2022-03-21

Saved by Rolling Rock

Statue of Sisyphus rolling a rock

Our friend Baquies asked a question that I like very much: my OED Traps Digest has a 10' diameter rolling rock trap, which I basically lifted from Moldvay's Lost City adventure (module B4, area 39), and he probably swiped it from Raiders of the Lost Ark the prior year. 

Now, I stipulate that after the boulder comes to a rest, it can be pushed aside 1 in 6 by a normal man. Is that reasonable?

Looking at the Rockhound Resource website, one of the examples in a table there includes a rock that's "Car sized | ~10 ft" weighing in at at about 86,500 pounds (and I double-checked the calculation: assumes about granite density).

An answer to a Quora question (by Charles Collins -- no relation, I assume) says that the optimal coefficient of rolling resistance on level ground is 0.10 (for a car with inflated tires, or a plane bearing). For our rock this gives a critical force of 86,500 × 0.010 = 865 pounds.

Can a man push that much? That's something I suppose a gym could answer. I think it's pretty common to bench press 100 pounds or so. An answer on Reddit here says regarding a leg-press machine, "People can easily hit up to 400-600 pounds or more on these machines, I would design for a force of 1000 pounds to have some safety factor built in."

So maybe we should dial down our rock a little bit, say to about an 8' diameter -- thereby letting it roll a bit more freely down our standard corridor, and also reducing the weight by half, to about 44,300 pounds, with a critical rolling force of about 443 pounds. This seems to put it squarely in the range that a fit man could roll, if he had his back against one wall, and pushed with both legs.

(And our friend Seeker points out that the easiest rock to carve for this purpose would be limestone, so let's say that's the material, which increases the weight a small amount, i.e., by 2% or so.)

What are your thoughts on that? Will it make Sisyphus happy?

2022-03-14

OED House Rules v.1.0.7

OED Player's Rules Cover

Presenting the state of the OED House Rules for 2022: we've bumped up both the Player's and Judge's rules documents to version 1.0.7. Some of the more important edits you'll find there:

Player's Rules

  • Combat Feats have been reworked & rebalanced for a better overall distribution. (In particular, Rapid Attack is no longer the hands-down best choice.)
  • Sweep Attacks are noted as a universal ability for all Fighters, as opposed to the ambiguous state it was previously left in (and the Cleave feat consequently removed). See numerous analytic posts in which we researched this issue in 2021; in short, if you're going to play with O/AD&D listed large numbers appearing for low-level monsters, then players need this ability to stay competitive.

Judge's Rules

  • Mechanics based on a d6 roll have been synchronized to follow a low-roll for success model, following the majority of the instances in the LBBs. See here for the analysis on that.  
  • Slime/ooze monster mechanics were edited to match results of recent polls we ran (to be presented in the near future).

Monster Database

  • At least as important as any of the above, we've recently significantly expanded the Arena simulator program to include common wizard spells, magic-using and exotic monster types, etc. EHD (Equivalent Hit Dice values) have been modified to reflect that; basic monsters (giant-types, etc.) mostly stayed the same, while some outliers had large changes (e.g., vampires, golems, etc.). 
  • All monsters now have a justified EHD listings (previously some special or spell-using types were left with a null entry). 
  • The database has been expanded with more monsters from the OD&D supplements (now over 200 listed!).
  • Quick copy-paste stat blocks are now at the OEDGames site; the complete database in spreadsheet format is kept in the repository at Github.

We'll plan to post more updates and reflections on lessons from that recent simulator work in the coming weeks. Big thanks to the Wandering DMs patrons for kicking around and giving invaluable feedback and motivation on most of these issues. If you play around with these rules, tell us how they play for you! 

OED House Rules v.1.0.7 at OED Games

2021-12-13

Wilderness Simulator Stats

Wilderness Encounters: Clear (log chart)

One more reflection on the Original D&D wilderness encounter charts. Last week we were using some tabulated charts to decide between two possible rules interpretations, and one was clearly much nicer. But that was based on just looking at the average EHD (Equivalent Hit Dice) for each encounter type, which is maybe a little sketchy. Since I'm obsessive about these things, I wrote a simulator program that actually rolls up the individual encounters (varying the number appearing by psuedo-random dice), and I had it spit out a thousand random encounters for each terrain type.

