Thursday, August 30, 2018

BTPBD Missile Fire

Follow-up to the last two posts, in which we reflected on how incredibly scrambled the D&D man-to-man scale has been from its inception, especially highlighted by its rules for ranged combat (which allow a person to hit another individual at incredible distances).

But let me present a case that comes further over the top than even that. Some of us have had the opportunity to look at the manuscript titled "Beyond This Point Be Dragons", which based on textual analysis is widely believed to be at least derived from a pre-publication draft of D&D. Here is that work's Table 30: Missile Fire:


Notice that each missile weapon has two rows: The second row exactly matches the Chainmail target numbers, which give rolls needed to score an instant kill. (Note that this is identical to how the Chainmail table for melee is used -- providing chances for instant kills, after a hit is first scored by normal D&D-type mechanics.) It is the first row that gives chances to score a simple hit, and these numbers are (obviously?) lower and easier to score than the instant kill numbers -- specifically they give, for most weapons against unarmored men (AC 9), automatic hits at almost every range (e.g., for light crossbow, longbow, composite bow: 2-2-3 on 2d6). And here there is no ambiguity about the implied range increments: the note to the table says this is definitively in tens of yards, up to 240 yards for a composite bow.

So whoever wrote this table thought it was reasonable for a longbowman to have a 97% chance to hit an active individual man at 210 yards, or a heavy crossbowman a 100% chance to hit at 240 yards, etc. Which I think we can all agree is outrageous lunacy, granted that grand-master champion archers in England today actually have about a 1% chance of hitting a like-size immobile target at distances like that.

Whatever errors were made by the earliest D&D author(s) in terms of mundane activities, the misunderstanding of man-to-man missile fire was surely the most thoroughly broken concept on the table.


Monday, August 27, 2018

Interpolating the Man-to-Man Scale from Chainmail Hit Rates

As a follow-up to last week's post where we considered the yawning gap in that Chainmail Man-to-Man Combat had no units of scale specified (and the years of headaches that followed), today let's try to compute what the distance scale should have been. Of course, more than one argument has been advanced in this direction. The most obvious one is to just take the figure scale in use and use the same or similar scale for ground distance; done. But here I'll take an approach I've never seen considered -- granted that Chainmail Man-to-Man Combat has no scale, it does have specified hit probabilities, and we can use those to back-calculate what distance scale is implied by those.

First, here's our standard simulation of archery hits at range, using a bivariate normal model (both error in the x- and y-axes simulated by a normal distribution), and now uploaded as ArcherySim on GitHub. An earlier version of this simulator was used numerous times on this blog, such as here and here. The simulator has been calibrated to match results seen last time from the UK National Clout Championships: at 180 yards range, a hit rate of 1% against a 1.5-foot radius target (equivalent to one man), and a 42% hit rate against a 12'-foot radius target (equivalent to a group of 64 men). Here's a table compiling the results from that program run on several different target sizes:



A couple comments about this table: Internally, all the simulator really does is for each doubling of distance, shrink the apparent radius of the target by half -- and likewise to interpolate any other distance. Therefore, each doubling of distance is perfectly offset by a like doubling of of the real target radius (and hence by a quadrupling of the number of men in formation), which can be seen by matching numbers running diagonally in the table. Of course, this presumes an immobile, defenseless, unarmored target (an aware and mobile man on the battlefield should shift these probabilities downwards by some amount). All of this is reasonable.

Next, let's look at the "Individual Fires With Missiles" chart from Chainmail. It looks like this:


For simplicity, we'll take the median missile range of 18 (as for a horsebow, light crossbow, or arquebus) as exemplary; therefore our supposed range categories fall at distance 6/12/18 inches, per the footnote on the table. Also note in the first column of results (armor class 1, which on this page indicates "no armor"), most of the hit targets are 5-6-7 (indicating the minimum score on 2d6 for a hit at each range category), with the outliers either up or down by one pip.

