The Effect of Sweep Attacks

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.

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?

Cursed Magic Items Through the Ages

A 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. 

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

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:

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?

Mohs Scale to Marvel

Regular readers of this blog may know how much I adore finding some real-world measurement scale that can be easily used as the core of a game system mechanic. If available, this ticks off all my desired boxes for gaming: (1) an elegant mechanic, (2) a presumably rigorous mechanic, (3) an opportunity to learn something about the real world, and (4) provide a pre-made way to convert from real-world data to the game. 

Of course, if we look back to the origin of the wargame form, the entire intent was to use real-world data as a source for mechanics and training for the battlefield (say, at least as far back as Korns' Modern War in Miniature, if not original Kriegsspiel). So, this instinct is really a callback to our source inspiration. 

Here's the thing I just discovered: the Mohs scale of mineral hardness. This dates to 1822 when German geologist Fredrich Mohs established the system to measure relative hardness -- a mineral of higher-rank is able to visibly scratch the surface of a lower-rank material. (Per Wikipedia: "The method of comparing hardness by observing which minerals can scratch others is of great antiquity, having been mentioned by Theophrastus in his treatise On Stones, c. 300 BC, followed by Pliny the Elder in his Naturalis Historia, c.  AD 77.")

It's an incredibly simple system: integer values only, from 1 to 10 -- with talc at the lowest level, and diamond at the highest. Note the picture at the top of a standard field-testing kit, with the 10 different canonical materials neatly boxed and numbered. 

Also I realized, if you're a fan of the the original Marvel Super Heroes RPG, this neatly lines up with the 10 named ranks in the Universal Table. To wit:

As usual, the neat thing is that having established this, there are now extensive tables of other materials with hardnesses measured in possibly fractional Mohs units; so for these other materials we have the option of just looking them up and converting to the nearest rank value. Example from Wikipedia below (click to go to full-sized table).

A number of these substance appear in the MSH rulebooks Material Strength table (like ice, gold, glass, iron steel, and diamond), and in most cases they do in fact appear at the same or within one rank. So kudos to Jeff Grubb for a pretty accurate system on that score; and that gives us confidence that we can interpolate these things reasonably in-game.

It's science, true believers!

The Landlord/Monopoly Game

On Twitter last week, Ethan Mollick, Professor of Management at the Wharton Business School, gave us a great reminder that the game of Monopoly was, ironically, ripped off from a prior game with partly similar mechanics and a totally different intent:

Of course, I share this as a reminder of our continuing reflection that games are not just about fun. The example here of Elizabeth Magie's "Landlord's Game" shows just one of the many other design goals that might be in sight -- and in fact, when the game was adjusted to strip out those other elements, we're really left with a degenerate, lesser form.

Now, I assume here when Mollick says that the game "has bad rules by design", that's shorthand for "rules that intentionally inflict pressure or pain on the players", so as to teach some kind of lesson.

What rules are in play in your personal game design that intentionally inflict pain on the players? And what lessons are being taught with those mechanics?

See the current publication of the original Landlord's Game here.