Here's the statistics that get produced looking at those samples of size N = 1,000 for each terrain category. Note that this includes accounting for the sweep-attacks rule (high level fighters get one attack per level vs. 1 HD types), and also reduced numbers for the outlier groups of Gnolls, Cavemen, Treants, and Vampires that seem necessary based on our analysis last time:

Wilderness Encounter Simulator Stats

As you can see, like we've said a few times, the danger levels across the different terrain types are a lot more constant than one might have guessed without inspecting closely. But of course, the various terrain types mostly feed into the same subtables, anyway. This is in stark contrast to encounters for different dungeon levels, which obviously represent a setting of increasingly dangerous tiers -- although note that the rate of encounter checks increases quadratically in bad terrain, so that does make for a significant difference in risk level. 

The mean EHD per encounter is close to 40 for any terrain, with a standard deviation around 27 or so; and the median is around 35 or something, with an IQR (interquartile range; comparable to standard deviation) around 30. The mean-higher-than-median indicates that the distribution is right-skewed, i.e., has a long tail to the right, with a number of very high EHD encounters occasionally occurring. In cases like this, it's sometimes interesting to take the logarithm of the data values (e.g., the general mean converts to log(40) = 1.6), and see if the distribution then looks like a normal curve. I did that below:

Wilderness Encounters Simulator Log Charts

Okay: They're kind of normal? None of these actually pass a statistical test for normality (rejected at P < 0.0001). That's not too surprising, since it's not like the encounter design in OD&D has any kind of systematic consistency (nor would I argue for it to that extent). But it's at least kind of suggestive: a log-normal distribution is reflective of many natural biological and demographic processes, and these encounters are sort of in that ballpark, which is nice. There's significant variation in the encounters to make the D&D wilderness challenging and risky, but it's not a lunatic level of variation, where you can't even imagine half of the creatures surviving for a week in the presence of the other creatures.

So overall this doesn't change our conclusions from last week much at all -- or, in other words, it gives added support to those conclusions. These distributions feel kind of nice to me. For a party sized 8 (all fighters in our sim), an average level of 5th should stack up against the average EHD of 40 pretty well. Although rarely you'll have an encounter in the EHD 100+ range, and then you'd darn well better engage with the Evading rules. Or if you Arneson-ify the wandering numbers down to about 1/3 book values, and play with a 4-person party, then 4th level can be okay -- at least until you delve into the lair locations for that sweet, sweet gold treasure.

How do those simulated stats look to you?

Wilderness Encounter Sim Stats (ODS file)

Wilderness Encounter Sim on Github (Java code)

2021-12-06

Sweeping Up the Wilderness

Horse-Drawn McCormick Mower

Last week I opened my personal journal on accepting sweep attacks (fighters getting as many attacks as levels vs. 1 HD targets) as a critical element throughout the O/AD&D rules, and my own game, and the effect they have on play. Today we revisit our analysis of wilderness encounter perils, in the context of including sweep attacks in the picture.

State of the Wilderness

Here's a recap. Back in 2019 I analyzed Wilderness Encounter Levels, and the overall distribution of danger on the OD&D outdoors tables. A first observation is that, on average, the different terrain types are actually pretty uniformly dangerous: we estimate they're roughly balanced for a 10th-level party (with a classically big size of 8 PCs, fighters only, and no sweep attacks). A second observation is that looking past the averages, the encounters have a very prickly distribution: lots of encounters at total 50 EHD or less; but also lots of encounters with EHDs in the 200s or higher. (EHD being "Equivalent Hit Dice", something a bit analogous to challenge ratings.)

In 2020, considering that problematic, I took a stab at considering Rescaling Wilderness Encounters; maybe dialing down some monster numbers to get things a bit more manageable -- possibly by Arneson's tactic in the First Fantasy Campaign (assume only about a third of any group is wandering outside the lair), or Moldvay's in the Basic D&D rules (drop humanoid numbers to around one-sixth the original). Here's a copy of the table I had there of EHD distributions for all encounters in the OD&D wilderness (note the logarithmic x-axis):

Frequency of Encounter EHDs
Now, as a statistician, you kind of hate to see that kind of bimodal shape in a graph -- the fact that there's not one but two upward spikes in totally different locations. (As noted: a whole bunch of encounters around 50 EHD total, and another big batch of upward of 500 EHD. The coin-flip of doom!) That usually suggests that you've got a problem with your polling process, in that you've likely munged together two totally different categories of things, and instead should be dis-aggregating and measuring them separately.

