Monday, June 17, 2019

Air Elemental Whirlwinds

Random math-y investigation: How powerful are air elemental whirlwinds? Pretty powerful. OD&D says this (Vol-2, p. 18):
Air Elementals: Air Elementals move only by flying, moving at a maximum rate of 36". When engaged in combat in the air they add +1 to damage scored from hits. They normally do one die roll of damage. They can turn into a whirlwind which will sweep all creatures under two hit dice away, the whirlwind being conical in shape, 3" diameter at the base, 6" diameter at the top, and as high as the number of hit dice possessed by the Elemental (16", 12" or 8"). Forming a whirlwind requires one full turn as does dissolving it.
A few other notes: The general elemental description on this page says, "Only magical weapons/ attacks affect Elementals", whereas OD&D Sup-I boosts that to, "Elementals are impervious to normal weapons and to magical weapons under +2" (p. 34). The "turn" in the last line is arguably the same as a "round" (or something), as they seem to be used interchangeably in this text, and the 1 turn = 10 minutes rule is not given until Vol-3 (e.g., the other elemental descriptions all say "move at a rate of 18" per turn" and the like). The AD&D Monster Manual limits the whirlwind to just 1 round duration, and adds a 2d8 damage factor to creatures it can't kill outright.

Consider using an air elemental against a large body of humanoids, such as in a mass-combat situation. If we use the by-the-book D&D scale that 1" = 10 feet, then the elemental can fly 360 feet in a round, and affect a 30' diameter along that path, for an area of about 10,800 square feet; if we allow one man per 5' square (25 sq. ft.), then that's about 432 men automatically destroyed per round by this rule. I'm pretty sure that makes the air elemental exponentially the most destructive mass-combat weapon in the game.

On the other hand, if we use the better-reasoned scale of 1" = 5 feet, then the distances are halved, and the area and number affected are thereby quartered: 180 feet move, 15' diameter path, 2700 square feet area, for about 108 men destroyed. I think it's then still the most destructive force against normal men, but not quite so stupendously overkill-y.

But there's a final limiting factor that's easy to forget; the rules for aerial movement in Vol-3, thought to be written by Dave Arneson, and inspired by "Dawn Patrol/Fight in the Skies" by Mike Carr. For air elementals (4th row down in the table on p. 26), the specifiers give "number of turns per move: 6", and "number of spaces between turns: 3". Given these and a hex map (specified in Vol-3 on the prior page), I attempted to find out what the most-compacting "sweeping" movement was that could be made by an air elemental in one round. Consider the following:

Path A: Trying to make the tightest loop possible; this depletes the available turns fairly quickly, and forces us to make a long straight path away from the fight at the end. Covers about 45 hexes in the initial loop, with a donut-hole in the middle.

Path B: Trying to make a back-and-forth sweeping action, but the required spaces-between-turns leaves sizable gaps between each "sweep". Each straight segment covers about 27 hexes. You need to have a packed-in army of about 30 rows x 15 columns (450 men) to hit a man on every hex of this path (for a total of about 100 victims, as noted above, assuming 1 hex = 1 man = 5 feet).

Path C: Here I have the elemental spin away and then back, so as to sweep a kind of contiguous block at the start and end of the path. The top-left part thereby has something approximating a 6 x 8 rectangle, thereby hitting about 48 normal men in close formation there.

Path D: An iteration on the previous strategy; again, we get a top-left block of about 6 x 8 = 48 contiguous hexes.

Conclusion: In open mass combat, I might summarize this with a rule saying that an air elemental in whirlwind form can wipe out about 50 normal men in formation in one turn. That's still very powerful, so before one shows up in your game you might want to consider interpreting or house-ruling things to a power level that you're comfortable with. For example, reducing the diameter of the whirlwind (AD&D took it from 3" to 2"), making the attack 1d6 damage or with a saving throw, etc. Another option is to strictly enforce the book's given rule, "Forming a whirlwind requires one full turn as does dissolving it", which would arguably make it still extremely powerful in (turn-based) mass combat, but basically not ever usable in standard man-to-man D&D action. Thoughts?

Monday, June 10, 2019

Prep Time Poll Results

On March 28 of this year, I asked on the Facebook AD&D group the following poll question: "As DM, how much preparation time do you take before a single game session?". Over the next few weeks I got 310 responses. As you can see below, a bit more than 50% answered in the range of "Hours".

In the comments/discussion attached to that poll, there were a small number of people who answered with "years", or "my whole life", which are very interesting ways to look at it, I think. :-)

Monday, June 3, 2019

Historical Costs Comparison

The following comes up regularly, and I think that it probably always will; given the incredibly kinked-up nature of the D&D economy, what's the best "correction" to bring it line with some kind of historical pricing basis? Or in other words: very generally, how do D&D costs compare to historical prices?

I'll look at this in three different categories: basic equipment, castle construction, and wages for men-at-arms. My primary resource for historical prices is the Medieval Sourcebook: Medieval Prices (MSMP), compiled by Kenneth Hodges, and currently hosted on a site at Goucher College. My primary strategy will be to run a linear regression between D&D price and Medieval Sourcebook prices and see if that tells us anything at all consistent.

First: Consider basic equipment. This may be the most tentative of the three classes, because it requires some subjective matching of item types, some of those have widely varying ranges and eras, there are many different possible horses and armor qualifications, almost no historical weapon prices, etc. While the D&D basic equipment list is fairly sizable, and so is the Medieval Sourcebook, there isn't as much overlap as I would have desired. The results are as follows:

As you can see from the chart, these prices are only vaguely linear related (R² = 0.57 only moderately related). That said: the regression here suggests that if you take D&D price units and treat them, on average, as historically something like three-quarters of a shilling then you'll be as much in the ballpark as you can be (technically: 76% of a shilling according to this regression; feel free to round to a half-shilling or whole shilling according to taste, any of those could be fine). There's a lot of variation there -- the two outlying high points are the two armor types (mail and plate); those are distinctly undervalued in D&D. The two outlying low points are the prices for the medium war horse and the cart. Also removed from the analysis was the MSMP stated value for a 13th century war horse: "up to L80", which would be 1,600 shillings, far off the upper end of the chart here.

Second: Let's look at castle construction costs. There are a few values in the MSMP (a gatehouse and tower), and I've also found a number of documented costs for castle construction on Wikipedia. You can see here for the full detail on the first occasion when I looked at that. The displayed D&D prices are dependent on my assessing the constructions in question and pricing them piecemeal according to D&D (a task which I did before looking to convert the historical prices, to try and avoid as much bias as possible):

This regression seems to look a bit more dependable at first appearance (R² = 1.00, apparently perfect correlation). Note, however, that this is largely dependent on what I estimated for the D&D construction of the large Dover castle (an "influential data point"). That said, it has a perhaps surprisingly similar conversion to the basic equipment list above: each D&D "gp" converts to something like a half shilling (specifically, about 40% of a shilling's value). To me, that seems interesting.

Third: Consider wages for men-at-arms. Now, these values in D&D seem to be at a distinctly different scale than those for other things in the game (basic equipment, castles, treasure, specialists, etc.). Fortunately there are several classifications that seem reasonably easy to compare in D&D and the MSMP:

This also seems reasonably linear in relationship (R² = 0.92, strongly correlated). Here if you take the D&D monthly "gp" and multiply by about 5, then you have something in the ballpark of actual medieval costs in shillings -- or in other words, the D&D units for men-at-arms costs are about a quarter of a pound sterling (i.e., roughly the value of an actual gold Noble coin; not something you can say about the units anywhere else in the D&D system).