Now we'll take a few theoretical different scales for these "inches", see what the hit rates against a 1.5-foot radius target (one man) would look like according to ArcherySim, and convert those back to a 2d6 basis (for example, using a table like the one that appears at the bottom here). We will consider the possibilities that 1" = 10 yards, 1" = 10 feet, or 1" = 5 feet.
  • 1" = 10 yards: Therefore the median missile range categories fall at 60, 120, and 180 yards. According to ArcherySim (using the detailed output option with the -L switch), the hit rates against the 1.5-foot target should be 7%-2%-1%. On the 2d6 basis, these percentages convert to target scores of 11-12-/ (i.e., effectively impossible at the longest distance).
  • 1" = 10 feet: In this case, the range categories are 60-120-180 feet, equivalent to 20-40-60 yards. The simulator says the hit probabilities should be 47%-15%-7% (you can see two of these values in the topmost table, in the leftmost column). On 2d6 these convert to 8-10-11. 
  • 1" = 5 feet: Here the range classes are 30-60-90 feet, equal to 10-20-30 yards. ArcherySim estimates the hit rates at 92-47-24%. On 2d6 these become 4-7-9. 
  • 1" = 3 feet: Range categories become equivalent to 6-12-18 yards.  Our simulator computes the chances to hit at 100%-83%-54%. On 2d6 that looks like 2-5-7.
These results are illustrated below:


The first thing that is visibly obvious here is that the Chainmail modifiers for range adjustments, at just a single pip per category, are far too small. In the chart this appears as the Chainmail hit targets (the green line segment) being a tiny little span compared to the real-world models at around the same values. A better simulation would be to alter the hit targets by around 2 or 3 pips per range category (equivalent to something like −6 to hit in D&D with the d20 system). Also, this could be better if the range classes weren't assumed to be linear (that is: 6-12-24 range units would be a better physical model than 6-12-18 units; then the long-range chance segment wouldn't be shrunk compared to the medium-range chance segment in each case).

The second only slightly less obvious fact is that the 1" = 10 yard and 1" = 10 feet scales (the ones actually used in D&D) are terribly poor matches; they don't even overlap the Chainmail 5-6-7 targets at all. The 1" = 3 feet proposal at least overlaps it, but is skewed off almost wholly to the left side (e.g., should be effectively unmissable at such a short range). The one that is best centered over then Chainmail hit interval is the 1" = 5 feet scale, and we can therefore use this as the true "implied" distance scale for Chainmail Man-to-Man Combat.


Thursday, August 23, 2018

On Free Retreat Attacks

This came up in our game last Friday: When a figure retreats from melee, does the opponent get a free back attack? Unlike most standard versions of D&D, I say "no" in my games.

I think that the germ of this rule is from Chainmail mass combat -- that a retreating unit loses a turn as they attempt to rally and can be attacked for free if desired (somewhat poorly having chosen to stand motionless for a minute with backs to the enemy)...


 ... and, echoing Monday's post, this wound up being carried through sympathetically to man-to-man combat in AD&D (DMG p. 70):


Serendipitously, I ran into a video today by Lindy Beige on YouTube on exactly this issue, dealing with both the real-world simulation and game-design balance aspects. We approve:


Monday, August 20, 2018

Lack of Scale Considered Harmful

The first and biggest mistake in the foundation of D&D was not specifying any units of scale in the Chainmail Man-to-Man Combat rules.

In general, specifying units of scale (for figures, time, and distance) was usually among the very first things stated in traditional wargames, often before the actual start of the rules themselves. For a specific example, these are given in the third paragraph of the Chainmail mass-combat rules, preceded only by a statement on what the Middle Ages were, and what size and brand of miniatures are recommended (p. 8). These Chainmail mass-combat rules came with a respectable pedigree of playtests, refinement, and editorial corrections; in the second paragraph, they reference the prior "LGTSA Medieval Miniatures Rules... the rules have been thoroughly play-tested over a period of many months..." (p. 8). Jon Peterson in Playing at the World tells us, "The LGTSA medieval miniatures rules resulted from Gygax's expansion of Jeff Perren's original four-page ruleset..." (p. 30), published in Domesday Book #5 (July 1970). Also, "The core system of Chainmail adheres closely to the earlier LGTSA rules; for example, the movement and missile combat system charts are copied verbatim..." (p. 40). Furthermore, these rules themselves were influenced my older systems such as those of Tony Bath, etc. (p. 31). As a result of this legacy of a wargame refined by diverse hands, we find that the scales of time and distance, movement and missiles, found in LGTSA/Chainmail mass-combat are fundamentally reasonable and match well with real-world data. 