In this case, the distinction is easy to determine: the big batch of super-high EHD encounters is precisely all of the humanoid bands appearing in numbers of hundreds (men, goblins, orcs, dwarves, elves, etc.). All of those kinds of encounters have average EHDs of 150 to 300 or so -- whereas the median for the overall set is only about 40. Likewise, the wilderness encounter subtables that have lots of these types (Men and Giant-types, i.e., humanoids) have average EHDs of 120 to 200, while all other subtables (Lycanthropes, Undead, Dragons, etc.) only have average EHDs of 25 to 50.

Earlier in 2021, I looked at Monster Numbers Through the Ages, specifically for the canonical wilderness encounters, and considered them in relation to the status of sweep attacks in each of those editions. A discovery there is that in some ways the numbers were pretty consistent from 0E to 3E, and then disappeared from monster stat blocks after that.

Start Sweeping

So recently I added a switch to turn on sweep attacks in the Arena Simulator on GitHub, and last week I presented that it has the effect of reducing the effective power of 1-HD humanoids to about one-fourth their actual hit dice (on average; and of course this varies enormously by the exact level of classed fighter-type they're facing off against). At some point, I went to the wilderness data tables from before, and dropped in those modified numbers. Here's what the distribution of encounter EHD totals looks like now:

Frequency of Encounter EHDs (with sweeps)
So: In one fell sweep, that solves the problem. The bimodal shape is gone, and now it kind of looks like a normal curve (after logarithmic scaling).

Some more details: The overall median is still around 40 EHD; but now the bands of humanoids have average EHDs in the range of 30 to 70 or so, that is, a much better match. Likewise, the subtable statistics become less jagged; mostly in the range of 30 to 50 on average (in other words, fairly spread around that 40 median). More on that later.

The difference in those two graphs is pretty much what single-handedly convinced me that if you're going to play an O/AD&D style, all other things being equal (like numbers appearing for humanoids), then it's pretty much a necessity to honor the classic sweep-attack rule.

Stones in the Field

But there are still a few exceptions: outlier encounters that have total EHD way outside the standard range of about 30 to 70. These are four specific cases that fall neatly into two classes:

  • Creatures with summoning abilities. When these creatures are encountered, they can summon other allies to help them, multiplying their strength (vs. their book hit dice, if that's all you were looking at when balancing the encounter size). With the summons respectively doubling or tripling their power, the average total EHD for Vampires is 140, and for Treants it's 360.

  • Creatures with 1 HD but a 2HD subtype. There are two humanoids with 2 HD, but are sub-types of a 1 HD primary creature class. Therefore they share the same high number appearing as the main type in the table (some hundreds), even though they're outside the range given for the sweep-attack rule. The average encounter EHD for Gnolls is 220, and for Cavemen about 310.

Let's be a little more specific about that latter category: In the OD&D Monster Reference Table, Hobgoblins and Gnolls share a single line jointly. The have the same AC, movement, % in-lair, treasure, and number appearing (20-200). But the hit dice entry says "1+1/2", i.e., Hobgoblins have HD 1+1, and Gnolls have 2. So while I'd interpret Hobgoblins as being in the range for sweep attacks, Gnolls would be out. In that regard, giving them the same numbers appearing seems to be a big mistake. This kind of gluing-together of types is in the tradition of Chainmail, where a lot of monsters were presented as tiny alterations of other classes. (In the past I've mistakenly said Gnolls were 1+1 hit dice in early drafts of D&D, but it turns out that was a typo in the later derived document called the Dalluhn Manuscript, so let's ignore I ever said that.)

Meanwhile, Cavemen don't appear in the table, rather being subsumed by Men, who have number appearing 30-300 and generally 1 hit die/man. But among the 9 different sub-types of Men described in the main text, Cavemen are uniquely noted as having 2 Hit Dice. (Actually, in the pre-publication draft of D&D, even that was ambiguous: the Guidon D&D manuscript says they "fight as 2nd level Fighting-Men", which could be interpreted a few different ways; when the LBBs were published, the entry was expanded to also say they "get 2 Hit Dice", apparently in response to some peoples' confusion. Thanks to Jon Peterson for personally answering a question about that.) Again, with this clarification, Cavemen stand outside the range of sweep attacks, but they still share the 30-300 number appearing like any other Men. 

Recall that up above I mentioned with sweep attacks, most of the wilderness subtables had average EHDs of 30 to 50. But I should point out that there's two notable exceptions: The Men (Mountains) and Giant subtables are both elevated up to around 90 instead, and that's entirely because those are the only tables with Cavemen and Gnolls (plus Treants) in them.