In summary: With the exception of wages for men-at-arms, the pricing units in D&D seem to correspond (very roughly!) to historical units of a half shilling or something in that general order of magnitude. For me, it's been a number of years since I started interpreting the D&D price units in terms of historical silver Groat coins (one-third of a shilling each), and I'll probably continue to use that in the near future.

Download an ODS spreadsheet of the data and regressions seen above here. 

Monday, May 27, 2019

Wandering Hommlet

If a DM considers possibly running the classic Temple of Elemental Evil campaign, one must first answer: Where is Hommlet? Interestingly, its official published location varied quite a lot in those heady early years.

Here's a timeline of relevant publications (all with Gygax's name on them):
  • 1979: The original monochrome version of AD&D Dungeon Module T1: The Village of Hommlet is released. In the first paragraph of the Background (p. 2), it says, "The village... is located some 10 or so leagues southeast of the town of Verbobonc..." This places it in hex #1 of the regional map above (each hex being 10 leagues in distance). 
  • 1980: The World of Greyhawk folio set and Gazetteer are published, including the fabulous continental map by Darlene excerpted above. In the single-paragraph entry on Verbobonc (p. 18), it states, "A temple and fortress were constructed in the wooded hills southeast of the town of Verbobonc, not far from the village of Hommlet. (Look for the VILLAGE OF HOMMLET and the TEMPLE OF ELEMENTAL EVIL modules from TSR)." So: no explicit change, although hex #1 noted above is not depicted with either woods or hills.
  • 1981: The multi-color version of module T1 is released. However, the booklet inside is identical as far as I can tell (even maintains the same inside logo and 1979 copyright, different from the color cover), so no textual changes in that regard.
  • 1983: The boxed-set version of the World of Greyhawk is produced, with the same map, but a pair of expanded books. The Glossography includes more detailed in-game statistics to various entities, including a section on "Adventure Locales" (p. 30), which gives specific hex coordinates for every TSR module published to date. For the Village of Hommlet (noted with a predicted change in code from T1 to WG1), it says, "The legendary villlage is located in hex O4-98 near Verbobonc". That hex is noted as #2 in the map above -- quite a surprising distance away; not 10 leagues, but rather some 40 leagues away from Verbobonc. And still not very much near the wooded area. 
  • 1985: The supermodule AD&D Official Game Adventure T1-4: The Temple of Elemental Evil is finally published (in the final year of Gygax's tenure with the company; finished with the help of Frank Mentzer). This includes what is mostly a reproduction of the T1 Hommlet module inside; although now the Player's Background section (p. 4) states that it is, "located some 30 leagues southeast of the town of Verbobonc" (not 10 as before). In addition, it comes with a rather sketchy wilderness "Map 1: From Hommlet to Nulb" that depicts Hommlet as being in hex #3 on the map shown above (indeed, 3 hexes, so 30 leagues from Verbobonc).
That's really quite a bit of wandering for a little village -- the triangle formed by hexes #1, 2, and 3 above is a bit larger than that formed by New York, Philadelphia, and Allentown, PA.

A secondary issue is: Given Hommlet, where are Nulb and the Temple in relation?

 Above is the wilderness map given in the T1-4 adventure. But perhaps I'm getting ahead of the story with that:
  • In the original 1979-1981 T1 text, Hommlet and Nulb are set fairly close together. The Background says (p. 2), "The folk of Hommlet tended to ignore Nulb, even though it was but six miles distant." Likewise, the T1 moat house is given as "about two or three miles away", along an overgrown track leading northeast off the Hommlet village map (area 33, text p. 8). The text to those ruins reiterates this, describing travel of "a mile or so" along the overgrown track, and then "two miles of distance" along a somewhat clearer pathway (total time: one hour on horse, two on foot; doubled on subsequent trips after clearing it). It concludes this description with, "The track continues past the ruins for many miles -- seven leagues, in fact -- until the temple area is reached." (p. 12) Note that this total of about 8 leagues (24 miles) to the Temple is considerably more than the 6 miles to Nulb in the opening Background.
  • On a related note, the T1 Background speaks of a "Lowroad" leading from Verbobonc, south of the river: "Many days' travel to the east, on the shores of the Lake of Unknown Depths (Nyr Dyv) is the great walled city of Dyvers". This first paragraph seems to be describing the various roads off the edges of the Hommlet village map; the one leading directly east (best matching this description) is labeled "To Nyr Dyv & the Temple". There is no mention in this text of any corresponding "Highroad". 
  • The Brief History in the 1980-1983 Greyhawk products (identical in both) spends a rather surprising amount of time focused on the area and action around the Temple. For a piece of text covering the entire history of the continent, 3 of its 11 paragraphs are specifically about the battle with the forces of the Temple (clearly, it was foremost in Gygax's mind at the time). Yet even here the location of things is just a bit garbled: the Brief History says the battle was, "below the city of Verbobonc" (folio p. 6), while the section on the Kron Hills mentions it as, "the battle above Verbobonc" (p. 23). 
  • With the 1985 T1-4 product you get the wilderness map above, but it seems mostly unrelated to any of the descriptions in the text itself. Note that it clearly shows Hommlet at Nulb as being at least 10 leagues (30 miles) distant as the crow flies; if I map and measure all the little twists and turns on the roads, then I count either 16 or 18 leagues (48 or 54 miles) depending on the route. But the Hommlet reproduced background still says Nulb is "6 miles distant" (p. 5), the track out of town still says the moathouse is "2-3 miles" away (p. 14), and the text to the ruins still describes the same "mile", then "two miles", then "seven leagues" to Nulb (p. 21); which again awkwardly implies a total of 24 miles from Hommlet to the Temple.
  • Meanwhile, the new Interlude section to T1-4 is also contradictory. The Players' Background says, "Just a half-day's journey afoot (only about two hours' ride), east along the High Road, lies the disreputable community of Nulb, and the Temple hidden in the hills nearby" (p. 27). Per standard AD&D/Greyhawk moves rates, this implies a road distance of about 5 leagues (15 miles). On the other hand, under Notes for the Dungeon Master, it says, "The adventure began in the Village of Hommlet, only about thirty miles west and south of the edge of the Nulb area map" (p. 28). 
  • Then the very next thing T1-4 says is, "You can construct your own campaign map by using graph paper of roughly the same parameters as that of the Nulb map, assuming 100 yards to the square. Two sheets of paper the west and to to the south cover all of the important territory, with Hommlet being located on the High Road, two maps west, one south near the map bottom, but in the southwest quadrant. (The Velverdyva river, by the way generally remains along the upper portion of the northern map additions...)". By my figures, the described map would only cover about 4 by 6 miles, although the description seems to cover an area at least 30 by 40 miles on the T1-4 wilderness map. Was this particular text accurate to an early placement close to Verbobonc (hex #1), and overlooked when the official T1-4 map was drafted? Or was it simply a total meltdown in someone's arithmetic?
  • Other miscellaneous comments about the T1-4 wilderness map: Note that while T1 mentioned only a "Lowroad", the new T1-4 sections have now switched to reference only a "High Road". Whereas T1 showed and spoke about a major road leading due east to the Nyr Dyv, the roads in T1-4 are highly kinked, going far to the south and then far to the north (not very useful for a major east-west highway). The map has no placement for the T1 moathouse or the overgrown track leading northeast off the Hommlet map. The relative location of the Temple seems to have switched sides of the road; in T1 you can go northeast of the main road and reach the Temple, while in T1-4 it is shown south of that road. It's weird that the "Low Road" is along the crests of the hills, while the "High Road" is in the depths of the forests; and also that while the T1-4 text speaks of the "High Road" as the major route to Nulb, on the map it is shown as an "unused trace road" with many points of Danger/Evil along the way. Likewise, none of those Danger/Evil areas are described in the T1-4 text.