But with the publication of Chainmail, we also get a new 3-page section on Man-to-Man Combat which, relatively speaking, appears to come out of nowhere. It does not claim to come with a history of playtesting, appears relatively slapdash, and is likely the conceptual work of a single author (Gygax?). Notably, while one figure now represents one man, there are no specifications given for time or distance units on the table; it seems to have not even been considered at all. Broadly speaking, these rules try to "cheat" the issue by silently assuming that the mechanics for mass-combat can be used without alteration in man-to-man combat ("Generally speaking, the rules for 1:20 scale apply to man-to-man missile fire...", p. 25) and so forth.

Of course, there are some things in the world for which, when we "zoom in" on them, the characteristics appear the same as when we "zoom out"; for example, fractals are geometric figures which act in this fashion, and are therefore called "scale invariant". You can almost get away with the assume-everything-is-the-same approach for movement (if distance and time are changed in proportion), and melee combat. But it's precisely with missile combat where the problems and contradictions spring into plain sight -- ranged combat is distinctly not "scale invariant".

Here are two of the top absurd positions that this oversight forced Gygax to defend constantly in later a years as a result of this initial oversight: (1) That man-to-man combat took place at the same 1-minute action cycle as Chainmail, and that therefore only one sling or crossbow-shot could be made per minute, etc.; and (2) That effective missile ranges were at the same 10-yards-per-tabletop-inch scale, such that it was feasible to shoot an individual man at 210 yards outdoors with a longbow, which is patently ridiculous. (See OD&D Vol-3 p. 8 and 17; AD&D PHB p. 39).

Of course, a claim is made that the distance scale shortens to 1" = 10 feet in the indoor/underworld environment (OD&D Vol-3, p. 8). As a result of this, magic spells likewise grow and shrink depending on whether they are used indoors or outdoors. In Dragon #15 Gygax writes what seems to be a correction and apology on the issue after Len Lakofka points out the problem here. Gygax calls the existing result "ridiculous" and that "the blame for the possible ignorance of player and Dungeon Master alike rests squarely on my shoulders" (read the article and my past analysis on it here). This altered rule, that magic ranges change indoors-to-outdoors, but areas-of-effect do not,  then gets incorporated into the AD&D PHB (p. 39), in a rather screechy all-caps passage, below:
For purposes of the game distances are basically one-third with respect to spell and missile range from outdoors to indoors/underground situations. Thus most ranges are shown as inches by means of the symbol ", i.e. 1", etc. Outdoors, 1" equals 10 yards. Indoors 1" equals 10 feet. Such a ratio is justifiable, to some extent, regardless of game considerations.

Actual effective range of an arrow shot from a longbow is around 210 yards maximum, in clear light and open terrain. Underground, with little light and low ceilings overhead, a bowshot of 210 feet is about maximum. Archery implies arching arrows. Slings are in this category as are hurled darts and javelins, all arching in flight to achieve distance. Crossbows are a notable exception, but under the visibility conditions of a dungeon setting, a yards to feet conversion is not unreasonable.

Magic and spells are, most certainly, devices of the game. In order to make them fit the constrictions of the underground labyrinth, a one for three reduction is necessary. It would be folly, after all, to try to have such as effective attack modes if feet were not converted to yards outdoors, where visibility, movement, and conventional weapons attack ranges are based on actual fact. (See MOVEMENT.)

Distance scale and areas of effect for spells (and missiles) are designed to fit the game. The tripling of range outdoors is reasonable, as it allows for recreation of actual ranges for hurled javelins, arrows fired from longbows, or whatever. In order to keep magic spells on a par, their range is also tripled. IT IS IMPERATIVE THAT OUTDOOR SCALE BE USED FOR RANGE ONLY, NEVER FOR SPELL AREA OF EFFECT (which is kept at 1" = 10') UNLESS A FIGURE RATIO OF 1:10 OR 1:20 (1 casting equals 10 or 20 actual creatures or things in most cases) IS USED, AND CONSTRUCTIONS SUCH AS BUILDINGS, CASTLES, WALLS, ETC. ARE SCALED TO FIGURES RATHER THAN TO GROUND SCALE. Note that the foregoing assumes that a ground scale of 1" to 10 yards is used.