(Now, one might theorize that's evidence that 2 HD creatures should be in the range of sweep attacks, too. But there's even even more monsters on the reference table with 2 HD that have small numbers appearing: e.g., Zombies, Ghouls, Dryads, Pegasi. If we allow sweeps on them, then their EHDs plummet below the normal range, and you have an even worse problem. Also: most Horses and Mules are at the 2 HD level, and allowing whirlwind-slaughterhouse attacks against them just doesn't feel cool to me.)

So I do think that the numbers appearing in the four outlier cases are oversights and should be fixed. For Cavemen and Gnolls, following the idioms on the OD&D monster table, I'd recommend making their numbers 3-30 (as for skeletons/zombies), or 3-36 if you want to use Platonic dice, which of course you do, because you're a person of excellent taste.

Meanwhile for Vampires and Treants, I'd recommend lowering both to the smallest-appearing die of 1d4. This places Treant encounters at an average of about 80 EHD (still one of the highest), and Vampires at around 100 EHD (thereby making them the #1 most dangerous wilderness encounter). I'd actually make Vampires 1d3 if it weren't for the fact that it appears nowhere in the original table. Either way, this solves the eccentric subtables and related problems.

Wilderness Encounter Levels

All told, here's our revised estimate for encounter levels in the OD&D wilderness. Again, this assumes an eight-person, all-fighter party. When we started, we estimated that the tables present, on average, a balanced encounter for 10th-level PCs (with a huge amount of dangerous variation). By merely flipping on the sweep-attacks switch, our estimate drops to one appropriate for 6th-level PCs (and quite a bit more predictability in the danger, even you're still dicing for exact numbers in each case). What a huge difference that one rule makes! 

In both cases, this danger level is pretty consistent across all terrain types. Furthermore, if you make the adjustments to the monster numbers for the outliers I mentioned above -- even though that's only four entries -- they're influential enough to further drop the estimate down to 5th-level PCs. And that's pretty darned close to what many of our intuitions say (e.g., from the D&D Expert set rules) about what level wilderness adventures should be happening at in the first place.

One of my favorite things in the world is when two apparent problems cancel each other out, in that they're actually the mutual solution to each other. And for me, what appeared to be the bizarrely wonky variable danger of the OD&D wilderness encounter tables, and the mystery of whether sweep-attacks for PC fighters were really intended within the OD&D mechanics, is just such a satisfying case.

Just One More Thing

So sweep-attacks are the solution to the specific problem of big humanoid numbers in the wilderness. And yet separately, I'm still somewhat sympathetic to Arneson's idea in the FFC of having only around one-third of the given numbers actually show up wandering around in the wilderness (with the rest holding down the fort, or lair) -- applied universally to all monster types, not just humanoids. In some ways that cools the numbers for mythic monsters down to something more in line with what I have in my head for fantasy tales (what feels better: 4 dragons, or unicorns, or 1? 6 balrogs or 2? 8 giants or 3? 12 pegasi or 4?). And it also adjusts for the smaller standard (non-convention?) party sizes we might be dealing with now. If you reduce monster numbers appearing to 1/3 listed, and party size to 4 (instead of 8), then the average wilderness encounter in OD&D in fact seems to be balanced for 4th level PCs (exactly in line with the Expert rules expectation).

Appreciate any of your thoughts on that!

Wilderness Wandering Analysis 1.0.3 (ODS spreadsheet)

2021-11-29

The Effect of Sweep Attacks

Conan the Destroyer

For quite some time, it's been left as ambiguous in my OED House Rules whether or not fighters get "sweep" attacks -- the hyper-accelerated mode where they take as many attacks per round as they have levels, but only against low-level (1 hit die) creatures.

One of the major themes for this year, both on my blog here (and here) and in discussions on the Wandering DMs YouTube channel, is my finally becoming convinced that (a) that rule really was intended consistently throughout Gygax's Chainmail, OD&D, and AD&D, (b) it's a critical aspect to balancing against the large mobs of 1-HD humanoids who appear in groups of hundreds, and (c) it's the single biggest rules difference between the O/AD&D lines and the Basic D&D lines (where the rule is removed, and humanoid numbers greatly reduced). 

So granted that, I think I need to make an explicit call about whether that's a base assumption for OED, and in my next update, in line with the classic game, I'll be highlighting that as an included rule. (And also removing "cleave" from the list of optional feats, but then I never saw a player pick that anyway, so it's a minor issue.) 