I hope that you'll forgive me for all that detailed nit-picking. But the contradictory nature of the T1-4 wilderness map has bothered me for a long time, and I think I've repeated this textual exercise a number of times, and wanted to document it here so I don't ever do it again. One last complaint I'll levy is how that map seems to imply that the PCs will need several more custom adventuring areas to gain XP between Hommlet and the Temple, when this simply isn't the case; the average danger level of the Moathouse is almost exactly the same as the first level of the Temple dungeon, by my calculations.

So, at this point I think I might come to the following conclusion if I were to ever run the T1-4 adventure: just kick that wilderness map entirely to the curb as incoherent, and make my own map in line with the original 1979-1980 descriptions, which suffered from somewhat fewer contradictions. Consider: perhaps Hommlet lies in the plains of Verbobonc, along a "Low Road" that runs generally due east (through wilderness and woods) to the Nyr Dyv. Meanwhile, there could be a "High Road" that loops north of the river and the whole area, through the safety and civilization of knighted Furyondy, and reaches Dyvers that way instead. (In fact: Gygax's Gord the Rogue books speak of a "High Road" running through the center of the City of Greyhawk; while not clear there, I might fantasize that this is the same major mercantile thoroughfare running all the way from Verbobonc, through Furyondy, then Dyvers, and then to Greyhawk itself. In contrast, there's no way to interpret the road on the T1-4 wilderness map as doing the same.).

A final thing I'll reflect on (a little bit of back-in-my-day-ism): Just think about the incredible wait time we suffered from the publication of T1 with all of its hints and promises about the soon-to-be-released Temple adventure, until the actual appearance of the T1-4 module. The former was in 1979, and actually my personal copy of T1-4 has a 1987 print date on the inside cover. That spans the time from when I was 9 to when I was 17, or in fact half of my life to that point waiting to get the damned thing. There's a reason why some of us have a small part of our brains kinked up over that production.

Thursday, May 23, 2019

House Con: Now You Try It

As a final-final thought to this year's HelgaCon wrap-up; I must reiterate that this house-con event is the singular highlight of my year for the past decade-plus. Having moved a few states away from where I was before, it's a priceless opportunity to connect back up with old friends, and somewhat surprisingly, some people I consider among my best new friends, whom I've only ever met or seen at this event. Thanks again to Paul Siegel who's been the motivating force and organizer for the event every year.

Along with that, some news I can now reveal (that I've been biting my lip on for months); after thirteen years of developing and refining the AI-driven software that serves to manage and schedule our mini-convention, in the last year Paul has been rolling out a website and associated tools to make it public and help assist other people in creating their own house cons. It's currently in beta testing and if you want to try it for your event, you should contact Paul directly. I can't recommend it enough; we've all been amazed by its seemingly magical powers (far better than any other convention I've attended) for years now. If you do a house-con or are thinking about, ring him up!

Also: We were unable to have a Wandering DMs show this past Sunday due to unexpected developments. We'll be back with a new show this Sunday June-2 at 1 PM EDT.

Monday, May 20, 2019

Helgacon: Lessons Learned

A top-ten (in no particular order) list of observations and lessons from this year's house con:

  1. I still need to get better about handling ("accordioning" per BJ) adventures for time constraints in the convention setting. I did better than Tomb of Horrors a decade ago, but still was over by an hour with the Tomb of Ra-Hotep run-through. 
  2. I'm liking bare-bones minimalist adventure text (like Ra-Hotep) more than towering wall-of-text give-all-details-imaginable (like in the Slavers modules). Easier to "own" the adventure and play loose and flexibly, with less note-lookups. Sometimes the wall-of-text approach (e.g., A2) loses its own plot, becoming incoherent or self-contradictory itself!
  3. In Outdoor Spoliation, I simply must offload the administration-handling to pre-game, if I run it again in the future. 
  4. There's surprising potential for a minimal PC team to do well in a game meant for lots of other players (e.g., the 4-person team in the stockade game). Does a streamlined communication network assist this? 
  5. On a related note, I got away from using the Caller role, and this might have contributed to bogging down the games with larger number of players (esp., Slavers Stockade part 2, Outdoor Spoliation). Part of what explains that is in the last year I've had a bi-weekly campaign that has a smaller number of players (usually 4-6) who also know each other and communicate/coordinate really well. So over time I simply forgot about Callers and if I thought about it, came to think I'd discovered they weren't necessary. But for larger groups (and those who may not know each other so well at a convention), it may in fact be very beneficial. I really need to keep in mind the need to switch protocols with a group of over 6 players, or something like that. 
  6. Also, I was trying out a new method for marching order in these games: Ask the players to sit down at the table the same as their standard 2x2 marching order; for round resolution I then went down the table likewise left-right, left-right and so forth. I officially made this optional but with a +1 bonus to all initiative if they did so. Every team took me up on this, and it seemed to work pretty well (didn't hear any complaints, and nicely represented the front-line people being in contact first). Note that Gygax specifically called out marching order as the one thing that was hard to handle for very large groups of around 20 or so players (I quoted him at Stack Exchange at the link there, from a 2005 ENWorld Q&A). So this real-world physical representation is feeling like a pretty good solution to me.
  7. For the last year or so I've used placecards (folded-up index cards) in front of each player to advertise what everyone's PC name, armor, and weapon are. That's largely so I can address everyone in-character on sight (I've seen a few people do this at other conventions, or else use lapel name stickers, etc.). This year I stumbled into the idea of having players also write their "preferred pronouns" on the placecard (granted that many of my pregenerated PCs have ambiguously gendered names, or else I'm just happy for players to pick which they want to play as in any case). This also may make me seem more "woke" than I probably really am. 
  8. For a climactic final boss fight in a convention game, a battlemap and minis (as used in Ra-Hotep) or something vaguely similar (as in the Slavers games) has a nice impact. This was complimented by at least one player. On the other hand, I need to gauge the extra time this may take. This may be unusual; most games I see with other people are either battlemap-all-the-time of else none-of-the-time. In all my games at Helgacon I had it as a possibility and made a call on the fly about whether to use it or not. 
  9. I may need to find a way to streamline calling distances in combat. The combination of feet (dungeons), yards (wilderness), and inches (rulebooks; 5' for me) definitely confused and frustrated some players. I'm thinking about trying to call all combat distances in "paces" (Roman paces, 5'), which would directly synch up to the "inches" specifier for movement and spells in OD&D. Haven't tried that yet as of this writing. (Alternatively, this possibly suggests the Holmesian approach of just jettisoning the "inches" and writing everything in terms of feet.) 
  10. Granted that intelligent swords were in use in all of my games, Paul's suggested streamlining of OD&D's complicated control-check rules to a Target 20 idiom saved me gobs of time in both preparation and at the table. Highly recommended; I just wrote it into my OD&D rulebook.

Monday, May 13, 2019

HelgaCon: Outdoor Spoliation Ep. 7

In the last reflection on my individual games at Helgacon this year, I also ran:

Outdoor Spoliation Ep. 7

This was probably the weakest performance in my games at Helgacon this year, and I'm fairly embarrassed and sorry for the players involved about what happened here. Particularly because the solution is rather obvious in retrospect, but it's taken me to years of lackluster session to realize what I should have done.

When I started running Outdoor Spoliation games a number of years ago, it was my attempt/experiment at running the OD&D wilderness rules as close to by-the-book as I could manage, using the famous (an truly masterful) Outdoor Survival map as a game board. This was a free-wheeling, free-booting game of amoral ne'er-do-wells in the Fafhrd & Gray Mouser mold, looting treasure and sacking castles willy-nilly in attempt to score a particular number of gold pieces for a "victory" (in-game, rationalized as achieving a level to be made barons by the king).