Now, a couple things to note about this passage. One: a cursory justification for the feet-to-yards conversion is made for missiles ("little light and low ceilings overhead"). Two: absolutely no justification is attempted for the expansion of magic spell ranges; it is purely a matter of raw game balance ("devices of the game... designed to fit the game"). In fact, to my knowledge, Gygax never attempted any in-world explanation or rationalization for this phenomenon. (You can of course make up your own: Do magic energies follow ballistic trajectories and get limited by ceiling height? Is every underworld locale uniformly imbued by dark counter-energies that reduce magic effects? Not to say that any such claim is in any rules text.) Ultimately Gygax hangs his hat on, "It would be folly, after all, to try to have such [magic] as effective attack modes if feet were not converted to yards outdoors, where visibility, movement, and conventional weapons attack ranges are based on actual fact." But this ignores the actual actual fact that shooting an individual man at 210 yards with a longbow is sheer lunacy in the first place.

Here's the thing that occurred to me a few days ago, and that I'm embarrassed at how many years it took me to observe: The whole notion of indoors-versus-outdoors is a false path and a distraction. The real issue is whether the action is at mass-scale or man-to-man-scale. Which again, is the original error, the essential oversight in the new section of Chainmail.

Let's look at some data. There's a notable real-world circumstance in our favor; modern archery competitions in the United Kingdom have the exact distinction that we're looking for here. There's standard target archery, at a fairly close range, with a target passingly close to the size of man; and separately, clout archery at a distance near the limit of a classic longbow, with a relatively huge target area (fundamentally simulating shooting at an army). Specifically: standard target sizes are 122 cm in diameter (approximately 4 feet, or 2 foot radius). Clout archery for adult men is held at 180 yards range, with a target area 12 feet in radius, and a central "clout" (bullseye) of 18 inches radius (that is, about the size of the entire short-range target, or roughly a single man's area).

Here are results for the Yorkshire Archery 2018 Clout tournament. For more, here are results from the National Clout Championships of 2016. Here's a data analysis by myself (ODS spreadsheet) of the latter tournament for the Gentleman's Longbow event . Some results of that analysis (N = 30, discounting last two outliers with only one point between them): The average hit rate on the 12-foot radius target at 180 yards was just 42% (ranging from 11% for the bottom-performers, to 83% for the winner). The average hit rate on the central bullseye/clout -- about the size of a man (assuming a totally immobile, defenseless one) -- was only 1%!. (Even the winner himself only scored a 1% hit rate on the centermost target; the two runners-up scored 6% and 8% bullseye rates, but these may be considered pure luck since their overall accuracy was not as good as the winner's, and in any event represent the equivalent of natural-20's for these almost-England's-best-archers).

The central lesson here is that it can be effectively impossible to hit a target in man-to-man combat at long range (1% vs. the central clout), while being completely feasible against a larger area/group of men (42% vs. the larger target, roughly the same chance D&D gives a 1st-level man to hit an unarmored opponent). If we take the small 18 inch = 1.5 foot radius as roughly the area of a single man, then the larger 12-foot target is equivalent to some 64 men in formation ((π(12)^2)/(π(1.5)^2) = 64). If we were to double the target radius again, to 24-feet and some 256 men, then this would be a 90%-something shot, nearly unmissable (using ArcherySim on GitHub). For emphasis: With a longbow at around 200 yards, hitting an individual man is a 1% shot or less, while hitting an army is a 99% shot a more. The cases are exact binary opposites. Note that Chainmail mass-combat had no rules or penalties for missile range, and we find this to be completely reasonable; but keeping the same or a minimal range penalty for man-to-man combat is, as Gygax would say, "ridiculous".