In some ways it's actually not my favorite rule; I'm less than thrilled with the discontinuity between 1 and 2 HD, and the possibility of a large number of dice being rolled. But the advantages of recognizing it include: (a) closer compatibility with the original game, (b) recreation of inspirational pulp stories (where heroes like Conan indeed hold off huge mobs), (c) some way for fighters to hold pace with high-level wizards, (d) less modification needed vs. reducing all the humanoid numbers appearing, and (e) a mechanic that legitimately makes high-level fighters significant in mass combat, such as Book of War

(And I'm less bothered by the OD&D FAQ/Swords & Spells presentation of, "base 1 hit die or less", versus the AD&D version of strictly "less than one hit die", which made the switchover difference a single hit point, e.g., leaving goblins in but taking orcs out.)

If a DM looks at OED and wants to snip out the sweep attack rule (and commit to changing monster numbers appearing), then that's fine and respectable -- and I think easier than if I left it out and another DM needed to add it back to the system. There were some other alternatives that I considered and tested along the way (like a generalized "cleave" rule, or changing every single monster number in the game), but I wound up rejecting those, so I won't go into them here.

Here are some other observations on the effect of sweep attacks, based on recent investigations.

Arena Simulator

Recently I modified the code in the Arena Simulator on Github to add an optional switch to turn on sweep attacks (-w). What we see is that on average, the power value of the 1-HD monster types gets cut down to about one-quarter basis. This is summarized in the following table; here, EHD is "Equivalent Hit Dice"; the average number of fighter-class hit dice the monster can evenly match up against.

Sweep Metrics Compiled

Normally the EHD calculation seems fairly robust to me, because it's an average over what I call the EFHD value (Equivalent Fighter Hit Dice) at each fighter level, and that latter number tends to be roughly constant over different levels for standard monster types (at least within a factor of about 2 or so). Some exceptions stand out for monsters with big area attacks or high hit-by magic (kill lots of low-level fighters, generating a right-skewed EFHD distribution), or ones with potent save-or-die effects (more easily wipe out high-level fighters' hit dice, giving a left-skewed EFHD distribution). 

And now, monsters subject to sweep attacks present another outlier case, because the lethality of the fighter-types suddenly varies so much by level, due to their many-multiplied attacks. (Normally fighter stamina is increasing by level, while attacks stay about the same; in this case fighters become quadratic, too.)

So let's look at that a little more closely. The interesting thing is that sweep attacks actually change the EFHD curve slope from positive to negative. For example, here's a listing of the EFHD values for an orc, matched against fighter levels 1 to 12, with sweep attacks on, from the Arena simulator (-e and -w switches):

[1.0, 0.67, 0.6, 0.5, 0.42, 0.35, 0.29, 0.25, 0.2, 0.18, 0.16, 0.14]

As expected, the value of the orc decreases from EFHD 1.0 at 1st level (indicating that a 1st level fighter can hold off 1 orc), to EFHD 0.14 at 12th level (indicating that a 12th level fighter can fight off about 12 / 0.14 = 85 orcs). Now, what might be more surprising is the EFHD curve for an orc before the sweep attacks get turned on as shown here (using just the -e switch):

[0.5, 1.0, 1.0, 1.0, 1.0, 1.2, 1.17, 1.14, 1.13, 1.25, 1.22, 1.2]

What that shows is that the pro-rated strength of an orc (or other basic monster type) is normally increasing somewhat versus fighter level; e,g., from 1.0 at 2nd level to 1.25 at 10th level or so. It may be easy to overlook, but that's not really a mystery: we've long identified that as the effect of the Packing Problem, in that mobs of low-hit creatures are effectively sponging up more wasted overkill damage, whereas high-hit figures are suffering full damage from every hit but the last.

The effect of sweeping is so powerful that I had to increase the MAX_ENEMIES cap in the simulator from the previous 64 to 256. (E.g.: a single sweeping 12th-level fighter can hold his own against some 80 orcs as above, 160 kobolds, or 240 rats). This had a side effect for certain powerful monsters that are only hit by higher-powered magic items, like elementals (+2 to hit) and golems (+2 for stone, +3 for iron). Granted that no low-level fighters can possibly have such magic weapons in the simulator, those monsters effectively stomp an infinite number of normal men. And when the MAX_ENEMIES number goes up, then their computed EHD goes up. So that will be reflected in the next OED Monster Database update. Iron Golems are now assessed at EHD 125!