(Side note: I've done this so much that several of us now accidentally say "Outdoor Spoliation" every time we're trying to say "Outdoor Survival".)

I think at the end of the 3rd season, the players actually succeeded at the goal. I thought that would wrap things up, but there was some demand for me to run it again, so I brought it back two years later. The next year or so after that, the players decided to follow-through and commit to the "barons" idea, taking over a castle permanently and setting up for an expanding dominion there.

So that obviously changed the game a lot, and I haven't quite managed to dial in how to handle that change in action. I realize now we might be trying to do something entirely unique: run a dominion as a team of oligarchs at a once-a-year session at a convention, in a 4-hour time slot. What I've done for two years is to come to the table with a budget and "menu" of possible improvements/investments for the expanding domain (a la the list of investments ideas in OD&D Vol-3, p. 24, under "Baronies"), each with a secret "complication" that would drive the need for some in-person adventuring. In the past I've had as many as a dozen players at the table; this year I had seven.

So problem (1) is that the level of complication and cross-complication to prioritizing the dominion budget can create a round-table debate which stretches on almost indefinitely (this year: maybe 1.5 hours? Ouch). If that weren't bad enough, problem (2) is that maybe half the players or more simply didn't sign up for an hours-long administrative council meeting, expecting the mercenary high action from earlier years, and so rightfully might get distressed or frustrated by that. And the problem (3) might be that once the "complications" are revealed, another (potentially very long) round of debate can take place over which of the resulting "quests" should be prioritized first, and how (e.g., Which is most important to secure? But which are conveniently located close to each other? Can we hire and trust NPCs to any of these jobs? Oh, that spins us back to the budget debate.)

Awkward, and I didn't handle the responsibility to rein it in well at all. Kind of upsetting on my part.

Almost immediately afterward, the answer sprang to mind: If I do this again in the future, I should offload the "domain administration" to an online survey mechanism in the days pre-game, and have people do ranked-choice-voting for the preferred budget priorities or things like that. If anyone's not interested in that component, simple; just ignore that online component, no problem (in fact, that would even nicely simulate that idea that only some of the PCs are willing to take on the burden of rulership roles while others drink and wench until the next plundering expedition). Possibly also address item (3) with a similar pre-game vote on what relevant "quests" to take on, so that D&D action can start more immediately when we get to the table face-to-face.

Ultimately decisions were made, and we did get to play out a little bit of nice negotiation with a powerful and semi-trustworthy lord-wizard, as well as two excursion into the mountains versus alien monsters for critical pieces of the political puzzle. But it was definitely slower-moving than I'd planned on, and not all the players were happy with me failing to meet advertised expectations. Mea culpa.

In this one, Jon's griffon-riding fighter got knocked out of the sky and then death-criticaled by one of a flock of roc-sized cockatrice. He was wished back to life, and then basically melted down again later against a squad of black puddings against which his weapons were useless. He wins the "most stoically abused" award for the weekend.

Favorite random scribble on PC sheet: This one.

Monday, May 6, 2019

HelgaCon: Tomb of Ra-Hotep

Continuing the Helgacon wrap-up this year. For the first time I also ran:

The Lost Tomb of Ra-Hotep

Originally written by Mr. Alan Lucien, this is the precursor and inspiration for Gygax's infamous Tomb of Horrors, and was recently published (for the first time to my knowledge) as a small part of the Dungeons & Dragons: Art and Arcana product. Small spoiler: it has the first invention/appearance of the sphere of annihilation and stuff like that.I did an OED-style conversion of the very sketchy original text (4 handwritten notebook pages) and ran it like that.

Part of my desire for running this is that I ran Tomb of Horrors itself over the first two Helgacons (one, two) and felt in retrospect that I didn't do a very great job with it (actually: only got to about 2/3 of it over two very-late-night running sessions). Major lesson in retrospect: GIVE THE RIDDLE from the first area no matter what (that totally shift the PCs from just blundering into trap after trap, to actively engaging the dungeon and giving them the tools to try and outwit each succeeding area). Also, I was still trying to run with actual 1E AD&D rules at the time, and a pretty strict reading of each encounter area as given in the text (so: achingly slow progress) -- so I wanted to see if my OED rules a decade on, and a hopefully more looser/flexible DM'ing philosophy, would make things run more successfully. 

This seemed to be my biggest hit of the convention. We had 9 players at the table (would've been 10 but for illness) with approximately 10th level PCs each (250K XP, to be precise). I think I initially estimated that I might have about 5 players, so the night before the game I decided to double all of the monsters and traps on the fly, and this seemed just about right in-game (of course I'd estimated danger levels in advance with my Equivalent Hit Dice system; also, I'd made sure to supply some magic weapons that could hit the invulnerable-to-everything-but-+2-weapons monsters involved).

I think it moved along pretty well and I gave players lots of chances to find ways to succeed (e.g., using passwall on the starting entrance to avoid technically opening the door and summoning extradimensional monsters). At a particular point in the game, I arbitrarily sealed off a side-wing to force the PCs more towards the climactic fight(s) at the end. Even so, the huge embarrassment for me is that I went over the allocated convention time (4 hours) by an entire hour, a tremendous faux pas (and surely anathema at a real convention, if I weren't playing at a table where everyone was friends). That said, I was immensely curious at how the last two encounters were going to play out (I really didn't know if they'd be total TPK's or not), so as a gaming scientist I couldn't stop myself from running them. I actually completely forgot about the problem of opening the final doors, even. I suppose I'm at least getting closer to "good" than when Tomb of Horrors was taking us 3 years and around 20 hours of play to get through (actually it hurts me to even write that).

One weird thing that came into play is that my friend Paul loaned me the piece of Art & Arcana to see this dungeon myself for the first time. Then his (brilliantly resourceful) automatic convention scheduler actually put him in the game, and neither of us noticed this until a single day before the convention. We quickly cycled an idea to have him run a "ringer" character, a lost reincarnated soul of Ra-Hotep in the world, with dim memories of the dungeon and a compulsion to be reunited with the master creature -- such that Paul could play the Adversary at the end like I did for him recently. When we reached the final area, a black beam annihilated his PC, I handed him a sheet for Ra-Hotep, and he studied that while I was rolling out a big battlemap for the climactic fight. (Note that these few minutes were the entirety of the study time for the monster that Paul had; I didn't give him anything at all prior to that time.)

Among the most beautiful pieces of play from this was that one of our friends (expert hobbit thief player) had been loudly trash-talking Ra-Hotep all through the adventure, using that to aggravate monsters into attacking them, etc., and at some point had turned to Paul and said, "Geez, I hope Ra-Hotep can't actually hear any of this!". (I was too busy to hear that myself.) So when Paul was revealed as actually Ra-Hotep himself, he pointed an outstretched finger at that player, and shrieked in the most evil voice possible, "You shall be the one to die first, in the most painful manner imaginable!". That was simply priceless.

Pretty compelling fight at the end. Arguably I should have also given Paul control of the mob of Ra-Hotep's evil minions. Having the PCs summon an earth elemental and cast haste on the whole party turned out to be critical in the enormous final tomb area. (Note that I give only double moves, no extra attacks or other side benefits from haste, and it was still a key to victory in 2 of my 4 games that weekend.) On the other hand, Ra-Hotep using his sphere and casting charm monster to turn the lead fighter to his side, and attack a PC wizard, was quite the nail-biter. In the end, he was beaten down by a crush of hasted PC fighters and thieves.

Also, Jon again fought all the way to the end here and then actually got disintegrated by Ra-Hotep in the final encounter.

Favorite random scribble on PC sheet: "Punching Mummies".