Some conclusions: One, the maximum effective range for man-to-man missile combat should be set at around 40 yards; this is especially true for a target that is mobile and defending itself (note that the real-world data above assumes a completely immobile, defenseless, unarmored target; hit rates should obviously be lower if that is not the case). This is true whether indoors or outdoors. Note that the legacy of this glitch has led to ranged attacks never being close to right in any edition of D&D. Over 40 years later, and in 5E D&D (from what I can tell), a 1st level fighter shooting a longbow at a mobile, active single man at maximum range of 200 yards still has a 42% chance to hit (AC 10 with +2 attack bonus, i.e., target 8 on 20, with disadvantage); coincidentally exactly the same rate that the UK's champion clout competitors actually have against an immobile, barn-sized target. That's twisted.

Two, in classic D&D, there should have been greater care taken in specifying scales, and distinguishing between the man-to-man and mass-combat situations; the two are not equatable. A random example: In D&D Vol-3, the Aerial Combat and Naval Combat sections seem to be closely related; they refer to each other in places, stipulate the same playing area, turn sequence, and written orders (compare p. 25 and p. 30), etc. But in truth, Aerial Combat is intended for man-to-man scale (each figure a single creature), whereas Naval Combat is intended for mass-scale (each ship model carrying tens or hundreds of men; missile fire as per Chainmail mass rules on p. 30, etc.; at least until a boarding action occurs and then we are directed to switch maps and rulesets to the man-to-man basis on p. 31). These are very different situations, requiring different distance and time units, tabletop missile ranges, turning radii (another characteristic that is definitely not scale invariant), etc., and this qualification should have been highlighted in the original rules.

Three, by Gygax's logic in the PHB, we should also calibrate the range and effect of magic spells on the reduced basis for game-balance purposes ("It would be folly... [for magic to contradict] where visibility, movement, and conventional weapons attack ranges are based on actual fact"). Again, irrespective of being indoors or outdoors; that is not a relevant distinction. Note that once this physical reality of the magic spell range is set by man-to-man scale, it implies that apparent range and usefulness in the mass-scale context is much reduced. Example: In Gygax's later Swords & Spells mass combat rules, spell ranges in inches are copied verbatim from the D&D rules, and hence have extraordinarily long-range effects on the battlefield (e.g., 24" for a fireball, i.e., 240 yards). Reversing the reasoning, we now consider that if the spell range was fixed at 40 yards, as per man-to-man missile fire, then on the mass-scale battlefield a fireball would only be usable at 4" or something like that. That's a fairly major change (perhaps in Book of War?), but upon reflection, it may be a better simulation of magic effects as seen in pulp literature and similar traditions. Some of the higher-level spells meant to influence large areas outdoors might prove troublesome, however.

To wrap this up, we look at a quote from Gygax in The Strategic Review, Vol. 2, No. 2 (April 1976), in his article "The Dungeons & Dragons Magic System" (p. 3), that some of us have been considering recently:
Magic in CHAINMAIL was fairly brief, and because it was limited to the concept of table top miniatures battles, there was no problem in devising and handling this new and very potent factor in the game. The same cannot be said of D & D. While miniatures battles on the table top were conceived as a part of the overall game system, the major factor was always envisioned as the underworld adventure, while the wilderness trek assumed a secondary role, various other aspects took a third place, and only then were miniatures battles considered.
This is somewhere between a strange thing to say and a ghastly oversight (that underworld adventures came first in the calibration of D&D magic, and miniatures battles a distant fourth), because in terms of time and distance, exactly the opposite is the case. The mass-combat miniature scales were carefully figured, and the underworld scales simply taken by theft of the same and without any real consideration. Even in the SR 2.2 article quoted above the issue continues to entirely escape Gygax's attention (the topic being only a defense of the Vancian memorization and daily-limit conceits). If only some assistant had been able to point that out at the earliest date.


Edit 9/1/18:  Around the time I was writing this, Jon Peterson had a new post about some of the prior systems that fed into Chainmail man-to-man combat. It doesn't exactly address my main criticism here, but it's quite interesting to know about for its own sake. Thanks to Jon for pointing this out to me.

Edit 9/20/18: Geez, I may be stuck in a fugue on this issue.