On the other hand, I don't intend to change the EHDs listed for the 1-HD types (mostly EHD 1), because: (a) I don't want to deal with fractions there, (b) I don't want to trick anyone into throwing 4 orcs at every 1st-level fighter, (c) as noted, the averaging process is a bit cracked in this outlier case, and (d) maybe some DMs won't be using sweep attacks in the first place.

Experience Awards

Classic versions of the O/AD&D game generally have a rule for pro-rating experience in the downward direction; that is, awarding only a fraction of the experience based on monster or dungeon level divided by character level. (E.g., from OD&D Vol-1, p. 18: "Gains in experience points will be relative; thus an 8th level Magic-User operating on the 5th dungeon level would be awarded 5/8 experience."). Personally, I hate this rule, most people I know ignore it, it creates unsolved problems with multi-character parties at different levels, etc. 

Generally speaking, I don't think that rule makes any sense when the XP leveling tables are already themselves designed on a geometrically-increasing basis. Assuming we think of XP awards as generally balanced to the danger of the encounter, as noted above, we find that EFHD values are usually about constant across levels -- or in other words, danger is really linear in standard hit dice. The takeaway is that XP as a constant multiplier by HD (say 100 points per HD), and without taking a ratio for PC levels, is not a ridiculous thing to do.

But in the particular case of sweep attacks, that's certainly not true; the relative danger levels posed by goblins and orcs in the face of Superhero Cuisinart attacks indeed drop like so many carrot peelings. So for the first time ever, I could see the twinkling of an argument for reduced XP by a ratio of levels -- if one were focused specifically on the Hero-vs-mooks case as a default D&D fight, then the ratio-reduction is in fact legitimate. 

I still don't think I'll use that rule in the general case, but I could start to imagine engaging it, specifically in the unique case of PCs versus armies of 1-HD humanoids who are getting mowed down for pulp narrative purposes.

And we're not quite done with the issue yet: next time, we'll revisit the OD&D wilderness encounter tables in the context of the sweep attack mechanic.

Do you use sweep attacks in your OD&D-flavored games? Or if not, do you drastically reduce the humanoid numbers appearing? And do you use the XP ratio-reduction rule, maybe just in this one special case?

2021-11-22

Cursed Magic Items Through the Ages

The Monkey's PawA week back on the Wandering DMs YouTube channel we had a nifty conversation on the status of Cursed Magic Items in D&D. Largely we came out in agreement that they're a nice spice that makes magic in general feel more mysterious and dangerous. In the after-party chat on Discord, one of our Patrons asked: What exactly was the frequency of cursed magic items in the early editions? Did it really change very much over time?

Which I thought was a very good question, and I started researching it. And looked at every single magic item in D&D. In every single edition over the years. (Core rules only, thank you.) I guess it's my curse, but I hope it benefits you, Gentle Reader.

Original D&D (LBBs)

Here we're looking solely at the Little Brown Books in the white box, specifically Vol-2, which has both the monsters and treasures (including magic items). As noted in the WDMs show, pre-3E, there's no "keyword" system, so in most cases it's hazy about whether an item should count as "cursed" or not. However, the need for a remove curse spell to get rid of it is a pretty good sign, among others (more on that issue later). I'm sure there will be one or two items you'd differ with me in adding or taking out of these lists, but it won't change the overall numbers significantly.

In this case, I can only count six (6) items as cursed -- the sword –2, potion of delusion, potion of poison, cursed scrolls, ring of weakness, and ring of delusion

Notice there are no cursed armors, non-sword weapons, wands/staves, or miscellaneous magic. Some of those will soon be added -- but there are no cursed wands/staves in any edition. The overall chance of cursed items turning up here is 8%.

Original D&D (Greyhawk Supplement)

Less than a year later, Gygax published D&D Supplement I, Greyhawk. It  includes extensive "Additions and Changes" to the magic item tables; although the master types table, and the scrolls table, are unchanged and do not appear in this story (that latter being something I almost overlooked in computing statistics here). 

Several new cursed items are added, seemingly in an attempt to cover almost any form-factor of magic item in the game, including: one sword, one other weapon, an armor, a shield, one ring -- and thirty-three (33) miscellaneous magic items. I won't list them all here, but suffice to say pretty much any form of miscellaneous magic in the LBBs now has a cursed analog in the world by which to trick players. I think the majority of new magic items in the book are these cursed iterations of pre-existing magic items. Previously no miscellaneous magic was cursed; now 30% of the time miscellaneous items are cursed. 

