.

Original D&D

MUMMIES: Mummies do not drain life energy as Wights and Wraiths do, but instead their touch causes a rotting disease which makes wounds take ten times the usual time for healing. A Cleric can reduce this to only twice as long with a Cure Disease spell if administered within an hour. Only magic weaponry will hit Mummies, and all hits and bonuses are at one-half value against them. Note, however, that Mummies are vulnerable to fire, including the ordinary kind such as a torch.
In OD&D Vol-2, Monsters & Treasure, Mummies have AC 3, MV 6, and HD 5+1; the above is the entirety of their explanatory text. Even with magic weapons you can only score half-damage on them.

Now, let's look at the rotting disease. It appears that the only effect is to reduce healing rates. But this effect is inescapably permanent. Even if you treat it with a cure disease spell (and it must be within the hour!), your healing rate is still half-normal, apparently forever -- failing that, the healing rate is ten times slower. That makes every combat you ever engage in for the future noticeably more dangerous. Ironically, OD&D doesn't actual set any "normal" rate for healing, so perhaps this really only affects magical curing, which is not called out explicitly; on the other hand, almost all future texts prohibit any magical healing whatsoever to subjects of the disease.

But wait, there's more. In the last few pages of OD&D Supplement II, Blackmoor, Dave Arneson expanded upon the subject of diseases of various types in D&D. And on the subject of mummy disease, the preceding wasn't nearly fearsome enough, and this author felt it needed to be made it much, much worse. He writes:
Advanced Leprosy: The social disease afflicting all mummies, this is what causes wounds to take longer to heal. It is automatically contracted on contact with a mummy. 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.

So, apparently on top of the forever-reduced-healing from Vol-2, Arneson gives mummy rot a 95% chance of death per day, and only marginally decreasing over time. The overall chance of surviving such a regime is less than 10−18 (that is: if there was an entire galaxy of Earth populations, and all of them were infected with Advanced Leprosy, then only around 1,000 people would survive to the end). Plus anyone who dies is un-raiseable (perhaps somewhat analogous to those slain by energy draining rising as similar undead).

There's an associated table that says for Advanced Leprosy, "% to Catch: 100%... Fatal %: 60% spec.". that 60% is a bit hard to parse... perhaps there's a 60% chance to die before one even gets to to 3-day mark? And it's also just slightly unclear how the magical curing works in conjunction with the core rule (Vol-1 says "within an hour", Sup-II says "within three days"). In any case, that seems like overkill upon overkill.

Finally: Note that "social disease" is an old-school way of implying "sexually transmitted disease", which I'm not entirely sure what that is meant to imply here in Sup-II. 


Mummies are undead humans with existence on both the normal and the positive material planes... The scabrous touch of a mummy inflicts a rotting disease on any hit. The disease will be fatal in 1-6  months, and each month it progresses the diseased creature loses 2 points of charisma, permanently. It can be cured only by a magic spell, cure disease. The disease negates all cure wound spells. Infected creatures heal wounds at 10% of the normal rate.

The mere sight of a mummy within  6"  will cause such fear and revulsion in any creature, that unless a saving versus magic is successful, the victim will be paralyzed with fright for 1-4 melee rounds. Note that numbers will give courage, and for each creature above 6 to 1 mummy, the creatures add  + 1  to their saving throw...  

Mummies can be harmed only by magical weapons, and even those do only one-half normal damage... Magical fires are at  +1 per die of damage...  Any creature killed by a mummy rots and cannot be raised from death unless a cure disease and raise dead spell are used within 6 turns.

In the 1977 AD&D Monster Manual, Gygax keeps the essence of mummy rot -- one-tenth normal healing; plus the negation of all curative magic (which will be in all editions from now on). And he at least borrows the overall intention of Arneson's supplement; the disease now also deadly, over a period of some months, with Charisma melting off in an apparently leprosy-like fashion. The resistance to even magical weapon blows is retained. He also adds a special fear ability, shown above. Hits have been increased by one die (to 6+3), just like all the undead except for the Ghoul.