Monday, August 13, 2018

Teleport Traditions

I do get a little weirded out when SF gets deeply injected into my fantasy. The top examples in OD&D for me are probably the spells ESP, telekinesis, and teleport. In particular, that latter spell's instant-death possibility always looked out-of-synch with other spells or pulp fantasy traditions (e.g., consider spell-casting screwups which land Cugel the Clever on a different continent, or Harold Shea in the wrong plane of reality). I previously wrote about it 4 years ago this month. From Vol-1:

Teleport: Instantaneous transportation from place to place, regardless of the distance involved, provided the user knows where he is going (the topography of the arrival area). Without certain knowledge of the destination teleportation is 75% uncertain, so a score of less than 75% of the percentile dice results in death. If the user is aware of the general topography of his destination, but has not carefully studied it, there is an uncertainty factor of 10% low and 10% high. A low score (1-10%) means death if solid material is contacted. A high score (91-100%) indicates a fall of from 10 to 100 feet, also possibly resulting in death. If a careful study of the destination has been previously made, then the Magic-User has only a 1% chance of teleporting low and a 4% chance of coming in high (10-40 feet).

For some time I've wanted to identify what part of the literature most inspired this. It certainly seems more SF than fantasy, but tracking that down in Appendix N is foiled because it doesn't list SF sources, only fantasy. Some of my top prospects previously have been Arthur C. Clarke's Travel By Wire! (his first short story, 1937), de Camp and Pratt's Harold Shea stories (listed in Appendix N as the first among the "most immediate influences upon AD&D", 1941-), and possibly Star Trek, especially their "Day of the Dove" episode (1968). See also many other entries at TVTropes' Tele-Frag article.

But at this point I'm pretty confident in theorizing that the most immediate influence on the teleport spell itself is Alfred Bester's The Stars My Destination (1957). Having recently read it, I'd say that it has at least a 90% correlation with the D&D spell. Crucially, we know from other places that Gygax definitely read Bester: on ENWorld he wrote, "That list was just a sampling of the SF authors I have read. Good grief, Poul Anderson, ERB, Alfred Bester, Eando Binder, Edmond Cooper, and a host of others aren't on it..." And this book was one of really just two novels for which Bester is known. (Major thanks to capvideo on the OD&D Discussion board for digging this quote up.)

Here are some bullets in which Bester's The Stars My Destination synch up with the D&D spell:

  • Teleporters ("jaunters") have a strict need of exact knowledge of their destination. Chapter 3 details people taking a class in that exact skill, opening with:
    "Bravo, Mr. Harris! Well done! L-E-S, gentlemen. Never forget. Location. Elevation. Situation. That's the only way to remember your jaunte co-ordinates. Etre entre le marteau at l'enclume. [Being between the hammer and the anvil.]"
  • Furthermore, the custom/requirement is that people visit a certain location in person, traveling there by conventional means the first time, and make a detailed study of the place, before being able to teleport there. Again from Chapter 3:
    The men were brought down from General War Hospital to the jaunte school, which occupied an entire building in the Hudson Bridge at 42nd Street. They started from the school and marched in a sedate crocodile to the vast Times Square jaunte stage, which they earnestly memorized. Then they all jaunted to the school and back to Times Square. The crocodile reformed and they marched up to Columbus Circle and memorized its co-ordinates. Then all jaunted back to school via Times Square and returned by the same route to Columbus Circle. Once more the crocodile formed and off they went to Grand Army Plaza to repeat the memorizing and the jaunting...

    As their horizons expanded (and their powers returned) they would memorize jaunte stages in widening circles, limited as much by income as ability; for one thing was certain: you had to actually see a place to memorize it, which meant you first had to pay for the transportation to get you there. Even 3D photographs would not do the trick. The Grand Tour had taken on a new significance for the rich...

    The bandaged C.P.O. nodded dubiously and stepped up on the raised stage. It was of white concrete, round, and decorated on its face with vivid black and white patterns as an aid to memory. In the center was an illuminated plaque which gave its name and jaunte co-ordinates of latitude, longitude, and elevation.
  • Teleporting blindly without awareness of the co-ordinates (including co-ordinates of the point of departure) is almost sure to land one in solid matter, resulting in explosive death. Chapter 5 is set in a lightless, labyrinthine prison under Gouffre Martel (a real-world cavern complex in the French Pyrenes), so situated because it's the only way to keep prisoners unaware of their bearings and thus unable to teleport. Nonetheless, some try it out of desperation and this is called a "Blue Jaunte":
    But every so often... once or twice a week (or perhaps once or twice a year) came the muffled thud of a distant explosion. The concussions were startling enough to distract Foyle from the furnace of vengeance that he stoked all through the silences. He whispered questions to the invisible figures around him in Sanitation.