And there's another issue that I'm not counting here, in an expansion of item types that are keyed to some class or alignment, helping the associated, but likely blasting others who pick it up. There's a special paragraph note (p. 59) that all manuals, books, librams, and tomes curse a reader who fails to benefit from it to hide and guard the book against anyone else successfully using it. (Dealing with the expansion of alignment-based effects would be an entire article unto itself.)

That said, the master table only sends you to miscellaneous types 5% of the time, so in the overall results this makes a very small difference, adding about 1.5% frequency (we've actually noted this both of the last two weeks in our WDMs chats on YouTube). But other stuff also adds to the chances: the new cursed armor & shield adds 2% to the cursed chance, and the chances for cursed rings expands to 1.5%. In total for this supplement, the chance of a cursed item now stands at nearly 13% (12.58%). This moment represents the high-water mark for cursed items in the game, and what we'll see in later editions is a slow erosion of the overall concept (including very few new cursed items added to the game after this point).

AD&D 1st Edition 

The AD&D Dungeon Masters Guide is very helpful for this study, because the tables effectively flag bad/cursed items -- by virtue of leaving the XP and/or GP column blank in those cases. For instances in other editions (both before and immediately after) where I couldn't confidently tell one way or the other, I've used this as an indicator to resolve the issue by designer intent. (With one exception: the jewel of flawlessness is clearly only beneficial, despite having a null XP entry, so I've left it out of my count here. Other stuff with both pro-and-con effects, like artifacts and the deck of many things, I've synchronously counted as cursed, but they're negligible factors in the final numbers either way.) 

Here, Gygax has kept all the same cursed types as seen in Sup-I, but seems to have notably dialed down their frequency in most cases of potions, swords, armors, and rings. The cursed miscellaneous magic is about the same (1.65% of the total; about 1% or 2% on each of five sub-tables). The total frequency of cursed items therefore adds up to only 7%, a single percentage point below what it was in the OD&D LBBs. 

AD&D 2nd Edition 

AD&D 2nd Edition has an interesting change in idiom to the tables for magic weapons; there are separate tables for weapon type, vs. magic effect, the matrix of which can generate many more varieties of magic weapons than what was seen previously. In the table for magic weapon bonus, there is a flat 10% (2-in-20) chance the modifier on any magic weapon is –1, which is a significant increase from earlier rules. 

However, there are no general rules or commentary on the status of these negative-modifier weapons that I could find. Is the player stuck with using it permanently until a remove curse can be accessed? Without explicit text on that point, my reading would be no. Likewise, the list of cursed scroll effects is radically reduced in power -- 0E/1E had a list of instant-death, removed from planet effects, etc.; 2E replaces those with a -1 modifier to checks, taking 2-6 points damage, growing a beard, etc.

So while the overall frequency of cursed items in 2E has gone up to 10% (due to the magic weapons table), arguably the impact of those baneful magic items is much reduced.

D&D 3rd Edition 

The 3rd Edition DMG makes the whole issue of cursed items optional; if utilized, then any discovered magic item has a flat 5% chance of being cursed (DMG p. 231). This sends the DM to a separate set of tables to find add-on effects modifying the magic item in question -- things like delusion, opposite effect, intermittent functioning, trigger requirements, certain drawbacks, etc. Generally these are fairly gentle side-effects (compare to 2E scrolls above). There is a 10% chance to be sent to the "Specific Cursed Items" table, which has about 30 items carried forward from the AD&D list (mostly miscellaneous magic, as to be expected). 

There's also a behind-the-curtains sidebar discussing the pros & cons of having cursed items in the game -- it suggests that items with both benefits & drawbacks make for more interesting tough choices in the game. And that PCs finding that they have a cursed item should be able to get rid of the item easily (a hard about-face from Gygax's O/AD&D). 

Some of that philosophy I really like: The benefits + drawbacks dilemma is very much in line with what we agreed to on our WDMs show. I also really like the structure of separate add-on tables for curses, so any such item gives room for creativity and customization by the DM, and likely any cursed item is a unique creation (as opposed to the very large amount of ink spent in OD&D Sup-I providing individual cursed types of every form factor). But the effects here in 3E are generally so weak that I tend to think most of them wouldn't have any interesting impact.

D&D 4th Edition

Many idioms of 4E, including magic items, are so different from any other edition that they're almost incomparable. For example, magic items are such a critical and expected part of character builds, that the whole list appears in the PHB (whereas all other editions have them in the DMG). I'm also told that having them fully, fungibly convertible to cash on demand is a key mechanic. 