But in this case the disease can apparently be entirely removed by application of the clerical cure disease spell -- at any time, in some sense trivial for standard PC parties of a certain level. Unlike Arneson, a raise dead is possible, but with cure disease, it must be applied within 6 turns of death of anyone slain by a mummy (only slightly less harsh). Fire attacks are specified as advantageous (+1 per die).


The 2E mummy is, for all practical concerns, a copy-paste of the 1E mummy. One thing stands out to me at the end of the combat block: the time frame to cure/raise victims of a mummy has been reduced from 6 turns to 6 rounds.

Also, there is a new separate entry for a certain "Mummy, Greater", which runs about 5 pages in my digital copy. These mummies are ranked by age (less than 100 to more than 500 years), with hit dice from 8 to 13, AC from 2 down to -3, increasing rates of disease progression, and all with spellcasting powers of an evil priest from 16th to 20th level.

This Greater Mummy is perhaps reflective of the overall inflation to monster abilities that occurred in 2E (esp.: dragons and giants), and perhaps borrowing something from Anne Rice's vampire novels which first appeared in 1976 and grew in popularity through the 80's.

3E D&D

Despair (Su): At the mere sight of a mummy, the viewer must succeed at a Will save (DC 15) or be paralyzed with fear for 1d4 rounds. Whether or not the save is successful, that creature cannot be affected again by that mummy’s despair ability for one day.

Mummy Rot (Su): Supernatural disease [slam, Fortitude save (DC 20), incubation period 1 day; damage 1d6 temporary Constitution.] Unlike normal diseases, mummy rot continues until the victim reaches Constitution 0 (and dies) or receives a remove disease spell or similar magic. An afflicted creature that dies shrivels away into sand and dust that blow away into nothing at the first wind unless both a remove disease and raise dead are cast on the remains within 6 rounds...

Resistant to Blows (Ex): Physical attacks deal only half damage to mummies. Apply this effect before damage reduction.

Fire Vulnerability (Ex): A mummy takes double damage from fire attacks unless a save is allowed for half damage. A successful save halves the damage and a failure doubles it.

In many ways 3E D&D "safety bumpered" PCs against the most harmful effects (for example: negative energy drains became temporary with a saving throw). Here, the mummy keeps its fear and resistance to attacks. But by wrapping the mummy rot in the standard 3E disease mechanic, it actually gets somewhat more dangerous; a victim can lose 1d6 Constitution every day, if a daily save is failed -- so likely dying in a few days instead of months as in 1E-2E.

However: The original reduced-healing effect, for both natural and magical means, appears to be removed here (and it might as well be, being effectively negligible compared to the likely death from ability damage in a few days). And fire is made even more advantageous, doing double damage instead of just +1 per die.

The "Greater Mummy" is not included, but a brief line in the stat block indicates "Advancement: 7-12 HD (Medium-size); 13-18 HD (Large)", broadly in line for the extra hit dice allowed in the 2E associated monster.

3.5 D&D

Despair (Su): At the mere sight of a mummy, the viewer must succeed on a DC 16 Will save or be paralyzed with fear for 1d4 rounds. Whether or not the save is successful, that creature cannot be affected again by the same mummy’s despair ability for 24 hours. The save DC is Charisma-based.

Mummy Rot (Su): Supernatural disease—slam, Fortitude DC 16, incubation period 1 minute; damage 1d6 Con and 1d6 Cha. The save DC is Charisma-based.

Unlike normal diseases, mummy rot continues until the victim reaches Constitution 0 (and dies) or is cured as described below.

Mummy rot is a powerful curse, not a natural disease. A character attempting to cast any conjuration (healing) spell on a creature afflicted with mummy rot must succeed on a DC 20 caster level check, or the spell has no effect on the afflicted character.

To eliminate mummy rot, the curse must first be broken with break enchantment or remove curse (requiring a DC 20 caster level check for either spell), after which a caster level check is no longer necessary to cast healing spells on the victim, and the mummy rot can be magically cured as any normal disease.

An afflicted creature who dies of mummy rot shrivels away into sand and dust that blow away into nothing at the first wind.