    "What's them explosions?"

    "Explosions?"

    "Blow-ups. Hear 'em a long way off, me."

    "Them's Blue Jauntes."

    "What?"

    "Blue Jauntes. Every sometime a guy gets fed up with old Jeffrey. Can't take it no more, him. Jauntes into the wild blue yonder."
  • Finally, there is at least one case of the protagonist believing that he has mis-teleported high, resulting in falling from a significant height and being injured. Now, this turns out not to actually be the case -- the building to which he's teleporting has been ruined and the particular floor gone missing -- but his first sure instinct (combined with emphasis on remembering "elevation", above) indicates that this is a well-known possibility. From Chapter 8:
    He jaunted to Robin Wednesbury's apartment in the lonely building amidst the Wisconsin pines. It was the real reason for the advent of the Four Mile Circus in Green Bay. He jaunted and arrived in darkness and empty space and immediately plummeted down. "Wrong co-ordinates!" he thought. "Misjaunted?" The broken end of a rafter dealt him a bruising blow and he landed heavily on a shattered floor upon the putrefying remains of a corpse.

Some other minor details in Bester's work that may or may not match the D&D rules: (1) The teleporter is self-motivated, that is, they can only move themselves, not stay in place while forcing another object to jaunte. This matches OD&D and the AD&D line; B/X allowed the possibility of teleporting another target instead, but no other edition followed suit. (2) That said, a teleporter can carry with them as much as they can physically pick up. There are at least two instances in the book of characters struggling to lift another person and hence teleport with them. B/X mentions the caster's normal encumbrance as a limit, 1E introduced a formula for how much extra weight can be touched and taken with the caster (e.g., 700 pounds at 13th level), and later editions sequentially increased that limit (e.g., in 5E any caster can take 8 other creatures). (3) There is an acknowledged limit of 1,000 miles per teleport for any person, and longer trips are made in sub-jauntes of this length (explained in the Prologue). This also implies no extra-world teleports, not through space, and not across the planes.

Can you think of any work other than The Stars My Destination, of which we can document Gygax's prior knowledge, which better parallels the D&D teleport spell?

Monday, August 6, 2018

More Dungeon Treasure

Looking at the OD&D random dungeon treasure table from Vol-3:


Consider that their are 7 rows/"tiers" to that table. (Tier 1 = level 1, Tier 2 = levels 2-3, etc.). I randomly generated a sample of 1,000 treasures from each tier. Statistics are as follows:


And compiling the relative frequencies into a chart shows us this (note that the x-axis is quasi-logarithmic, using the 1-2-5 preferred numbers series):


Note how incredibly skewed the first two tiers are (i.e., dungeon levels 1-3). For example, at level 1 the median treasure is only 60 gp (in OED games we translate this to sp, but costs are all cut down in proportion, so purchasing-power is identical). 85% of the time you'll get a treasure less than 100 gp, which adds up to negligible XP for the party. But if you roll positively on the 5% gems/jewelry chance, then that treasure will be likely in the 1,000's of gp's (even possibly on the order of 40,000 gp maximum!). If you were to roll consistently and faithfully using this table then it's possible that you never get any large-value treasure in a given 1st-level dungeon (granted that by the book less than 1/3 of rooms have any treasure at all); or alternatively, you might have one outstanding treasure worth 20,000 gp sitting by some zombies or giant frogs (as happened the other day when I was doing some rolling experiments).

I think this highlights the need for the DM to intentionally place one or two "big hauls" on the first few levels of the dungeon, including gems and/or jewelry, in order to support PCs advancing levels at all before hitting lower levels of the dungeon. I think that Paul S. would further suggest that players be made aware of this from the get-go as an initial quest/mission/ante to get the action started. If one accesses the more advanced tiers, the gem/jewelry frequency increases, and therefore treasure gets a lot more evenly distributed at those levels (that is, by tier 4/level 6, about half of all random treasures have either gems or jewelry or both), which might indicate that we can then rely on the random method more for a useful amount of treasure.