Monday, April 29, 2019

HelgaCon: The Slavers Stockade

Here's the first part of a belated recap of our HelgaCon house-convention action from the first weekend in April. This year I ran 4 games across the 5 sessions of the weekend. These included the following:

Secret of the Slavers Stockade (Ad&D Module A2)

I'm on year 2 of a multi-year run to play through the famous A-series, which I've never done, sticking to the "tournament" subsections, rules, and scoring guidelines. This was (obviously) two separate sessions: one for the above-ground hill fort, and one for the below-ground dungeons section. Of course, I'm translating the content as best I can to OED rules, clerics become fighter/wizards or a fighter with a special-power sword, etc.

One thing in trying to recreate the "tournaments" on a small scale is that you can't guarantee you'll get all 9 players expected by the original setup. In the first session of A2, I actually only had 4 players at the table (another was scheduled but got sick). I started out halving the number/power of the monsters, but found these players were just carving through everything like a knife through hot butter, so I ramped up the proportion from half, to three-quarters, to full-strength by about the half-way point. Still they plunged into the final encounter and swept the board for a victory. It seemed like they could do no wrong.

For the second session, I had 7 players (again, missing the same extra player). It seems like this group didn't have a noticeably easier time with the event. They overcame traps/puzzles admirably and fought through the final encounter. Here, the boss wizard let loose with an opening lightning bolt that felled either 2 or 3 of the party's 4 wizard PCs. The two sides then basically fought to a nail-biting standstill until the remaining party wizard used his last spell, suggestion: "I suggest this fighting does neither side any good and we should part ways in a truce," which was successful. So: a draw, although the party still scored almost all the points for the game.

I'm a little baffled at how the 4-player group did so remarkably well with the hill fort scenario (I expected to roll in replacement characters, but none were needed). Is the first session simply easier? Does the smaller group make it simpler for the team to communicate and coordinate?

Regarding this and other A-series modules that I've seen: (a) the text seems wall-of-words copious (many paragraphs per area) and frankly it's a real burden to parse and translate it (both before and during the game), and (b) many of the puzzles/traps are somewhere between inexplicable-unworkable-incomprehensible, both in terms of describing/explaining and running them mechanically. Example of the former: The text for the single new "cloaker" monster, with all its various "subsonic" powers, alone spans 7 big paragraphs in the adventure text (I'm pretty sure I missed some components in-game). Examples of the latter: Many of the A-series traps are hard-to-believe mundane traps (toppling stuffed bear, pillowcase in flue that looks like a ghost, humanoids dressed as mummies in angled mirror) so you can't even hand-wave it away as "it's magic". For the players' benefit I started to set expectations with, "the slave lords might just be mentally ill", and on my end, I tried to be sensitive to the point when we all started becoming disinterested in a particular barrier and then say "yes" to whatever idea the PCs came up with to bypass it. I think I'm coming to a philosophy that the very-wordy classic AD&D modules are not my favorite thing to run; I'd really rather have very terse, couple-line areas that I can expand on improvisationally during the game (and very clear stats for monsters, tricks, and traps).

I should point out that the design for the A-series is extremely regimented. It's usually a linear path (no surprise), with the 5 sessions from A1, A2, and start of A3 all with about 16 areas areas each, 9 "significant" ones for scoring, with exactly 5 monster encounters and 5-7 traps (and also one "new" monster per section). I will say that this seems pretty well-timed, as both my groups reached the final encounter with a comfortable amount of time (although last year in the dungeon part of A1 we did not reach the final room). The scoring system is surprising: although given as a table, it boils down to 45 points for each of 9 significant areas cleared out (not explicit in the text; you must decide which 9 of the 16 areas count), minus 5 points per character death. Note that the lives of the entire party are worth the same as a single encounter area (45 points in each case); so this equivalent to a scoring system of, "count areas cleared from 1-9; for a tiebreaker, count surviving party members". I suppose for brevity this system means the one table can be used for all the sessions in A1-4 uniformly; although more recent tournament scoring I've seen has more detail in terms of specific tasks accomplished, which I think I do prefer (not having tested them to date as a DM).

One other thing I stumbled into is that (for example) the A2 module has "battlemaps" with detailed furnishings and monster starting positions for three of the most climactic encounter areas. I blew these up to a full-page each and printed them out, but didn't actually expect to use them. (They're sized so a single letter-size page can only show them at about 1" = 10' scale; for my preferred 1" = 5' scale, I'd need to split and paste together 4 sheets each, i.e., 12 total pages, which was more work/resources than I wanted to spend.) But when the first such encounter came, I did find myself pulling out the blow-up and handing it to the players as a shortcut to explain all the details. We didn't use minis, but instead just jotted some notes in pencil as the action took place. This seemed to work out very slickly and I continued that for the other areas that had such blow-ups.

Special shout-out to my player Jon who took the modified Eljayess character, scratched out my "wizard" and wrote in "cleric", and then got KIA'd in the final encounter of both sessions.

Favorite random scribble on PC sheet: "Leave No Door" (this from Elwita's player, usually following behind the max-strength "Ogre" character who tended to smash all the doors to splinters; and in other cases tear them off the hinges to use as platforms over pits and such).

More to come. In the meantime, you can look back at the Wandering DMs wrap-up livecast we did when when Paul & myself were still hot from the convention just wrapping up a few weeks ago. 

Monday, April 22, 2019

OD&D Critical Hits

I'm recovering from "convention season", and running a week or two behind on blogging and responses to emails. Still need to write a short recap of this year's HelgaCon games. I just got to our school's spring break week, so hopefully I can catch up soon.

In the meantime, here's a little historical note that came up on yesterday's Wandering DMs livecast on critical hits, death, and reincarnation: Does OD&D have critical hits? The obvious answer is "no", but the semi-snarky answer is "yes". In the original LBBs (little brown books), within the Vol-3 Aerial Combat section (p. 27), you do have a specific Critical Hit Table just for flyers. Here you get the following tables and no other text explanations (apparently checked with the 2 or 3 extra rolls on every single hit):

I've done some playtesting with streamlining those rules (actually: that fed into my friend B.J.'s game at HelgaCon two weekends ago), and therefore played a number of games with my partner Isabelle. I kind of like the extra spice from those tables, but Isabelle rather hates the whole concept as an unwanted surprise/complication. Obviously she's not the only person to ever feel that way.

The other thing that exists in OD&D with critical-hit-like capabilities is the "Hit Location System" in Supplement II, Blackmoor, by Dave Arneson. This runs about 7 pages and dictates apportioning creature hit points into separate limbs and body parts, and rolling on tables for each hit to determine which part takes the damage. For example: once the fraction of "head" or "body" hit points are depleted, then the creature is immediately dead. There are separate charts and specification for different types of creatures (humanoid, flyer, reptile, insectoid, fish, snake), and also a 20 × 20 matrix of attacker-versus-defender height comparisons (in one foot increments) with various adjustments or restrictions to what body parts can be hit. Here's an excerpt just for humanoids:

Nowadays there's an opinion in some quarters that Dave Arneson represented the "radical freedom" side of D&D, and that he ran his games in the spirit of total improvisation, without regards to any systematized rules whatsoever. I find this pretty hard to digest when it seems like he has his name on the most complicated and baroque parts of the OD&D game system: the aerial combat, the naval combat, the hit location tables, etc. Some might defend this as "he wrote them but didn't play them", but to my ear that comes across as "fraud" or something very close to it.

On the other hand, I now read many of the Gygaxian comments in AD&D as mostly responding and rejecting to these complicated ideas by Arneson in Sup-II. E.g.: "[D&D] does little to attempt to simulate anything either" (in the "The Game", p. 9), and "... the location of hits and the type of damage caused are not germane to them... Lest some purist immediately object, consider the many charts and tables necessary to handle this sort of detail..." (opening to "Combat", p. 61). Any argument that D&D has "fully abstracted combat" or whatever definitely has to play monkey-covers-its-eyes in regard to these kind of rules from OD&D; and indeed they've mostly been successfully shoved down the memory hole at this point.