I'm unaccustomed to the 3.5 edition making things more dangerous than 3E, but it does so here (well, a little bit). First, the mummy hit dice are increased from 6 to 8 (with the possible advanced types running from 9-24). The fear effect is about the same. But the mummy rot doubles up the 1d6 daily Constitution loss with a 1d6 Charisma loss (hearkening back to 1E/2E). Normal healing appears unaffected, but unlike 3E, magical healing (perhaps the type PCs are most interested in) may possibly fail if a caster check does. And the window for raising (6 turns in 1E; 6 rounds in 2E) appears to be entirely eliminated, with a dead victim apparently blowing away as sand instantaneously.

Cure disease no longer has any effect on the victim of mummy rot, as it is now qualified as a curse instead; so something like remove curse is instead required. There is a certain charm to this, inasmuch as the pop-culture conceit is one of the "Pharaoh's curse" (see top), not the "Pharaoh's disease"; although this makes a cure somewhat easier to access, because remove curse is on both the cleric's and wizard's spell lists. Also: the half-damage from blows is gone, although it uses a "damage reduction" ability that shaves 5 points off any attack (so: even nonmagical attacks of sufficient strength can damage it, something not possible in any prior edition).

Holmes D&D

Mummies are also members of the undead. They do not drain life levels, but their touch (if they make a hit) causes the dreaded rotting mummy disease which makes wounds take ten times the usual rate of healing. A cleric can reduce this healing time to only twice normal with a cure disease spell if it is administered within an hour. 

Only magic weapons can hit mummies, and they take only half damage from a hit. Note, however, that mummies are vulnerable to fire, including the ordinary kinds such as a torch, although it only does half-damage to them.

When a mummy is first seen a saving throw vs. a spell must be made or the individual is paralyzed with fear and cannot move until the mummy strikes him or another member of the party. If the party numbers above 5 each member gains a +2 on his saving throw, as their numbers help dispel fear. 

Here's where we check in on the D&D Basic line, starting with Holmes in 1979. The primary project of Holmes was to closely duplicate the rules in OD&D with some of its supplements, with better organizational editing, and only rarely filling in a few gaps with extra rules; and this set the tone for most of the Basic D&D line(s) in the 80's and 90's.

This is almost entirely true for this case of the mummy. Hit dice are the same as in OD&D (5); that is, without the inflation seen in AD&D (and this will remain fixed throughout Basic D&D). The half-damage from hits is the same. The rotting disease is old-school awful as in OD&D; a permanent healing reduction, not fully removable even with cure disease. As in Vol-2, it does not mention magical healing in any way. More importantly, it entirely ignores Arneson's escalation of the disease in Sup-II -- so that while distressing, it is not automatically fatal within a few days of catching it. It does not address or prohibit raising the dead victim in any way (not that raise dead is part of the Holmes level 1-3 basic ruleset).

Now, Zenopus Archives tells us, looking at an early pre-publication manuscript, that "Holmes follows the description in OD&D closely, with no conceptual changes. The two paragraphs in the manuscript are retained in the published rulebook, which adds an entirely new third paragraph describing the fear induced by a mummy."

I think it's been well established at this point that it was Gygax who took Holmes' manuscript and did an editorial pass on it, adding various rules to make it more aligned with his AD&D work. So in this case: The first two paragraphs are really from Holmes, encapsulating the OD&D mummy; and the third paragraph is Gygax, adding in the new fear power from AD&D. Gygax has a bit softer touch here, making the paralysis end as soon as any member of the PC's party is struck by the mummy (instead of a fixed 1-4 rounds).

On the other hand, what Gygax missed in the second paragraph is that Holmes gave mummies only half-damage from fire, whereas in AD&D Gygax gives a bonus to fire damage, so in that respect the two game lines are now running in opposite directions.

Basic D&D

Mummies are undead who lurk near deserted ruins and tombs. On seeing a mummy, each character must save vs. paralysis or be paralyzed with fear until the mummy attacks someone or goes out of sight. In melee, a hit by a mummy does 1-12 points of damage and infects the creature hit with a hideous rotting disease. This disease prevents magical healing and makes all wounds take 10 times as long to heal. The disease lasts until it is magically cured. 