That said, I can't find any bad/cursed items in the 4E list. There's a power called warlock's curse, and some items boost that to the benefit of the caster/owner. There is an item called curseforged armor, but that's just flavor-text (crafted by bitter halflings), and again, beneficial to the wearer. So as far as I can tell the frequency of cursed items is zero (0%).

D&D 5th Edition

D&D 5E has a very small number of classic cursed items return to the game. By my count, these are: armor of vulnerability, bag of devouring, berserker axe, demon armor, shield of missile attraction, sword of vengeance (the classic cursed sword), and dust of sneezing & choking. That's close to the same number as in the OD&D LBBs. Most of these are tagged explicitly with the "cursed" keyword; the bag of devouring and dust of sneezing & choking are not, but I've counted them anyway (in line with the 1E understanding). There's a very curt 5 sentences on the general status of cursed items (DMG p. 138-139). Some of the effects are notably changed from older editions. Note that 5 of the 6 items are weapons & armor; there is now only one cursed miscellaneous item, that indelible and infamous bag of devouring (contrast sharply with OD&D Sup-I!).

Now, calculating the frequency of appearance here is a tougher problem, because the magic item tables are split up by level of power (into tables A through I), and those are keyed not from a master table, but from the encounter-level tables, which produce different possible packages of treasure. So parties of different levels will be running against different result tables, and hence different chances of cursed items, over the course of their adventuring careers. Tables A, C, E, and I have no cursed items. The others have either 1%, 2%, or in one case 3% frequency of cursed items (just a single cursed item each on tables B, D, F, and H, but three items on table G alone). Let's take a rough average over all the tables and say the frequency is about 1%.

Conclusions

Below is a summary table of the chance for a random magic item to be cursed in any edition of D&D to date. As you can see, the idea in Gygax's mind circa the Greyhawk supplement for magic items to be commonly cursed and dangerous to the players, and appearing in any form-factor that a beneficial item might, washed away with the tides, becoming less frequent, and much less punishing over time. As of the last 3 editions, many campaigns have been run with official support for no such items appearing whatsoever. As a guess, it seems quite likely that they might be totally absent (again) from the core books of whatever the next edition from WOTC might be. 

Cursed Magic Items Frequency Table

Download a work spreadsheet here with comprehensive listings of every cursed item (ODS format).

2021-11-15

Demographics Quick Rule-of-Thumb

I was thinking again about medieval demographics the other day. This follows on an earlier summary article I wrote here

Thing is, I was trying to do some large-scale number crunching in my head, and found that I got a little tangled up about it. So in response, I came with a very rough rule-of-thumb based on units in powers of 10 that I could mentally juggle, and is roughly on the right order with what we know of medieval European societies. Here it is:

Medieval demographics rule-of-thumb

So in the grand total, that represents a 4-million population that might be an entire country on its own, or something. For example, England fluctuated from about half this population size, to the full unit, and back again (between the Dark Ages and the Black Death). On the lower end, recall that for a medieval village, it's pretty accurate to roll 1d6 × 100 for the population (giving an average of 350 each).

How much land space would this total organization take up? Well, that depends, because (much like the English example) population density varied a lot over the medieval period, and besides that we only have estimates anyway. A few possibilities:

  • 10 people/mi² -- Polity takes 400K mi² (600 × 600 miles); the lowest density estimate anyone's proposed for the Dark Ages in Europe.
  • 20 people/mi² -- Polity takes 200K mi² (450 × 450 miles); a more common estimate for Dark Ages population density.
  • 40 people/mi² -- Polity takes 100K mi² (300 × 300 miles); density of England at its low point, start and end of the middle ages. 
  • 80 people/mi² -- Polity takes 50K mi² (200 × 200 miles); density of England at its high point, middle of the medieval period, and matching its actual land area. 

Now -- that's a lot of real-world content. It's likely that you certainly don't want to detail quite that much stuff in your campaign world. As I've noted before, an obvious reasonable method is to just abstract away all the stuff below a particular map level that you're using. (For example, if you use low-England density and a 30-mile hex map, then your country might take up about 10 ×10 hexes; so you could explicitly place the capital and 10 cities, but just hand-wave, without drawing anything, the fact that most every such hex has its own town, 10 castles, and 100 villages). Alternatively, fantasy writers seem to have a tradition of much lower densities than ever occurred in reality, so you can feel free to follow suit.

So anyway, that gives me a couple of simple, memorable numbers I can remember when I'm doing mental estimates for this kind of thing. Is it helpful to others?