Saturday, April 6, 2019

Stats Saturday: AD&D Wandering Monster Rankings

Commentator G. B. Veras has generously shared with us this delightful piece of work; a complete analysis of the relative chances of encountering any AD&D monster in the dungeon, based on the encounter tables in the 1E DMG. Stunning! It's best if you download the spreadsheet locally and poke around at the chart (which in Libre Office lets me select certain bars and easily see which of the 165 monsters they represent). Thanks to G.B. for making this available!

Monday, April 1, 2019

Co-DMs for Boss Fights

I must reflect on an experiment from last month's TotalCon that worked smashingly well (likely my favorite event of the con). My friend and co-Wandering DM Paul invited me to join him for his recurring Sunday-morning "Boss Fight for Breakfast", a two-hour all-out fight between players and some major D&D bad guy in an interesting lair with various environmental hazards.

In this case he invited me to participate as something of a co-DM, namely, the dedicated brains behind the boss -- here, Flame, an ancient red dragon of maximum size, power, and spellcasting ability, from the Dungeon Magazine #1 adventure "Into the Fire".

Specifically, my role was this guy.

I was really thrilled by how this worked out. Sometimes with a single large bad guy there's a danger that PCs are going to swamp him with the "action economy" of getting lots of actions while the boss only gets one per round. There were 9 high-level PCs coming at me with lots of spells, magic items, cold abilities, magic detecting swords, etc., etc. -- which I was not allowed to inspect before the game -- so I was worried this was a distinct possibility.

Situation as PCs saw it at the start.

But as it turned out I was really quite happy with how challenging I could make this. I used illusions layered on illusions on top of other illusions to distract the players. I hit them with two 88-point flame breaths while they were carefully trying to avoid a major trap. I got one player to run to their death into a hidden chasm. Another, flying on a magic carpet, conked their head on a cavern roof hidden by magic. I hit a batch of them with a hold spell (although all but one made their saves), and managed to drop a portcullis trap on them. I even taunted them into using the one spell against which I had an item giving me immunity. I was defeated in the last 5 minutes of the session, but I think I put up a fair game.

Situation as everyone saw it at the end.

When we left the convention, both Paul and I shared the same observation; neither of us could have made that game work the same way working alone. As referee, your hands are definitely full going around the table adjudicating (high-level) player actions, questions, details on spells, saving throws and damage, etc., etc. When it gets to the monster turn, I would feel compelled to take an action in 5 seconds or so -- the same as I permit players, to keep the action fast-paced -- regardless of whether it was a very well-considered move or not. But by separating the jobs here, Paul could focus on rulings on player actions, while I had the whole 10 minutes or so to meditate on my options, look at my big hand of spell cards, estimate distances, reflect on player actions, etc., and come up with the best and most devious response possible.

In particular for these kinds of "genius-level" take-no-prisoners opponents, this approach definitely resulted in me running the most devastating boss monster that I've accomplished to date. I think that may be generally true; simply put, getting 100 times more processing power is going to make your simulation look a whole lot smarter than normal. That may not be something feasible all the time (e.g., in a campaign game where combat is not happening all the time, there wouldn't always be something for the boss-actor to do), but in climactic set-pieces with mastermind spell-casters, now I might think this is the best possible thing to do, if I can find a co-DM for it.

More: Our March 10th Wandering DM livecast was on the subject of Dragons, and lessons that we'd learned from the very game. Watch it here.

Saturday, March 30, 2019

Presumed Axiom for AD&D

A poster on the Facebook AD&D shared this comment from Frank Mentzer earlier in the week, in which he recalled a rules discussion with Gygax on the issue of magical light. Here it is:

Now, I'm not super thrilled about this (baroque?) ruling, and I wouldn't use it in my game. However, the way it was reasoned was considered a "real eye opener" for the person re-posting it on Facebook. Namely this part:

Probably for us here this is not very surprising; we've read enough of Gygax's writings, and his close associates, to at the very least interpolate that this was their standard thought process. Gygax would frequently write "O/AD&D" as a game system in the singular, and so forth. Many essential rules were not bothered to be copied forward from OD&D, even though the AD&D text in places just doesn't make sense without them, etc. But to some other gamers this may in fact be quite jarring, who want different editions clearly delineated and compartmentalized in a completely Cartesian fashion. So it's nice for Mentzer to clearly state this for once in exactly in the fashion here.

Actually, I wish that Gygax or some other editor had been willing to be more free about cutting out or overwriting certain bits when transitioning from OD&D to AD&D; treating the work as purely additive in all respects creates something... occasionally fossilized and burdensome. In software engineering we recognize the need to sometimes surgically cut out bad stuff as "refactoring". But nonetheless, it's useful to recognize the mind-state of the original designers in this regard, when interpreting the AD&D rules and associated writings.

Monday, March 25, 2019

Infravision Instances

I've spent a silly amount of time recently thinking about infravision. In particular: Should it be nullified when nearby to a torch or lantern? And what is the point of that rule in the first place?

See, in OD&D by the book there is no such rule for infravision being spoiled near artificial light. It seems like a rule that Gygax came to between the OD&D and AD&D publications. It is on AD&D DMG p. 59. It was missing from the Holmes Basic draft manuscript, but was added for publication, presumably by Gygax (p. 10; see Zenopus Archives). We're told by Ernie Gygax that what Gary had in mind was specifically this scene from the original Westworld (1973).

But it makes so little difference in-game that I've been ignoring that rule for a long time now. The DMG says, "It requires not less than two segments to accustom the eyes to infravision after use of normal vision" -- two segments being a small fraction of a round, so I'm not sure how that would ever make a difference in play. I suppose there's the range issue: infravision is 60', and torches as of AD&D light a 30' radius, so I suppose that cuts down the distance. But on the other hand, OD&D says that monsters are seen at 20-80' (Vol-3, p. 9), and AD&D likewise says "A light source limits the encounter distance to twice the normal vision radius of the source" (DMG, p. 62) (as well as real-life experiments supporting the same thing, here; login required) -- so it seems like effective visibility is back to at least 60', equal to PC infravision. Moreover: I'm pretty sure none of us play like the monsters are blinded by PCs with a torch as in that Westworld clip, right?

So in these cases my approach is usually to research what would happen in real life as always the most solid, stable, and consistent way to play it. Previously I've used thermal-vision goggles as a serviceable model. Looking for real-world biological organisms with infravision is somewhat more elusive. Interestingly, there seems to be a lot of active progress in this area in recent years among biology researchers:
  • Snakes have specialized heat-sensing pits on their heads (2010).
  • Mantis shrimp can see deep into ultraviolet and deep red wavelengths (2014).
  • Zebrafish and bullfrogs produce special chemicals that can situationally shift their vision to near-infrared (2015).
Then, most incredibly on the day that I wrote this post, a new piece of research broke: Researchers in China and at U. Mass injected nanoparticles into the eyes of mice, altering them to perceive near-infrared light -- and this might soon work for humans. Pretty amazing! The claim also is that this treatment leaves the standard visible-light perception unchanged.

For all this, the burning question remains; if an infrared-sensitive creature stands near a hot torch or lantern, is its infrared visual capacity ruined? This does not seem to be a thing that anyone has tested to date. In fact, a few weeks ago I emailed one of the leading researchers in this area and asked, "If there is prey nearby and another very hot artificial source (say, fire), does the animal fail to detect the prey?". He kindly took the time to reply with: "Daniel, I don't know the answer to your question" (and also sent the inquiry to a second researcher). So: Still unknown as far as we can tell from current state-of-the-art science.