Mummies can only be damaged by spells, fire, or magic weapons, all of which will only do half damage. They are immune to sleep, charm, and hold spells.

The text above is from Cook's Expert D&D (p. X36, 1980). Note that the disease now includes the prohibition on magical healing (not in the prior OD&D or Holmes; first seen in 1E AD&D); however, it is more generous in apparently allowing the magical cure to completely remove the ailment. It retains Holmes' half-damage from fire, in opposition to the AD&D line. Also following Holmes, it is silent on the issue of raising the dead (even that that spell is in this volume). It keeps the paralysis-fear, and ends it if either a PC is attacked, or the mummy moves out of sight; and Cook edits out Gygax's fiddly save modifier depending on number of people in the party.

Mentzer's Red/Blue Box rules (1983) keeps almost the exact same rules text as in Cook. I can see only one change; the sentence about mummy fear does not end the paralysis on a PC being struck -- now, only if the mummy moves out of sight. Allston's Rules Cyclopedia (1991) mummy is word-for-word identical to Mentzer's, except for an added flavor-text paragraph. The half-damage from all blows is retained throughout all Basic editions.

Poll Results

I asked about mummy rot on the Facebook 1st Edition AD&D group. In one of the more lopsided results that I've seen, almost everyone there did seem to prefer the 1E long-acting version of the disease.


Looking at OD&D, we must admit that there are two separate, really incompatible takes on the mummy's curse of disease. Gygax in Vol-1 plans on the disease being a long-term degradation in recovery ability, over the course of months, perhaps. Arneson in Sup-II expects the disease to very quickly be fatal, within just a few days -- such that the slow-healing effect becomes a forgettable non-issue for practical purposes. Gygax's view held sway in 1E/2E AD&D and the Basic D&D line. But later editions from 3E on recast the disease as did Arneson, fatal in some days if not cured.

Gygax's long-term disease is more in line with the classic pop-culture understanding of the Pharaoh's curse, in which tomb-intruders die horribly months or years later. But Arneson's quick-acting leprosy may possibly be more urgently, dramatically gameable. Which is your preference?


Medieval Demographics in Brief

Historical map of Kudna area 1870s

When I’m developing a wilderness map, I always have to decide, “At what frequency should I place villages, cities, and castles here?” Below you'll find a short document that I've drafted on research for a model on medieval-level demographics. Of course, I'm not the only person to do this, and in fact I don't think this is the only time I've done this; but the document includes copious endnotes so I hopefully stop re-doing this and forgetting which parts are based on real-world data, and which parts I made up for the game.

Here's an executive summary. We use as the basis for our model data from England around the 11th or 12th century;  the population then was around 2 million. (Earlier in the Dark Ages it might have been half or one-quarter this level; later in the High Middle Ages it would be around 5 million, and then collapsing back down to 2 million at the time of the Black Death.) For our baseline in history we find, in round numbers:

  1. Cities: One per 1,000 square miles.
  2. Castles: One per 100 square miles.
  3. Villages: One per 10 square miles. 
(When we say "cities" here we really mean any walled towns.) A variety of examples from Gygaxian rulebooks shows a markedly less dense population, by roughly an order of magnitude (about 10 times fewer features per equivalent land surface area). For game campaign maps, this author is currently using a value about halfway between the two, that is, about one-quarter the baseline medieval population density (i.e., Dark Ages levels). More precisely, we assume that only about one-quarter of the land area is inhabited by humans, with density in those areas approximately the same as medieval England (the rest of the map is left over under the control of various nonhuman races and monsters; in particular, almost any non-plains locations). Therefore this author currently uses, for fantasy realms:
  1. Cities: One per 4,000 square miles.
  2. Castles: One per 400 square miles.
  3. Villages: One per 40 square miles.
This can easily be converted to a recommendation or average on a game map per-hex basis with a little math. Note that the area of a hexagon is \(S^2 \cdot \sqrt{3}/2 \approx S^2 \cdot 0.866\), where \(S\) is the length of the hex measured across opposite edges. (For example, a 24-mile hex is close to 500 square miles; a 6-mile hex is about 30 square miles.) We currently use something like the following map scales:
  1. 100-mile hexes: Shows capital Cities (1 per 30 hexes).
  2. 24-mile hexes: Shows walled Towns (1 per 8 hexes)
  3. 6-mile hexes: Shows baronial Castles (1 per 12 hexes)
  4. 1½-mile hexes: Shows individual Villages (close to castles)
We can otherwise express this by stating that, on average, at Level 1 there is one walled town per hex; at Level 2 one castle per hex; and at Level 3 one or more villages per hex, and therefore these features are not shown on the maps at those scales. The 6-mile hex scale is expected for use in standard wilderness adventure and exploration (smaller sizes permit the entire map to be crossed in a single day, and are generally only used for introductory level adventures, or for added flavor, not strategic movement). We emphasize that at this exploratory level, it makes no sense to depict individual villages (historically, there would be multiple villages per hex); instead, we place castles as shown and assume that each of the adjacent hexes has between 1 and 3 villages in fief (within range of daily patrols, or for a runner/rider to get help within an hour or so). We further assume that the villages mostly have no amenities of interest to PCs (inns, taverns, general stores, etc.) In general we find this makes for attractive and gameable maps, with plenty of space left over for exploration and monster lairs.

Finally, populations for each of the urban features can be simply approximated by the following (this generally hews pretty closely to both historical data and classic D&D rules):
  1. Cities: 10,000-60,000 people.
  2. Towns: 1,000-6,000 people.
  3. Villages: 100-600 people.
A further research question might be this: Is the population scarcity shown in the writings of Gygax consistent with other works of fantasy literature? While likely harder to quantify, this author would hypothesize so. (Consider: Featuring only a single central city in an area that would historically have several, needing to focus the narrative on a few key features, etc.)

See full details in the document below, with appropriate research citations (PDF):


Rappan Athuk DM's Log Index Cards

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


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 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!


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 C1 was made just for that publication, and not used at Origins). As an aside: If you're curious, the only other "Collector's Edition" monochrome-and-numbered item was Ghost Tower of Inverness by Allen Hammack (later 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 in the single-digits and teens (as seen above), is a complete 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

Proto-Boxed Text -- Initial descriptions for each area are given, not exactly in boxed text, but in specially quoted and indented passages. Perhaps this marks the first germinal attempt at what would become boxed text? Thanks to commenter Test for asking about this, as it didn't even occur to me when I read it the first time.

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.


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 make, 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 not 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?

Edit: Related, you should also  check out DH Boggs' analysis of prices relating to OD&D, real-world castles and wages, evolution from Arneson's First Fantasy Campaign, and more. Highly recommended!


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 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.


OED Monster Database

One of the places that OD&D can be most successfully criticized is in its presentation of the monster listing. In many places in the original work key details are missing, contradictory, or left to the DM (e.g., all of the normal and giant animals that appear in the encounter charts). As of the first supplement, one had to look in at least four different places for all of a monster's information: (1) the main table (HD, AC, MV, etc.), (2) the alternative attacks/damage listing, (3) the alignment category, and (4) the main text description, each of which appeared in different far-flung sections, even different books for one monster. The overall situation is what motivated release of the Monster Manual as the first hardcover book, which compiled all the statistics from OD&D monsters in one place, before any other volumes of the AD&D rules.

Below you'll find the OED Monster Database, a compilation I've made over the years for OD&D monster statistics, in line with my OED games and house rules. This gives me a convenient one-stop resource for OD&D monster statistics when I'm writing other material. One might ask: Why not just use the Monster Manual? One reason is that I very much like to stick with the original d6-based hit dice, attacks, and damage, as found in the LBBs (i.e., we do not recognize the alternative monster hits starting in Supplement I). Moreover, here are other reasons why I think this exercise was worthwhile:

  1. Provides a consolidated listing of OD&D-style monster statistics.
  2. Creates automatic summary stat blocks for insertion to adventures (see sheet 2).
  3. Software can provide data-integrity checks for monster records.
  4. Software also assesses "equivalent hit dice" valuations for encounter balancing and XP awards.
  5. Forced me to think through any ambiguous adjudication cases in code (this prompted many "rules archeology" investigations and margin notes that you see on this blog).

Generally I've compiled everything I could find from OD&D Vol-2, Sup-I, land creatures from Sup-II, and TSR (The Strategic Review) No. 1 and 2 -- for a total of 147 monsters. Not included are aquatic monsters from Sup-II, demons from Sup-III, or deities from Sup-IV. For things like giant animals I turned to the Monster Manual and back-ported the information there, translating variant damage into units of d6's as we would normally expect/prefer.

Among the things you'll see is that any kind of special ability is given a keyword (and optionally one numerical parameter) for readability by my "Monster Metrics" program (more on that this Saturday); hopefully a knowledgeable DM can parse what those notes mean. The third-to-last column shows the EHD (equivalent hit dice) as determined by that program. A number of monsters are fundamentally outside the ability of my model to determine EHD, and so currently indicated by a question mark (?). These would include monsters with expansive wizard-type spell ability or need spells to defeat -- for example: the lich, lammasu, gold dragon, beholder, titan, and oozes with total weapon immunity.

XP Awards by EHD

Let's consider XP awards for a minute. My preference is to award XP by simply multiplying HD by 100 (and this is supported by evidence of a fundamentally linear relationship between risk and HD). Of course, this method from OD&D Vol-1 overlooks the value of special abilities. Sup-I introduced a variant XP table, and a secondary column to award bonuses for special abilities (which was of course carried forward into later editions like Holmes, B/X, AD&D, etc.). But in most of these works the DM still needs to make a subjective decision about what abilities warrant this bonus -- and I would argue in many cases it vastly undervalues some very nasty abilities (esp. on creatures with low HD).

There's a much easier way to do this, without any new tablature required or DM subjectivity, by just assigning a revised hit die value for XP purposes, which I've taken to calling "equivalent hit dice" (EHD). I gauge this with my Monster Metrics program by running several thousand fighters of different levels at each monster until we can determine a "fair" fight in each case. But the core of this idea (as simple as it is) predates the Sup-I and later variant XP charts, appearing first (briefly) in The Strategic Review, Vol. 1, No. 2 (Summer 1975), p. 4:

For purposes of experience determination the level of the monster is equivalent to its hit dice, and additional abilities add to the level in this case. A gorgon is certainly worth about 10 level factors, a balrog nut [sic] less than 12, the largest red dragon not less than 16 or 17, and so on. The referee's judgement must be used to determine such matters, but with the foregoing examples it should prove to be no difficulty.

This seems like a much more elegant way to assess the risk/reward of exotic monsters, and it's also the simplest measurement model I could construct in my software, so this is what I now include for each monster (where appropriate) in the Monster Database. Let's just briefly compare the sample evaluations from TSR #2 to what comes out of my program for EHD:

So we can see that, compared to our model, Gygax seemed to to undervalue the more exotic special abilities of monsters (in this case: petrification, immolation, and fire breath), which is consistent with his low valuation for specials in the variant Sup-I XP tables. Perhaps on closer inspection we could generously grant that Gygax's numbers correctly assess the minimum fighter level which could possibly match the creature man-to-man, but this is not an ideal metric of the danger to parties of several men of lower or higher levels.

Finally, let's look at the distribution of the EHD values currently recorded in the monster database:

Here we see that the distribution is a nice logarithmic curve, with the largest number of monsters at the lowest level (EHD 1-5), and decreasing regularly after that. (If we zoom in a bit more we'd see that the highest number of monsters are actually the level of EHD 2, outnumbering EHD 1 by a small margin.) This seems to be useful for a fantasy campaign, and nicely echoes the curves we'd expect to see in demographic and economic statistics from real-world data.

That being said, here's the link to the current OED Monster Database, at the OED Games website (ODS format):