But I still can't quite see what the point of that rule was in the first place, actually. Perhaps it's just a totally academic issue.

Saturday, March 23, 2019

Stats Saturday: Hydras

Generally we've found in our analyses of Equivalent Hit Dice (EHD) power-ratings for OD&D monsters that the danger level is linear in hit dice (for example, see here or other "Monster Metrics" posts). We've taken this to  support a linear system of XP awards per Hit Die (e.g., the original Vol-1 system of 100 XP/HD over the later graduated table from Sup-I and all later editions).

Here's one notable exception: Hydras. As you can see in the chart below, Hydras are distinctly quadratic (parabolic) in their relation between HD and EHD. This isn't too surprising, because unlike other monsters Hydras are getting a double increase in attack potential per hit die (head): both adding to numbers of attacks, as well as increased chance to hit per attack (as by HD). In other words, they escape from the standard "action economy" limitation of most boss monsters, and wind up confronting PCs with staggering numbers of high-potential attacks per round.

Alternatively, one could approximate Hydra EHD in the allowed ranged with a linear regression of EHD = 2.26 Heads − 4.73 (R² = 0.99), or whatever level to which you want to round that off.

Tomorrow on the Wandering DMs Livecast:  We plan to discuss issues around adjusting your game for Conventions versus Campaign play. Tune in Sunday at 1 PM EDT (UTC -4) and add your comments and questions to the chat!

Monday, March 18, 2019

More from Three Hearts and Three Lions

I recently re-read Poul Anderson's Three Hearts and Three Lions. This is, of course, a critical piece of literature for D&D scholars (and other Appendix-N readers), granted how many ideas that were baked into the DNA of D&D originated here. Most of us are aware of the big-ticket items: Alignment (the cosmic system of Law-vs-Chaos; prior looks one, two), the paladin with a holy sword, a Scottish-speaking dwarf, and the swanmay (see also: mythological swan maidens).

However, with this read-through I was paying more attention to lesser-known, possibly overlooked tidbits, that either are or could be used as core parts of our game. My notes follow (page numbers from 1993 Baen printing):
  • General emphasis on smells in sense-descriptions.
  • Ch. 5, p. 46: Land permanently in twilight for Chaos types (e.g., goblins).
  • Ch. 6-9: Lots of interesting faerie magic, customs here.
  • Ch. 7, p. 55: "All of them [elves] seemed to be warriors and sorcerers"; menial work done by goblin/kobold slaves. (Meanwhile, elves cannot bear the presence of a cross or hearing holy words; see Ch. 3, p. 33; and Ch. 9. p. 76.)
  • Ch. 7: p. 57: Castle with magical moat, always circulating. Lord’s host sallies forth from castle (compare to Vol-3 castle behavior?). 
  • Ch. 8, p. 70: Doorknob turns to speaking mouth (magic mouth?) in castle of Faerie Duke, among many other enchantments.
  • Ch. 10, p. 85: Supernatural enemies harmed by ultraviolet light. 
  • Ch. 12, p. 102: Law/chaos used interchangeably with good/evil (last line of big paragraph). 
  • Ch. 12, p. 107: Giants always carrying gold (and p. 113). Giants (“Great Folk”) sit in wintry halls for centuries practicing contests of skill, especially riddles. 
  • Ch. 12, p. 114: Giant (et. al.) turned to radioactive stone by sunlight.
  • Ch. 13, p. 118: Iron passes through werewolf’s body without doing harm. 
  • Ch. 13, p. 119: Lycanthropy is generally inherited. May be bear, boar, wolf, “or whate’er the animal may be for the person”. Lycanthrope “Wounds knit upon instant” (from non-silver). Possible recessive-trait werewolf who turns only when chaos magic ebbs over the land.
  • Ch. 14, p. 132: Iron hurts lycanthrope in human form.
  • Ch. 15, p. 142: Description of enchanted Avalon, magical island drifting over sea.
  • Ch. 15: p. 144: “Ever-filled purse” advertised on magician’s sign (as Bucknard’s everfull purse). See also Ch. 17, p. 162. 
  • Ch. 15, p. 145: Magician with diploma from magic university.
  • Ch. 15, p. 146: Invisible (unseen) servant.
  • Ch. 17, p. 160: Geas prevents spirits from assisting with divination.
  • Ch. 19, p. 176: Nixie who tries to capture the protagonist. 
  • Ch. 19, p. 180: Undersea weed-house.
  • Ch. 22, p. 217: Troll fights with dismembered hand, leg, jaw, ropy guts (!).
  • Ch. 24, p. 230: Presence of Hell Horse (note 1941-1944 art journal in occupied Denmark called The Hell-Horse [Helhesten]; "hell horse" is a synonym for the nightmare as per MM p. 74). 

Edit: Mike Mornard helpfully confirmed on the OD&D Discussion board that the Vol-3 castle behaviors, as established by Gygax, were in fact inspired by the action in Three Hearts and Three Lions (as well as various Arthurian tales). See here.

Monday, March 11, 2019

Magic Distribution in OD&D Dungeons

An observation: Boy, magic is really rare if using the dungeon treasure table in OD&D Vol-3 ("The Underworld & Wilderness Adventures", i.e., the DM's book). Prior to this table you get the dictate, "It is a good idea to thoughtfully place several of the most important treasures... Naturally, the more important treasures will consist of various magical items and large amounts of wealth in the form of gems and jewelry." Then for the rest of the dungeon, rules that 2 in 6 of rooms have monsters; with treasure present 3-in-6 with monsters and 1-in-6 without. Then this table is given for such treasure:

Now, I've sort of made my peace with this table for gems & jewelry; while rare (esp. at the lower-numbered levels), when present they come in batches and generally large values, so they sort of give some reasonably high value. (A bit like hockey or soccer: scoring is rare but each goal makes a big difference!) However, magic is very rare throughout dungeon levels 1-3, apparently only shows up one item at a time, and has the added limitation that when you turn to the magic tables, 25% of the time it turns into a treasure map, and not actually any magic.

Let's compute. Say on a standard piece of graph paper you get around 40 rooms per levels (that's what I tend to get), and randomly stock the whole dungeon with this method. Then on the first 3 levels combined you'd expect (adding terms for both with-and-without monster cases): 3 levels × 40 rooms × (2/6 with monsters × 3/6 treasure + 4/6 without monsters × 1/6 treasure) × 5% = 120 × (1/6 + 1/9) × 5% = 120 × 0.277 × 0.05 = 1.66 positive results for magic items. Adjusting for the chance of maps, we get 1.66 × 0.75 = 1.25 actual magic items. So on average we may likely get just one single potion on all of levels 1-3 of the dungeon, and no other magic whatsoever. That could make it a bit hard to fight 4th-level monsters like lycanthropes, gargoyles, or wraiths, that start showing up on the [checks notes]... um, 1st level of the dungeon.

Anyway, here's a complete table of expected number of magic items (discounted for chance of maps) per dungeon level under these assumptions:

As we've seen, on levels 1-3 we only expect about 1/3 of a magic item per level, so rounding to the nearest integer, this appears as zero (0) in the table above. At other levels you may get 1, 2, or 3 magic items on average from the Vol-3 random method. If you make a dungeon of 12 levels (~500 rooms?), then we'd expect a grand total of around 14 magic items in the whole complex.

So I think that most of us would agree that simply can't stand; we have to do something else to supply fighters with magic arms and armor, wizards with wands and spell-scrolls, non-renewable potions of healing et. al., and other stuff. The most obvious way is by DM fiat, thinking of the "thoughtfully place" dictum. But then we are left with no other guidelines for what kind of distribution is recommended in that advance process.

Perhaps one faint idea is to shift magic-positive results from one single item to 1d6 at a time (roughly tripling the numbers estimated above, on average). Any other ideas?

Edit: Some folks in the comments take the interpretation that maps should not be generated from that dungeon-treasure table, actual magic only (maps for wilderness treasure only). There's definitely an intriguing case to be made there, but I'm not sure it's ironclad.

On the other hand, if we do permit maps in dungeon hoards, then perhaps we should account for the magic items to which they can lead you. Random maps have a 30% chance of leading to a "Magic Map" table, and 10% to a "Magic & Treasure Table". Those are both d8-based, and coincidentally, they each have an expected production of 19/8 = 2.375 magic items (individual results go as high as 5 items!). So together any random map expects to lead to 0.40 × 2.375 = 0.95 magic item. We might as well round that to "1", which tells us that we can effectively just ignore the map discount itself (each map leads to an average of one magic anyway). Either way, we're then back to an expectation of 1.66 items in the first three levels of the dungeon (not a big difference).

Or taking Daniel Wakefield's idea, maybe that gives us a clue for what a thoughtfully-placed "big magic cache" might be: 1-5 magic items or something like that. Other ideas are to scale it to the expected number of items PCs might have per level (almost embarrassed I didn't think of that earlier).

Consider: These days I roughly assume that pre-generated PCs might have a 1-in-6 chance for magic per level in each of 3 categories. (So: a 6th-level fighter with +1 sword, shield, and armor seems reasonable.) That implies about 3/6 = 1/2 item per level. If one PC level correlates with one dungeon level, and we have 4 PCs, then it suggests we want 4 × 1/2 = 2 items per level (permanent items?). Compare that if we say that random magic finds include 1d6 items (similar to the 1-5 range in the maps), then that multiplies our earlier per-level expectation and get 0.553 × 3.5 = 1.94 ~ 2 items per level. So those figures seem synchronous.

On the other hand, if you have big 8-person parties then you might consider the need to double that again? Geoffrey McKinney's stats for B2 indicate the per-area magic rate at about 80% × 50% × 46% = 0.184. So one of my 40-room levels would expect 40 × 0.184 = 7.36 items, or almost quadruple the figure in the prior paragraph. Hmmmm. At least that gives us a starting upper/lower bound for what we might choose.

Monday, March 4, 2019

More Missile Modeling

I've written so many letters on the physics and statistics of missiles, archery, and ballistics that it could sink a warship (search the blog, you'll see). So much so, sometimes it's easy to lose the plot at this time. I figured I'd summarize some of our findings to date.

We have two primary sources of data. One is from Longman and Walrond, Archery (1894) -- as reported by Barrow in Dragon #58, "Aiming for realism in archery" (Feb. 1982). He writes (first noted on the blog here):

English archers use a 48-inch-diameter target in tournament competition... A compilation of the twelve highest tournament results during a one-year period shows that the “hit” percentages of England’s finest archers at three ranges were: 92% hits at 60 yards, 81% at 80 yards, and 54% hits at 100 yards distance.  

A second source of data is from more recent UK "clout" long-distance longbow competitions. Results from a competition in 2016 show that at a range of 180 yards, competitors hit a 12-foot radius target 42% of the time, and an 18-inch radius central target only 1% of the time. (Full data and spreadsheets on the blog here.)

Using that as a guideline, we've developed a simple physical simulation to model archery shots, using an idea I first saw in Conway-Jones, "Analysis of Small-Bore Shooting Scores", Journal of the Royal Statistical Society (1972). The idea is fairly simple: model shooting error in both the x- and y-axes directions as two independent normal curves, which we call the "bivariate normal distribution". (First noted on the blog here.)

The simulation of that is written as a Java program and posted to a public code repository at GitHub (here). If we run that program with settings of precision = 6.7 (extremely high skill!), target radius = 2 feet, and long output form (that is: parameters 6.7 2 -L), then we get to-hit results very close to the 1894 Archery figures (compare highlights to quote above):

Likewise, if we run the program with precision = 1.6, target radius = 12 feet (parameters 1.6 12 -L), then we get results very close to the recent UK clout tournaments:

Also, if we set the target radius of this latter experiment to 1.5 feet (that is, 18 inches), then the hit rate at 180 yards becomes 1%, exactly as seen in the real-world data. Comparing these two data sources, we might be led to think that English archery skill has dropped off precipitously between 1894 and 2016 (precision 6.7 in the former and 1.6 in the latter). But based on the short quote regarding the first data source, we might say that it was cherry-picking its data; the best dozen results across all tournaments in England in a year. Contrast that with the second data source which includes all 30 competitors in one single tournament, whether they performed well or not. So the jury is still out on that issue.

That ends the recap. Now for a new thought: What is the best statistical model for these numbers? Clearly it's capped above and below: the chance to hit (or miss) cannot possibly be more than 100%, or less than 0%. Presumably we want a smooth, continuous curve, and one that can theoretically handle any arbitrary distance. Effectively we have just given the definition for a sigmoid curve, that is, an S-shaped curve seen in many probability cumulative distribution functions. The simplest model for this is the logistic function, as applied in logistic regression analysis.

One problem with this observation is that logistic regression of this sort is not built into standard spreadsheet programs (Libre Office, Excel) like many other types are (linear, polynomial, exponential, etc.) So what I've done below is this: Used the model derived from 2016 clout shooters (second experiment above; precision = 1.6, set target radius = 2 feet); increased granularity of the output to increments of 2 yards (for added detail); converted hit chances to miss chances (because the logistic curve expects numbers to be increasing from left-to-right), and used the online Desmos graphing calculator site (here; thanks immensely, guys!) to regress it to a logistic function. We get the best possible fit as follows:

Note that our regression (orange curve) has an R² = 95.87% match with the numbers from our simulated physical model of UK long-distance clout shooters (black dots). One possible downside: the logistic formula shown in the bottom-left is probably too complicated to use in a standard D&D gaming session. However, a second observation occurs to us: in the central part of that curve, at distances from around 20 to 40 yards (that is, ignoring the parts that are close to 0% or 100%; i.e., the part with maximal rate-of-change), the curve is practically a straight line.

Let's find an approximating line for that "critical" part of the curve. Our regression formula generates the points (20, 0.28) and (40, 0.73) -- so, this is the region where hit-or-miss chances vary from about 25% to about 75%. Solving for an equation of a line through those points (using Wolfram Alpha or good ol' college algebra) gives: y = 0.0225x − 0.17. Note the slope m = 0.0225, which means the chance to hit drops by 2.25% per yard on that region. Converting to feet we get 0.0225/3 = 0.0075, so: 0.75% per foot, or 7.5% per 10 feet. Note that this is freakishly close to the 7.6% per 10 feet figure we saw in the Milks spear-throwing experiment a few weeks ago.

In conclusion: It seems like our data and multiple models are telling us that there's a consistent dropoff in hit rates of around 7.5% per 10 feet, in the part of the range where it matters (neither a near-automatic hit or miss). This is why in the last few months in my D&D game I've shaved this number off to 5% and simply said there's a −1 chance to hit per 10 feet, on a d20 attack roll. But how to account for the extended upper and lower parts of the sigmoid S-curve distribution (where the chances are almost, but not quite, 0% or 100%)? Well, the classic rule to auto-miss on natural "1" and auto-hit on "20" (or something close to that: say they count as −10 or +30) does a fair job of recreating the rest of that model.

(P.S. Keep in mind that the exact hit-or-miss numbers shown above assume a single unmoving, undefended, man-size target of radius 2 feet or so. In practice, we need all kinds of extra modifiers to account for aware, defensive men in the field; shooting at a clustered army of bodies; and so forth. But from what we can tell the specific range modifiers increments would be generally consistent regardless of other considerations.)