## Monday, May 31, 2021

### Maim is the Name of the Game

Last week we looked at the status of "cleaving" type attacks through the ages of D&D editions -- and were somewhat surprised to find it listed in the core rule books (maybe as an optional rule) of every edition to date! Okay, except the 80's Basic line, but everything else.

A side-point we've made there, and in the Wandering DMs chat on the subject, is that since the core books from Original, 1st, and 2nd editions never gave any identifying label to the ability (fighters getting multifold attacks vs. very-low-level enemies), a crazy kaleidoscope of different names sprang up in supplements, video games, 3rd-party works, the OSR, etc. My recent work made me pursue what the most recognizable name would be among those many options.

A total of 146 votes were cast here. As you can see, by far the most popular option there was simply Multiple Attacks with 94 votes cast (64% of the total). However, I am incredibly not fond of that as an option, because it explicitly gets used in the rulebooks multiple times for other types of abilities in both OD&D and AD&D. For example, monks are described as getting multiple attacks in their first appearance in OD&D (Supplement II, Blackmoor, p. 1):

... monks of higher levels may make multiple attacks during a melee round (see STATISTICS REGARDING CLASSES)
And more definitively, here for creatures hostile and benign in the 1st Edition AD&D Monster Manual (p. 5):

Multiple attacks usually indicate the use of several members such as multiple hea[ds] or two paws raking with claws and a bite from the monster's jaws.

Clearly, none of these are what we're talking about in regards to the fighters-versus-mooks mode of combat, so using the term for that would only cause confusion, I think.

That aside, the next most-favored choice by a large margin is Sweep Attacks, garnering 30 votes (21% of the total), noted in last week's blog as recognizable to anyone who played the very popular AD&D Gold Box video games circa 1990. This is what I plan to call the ability myself in my classic-D&D materials in the future.

Other options, like Cleave Attacks, Heroic Fray, Fighting the Unskilled, and Combat Dominance only garnered between 1 and 5 votes each. (Note that there's a possibility of bias in the poll, since Facebook only shows the top 4 options at any time, and participants need to see and click on a "Show More" button to access the rest.)

As part of our research, I think we compiled a pretty interesting list of names used in a variety of video games and OSR materials, for this or closely related abilities:

• Heroic Fray (2nd Ed. AD&D Combat & Tactics supplement)
• Heroic Fighting (Hyperborea)
• Fighting the Unskilled (OSRIC)
• Combat Machine (Swords & Wizardry; previously "multiple attacks")
• Combat Dominance (Castles & Crusades)
• The Cuisinart (Wizardry video game)

Furthermore, the Facebook AD&D group poll has the option for "something else" which generated yet a larger and growing list of options -- some serious, some in jest, and some in a range of good taste. A selection the examples include (generally just a single mention each):

• The Cuisinart (gaining 4 mentions)
• La Machine (French analog to the Cuisinart)
• Meat Grinder
• Lawnmower Mode
• Mowing the Grass (despite "Mowing" being unvoted in poll)
• Weed Whacking
• Snicker-Snack
• The Aragorn
• Minion Attacks
• Rabble Attacks
• Fight the Horde
• Shredding Mode
• Pest Control
• Zero Level Attack
• Cutting the Chaff
• Spartan Attack
• Full Auto Attack
• The Mouli
• Cinematic Attacks
• Hackmastery

Notably, eminent D&D author Frank Mentzer (creator of the entire BECMI line, which is the only edition to expunge the rule) offered "Slice & Dice" as his term of art for the ability which he explicitly disliked so much (see prior post for details).

Are there any other prominent names that I still haven't discovered? What's your favorite?

## Monday, May 24, 2021

### Cleaving Through the Ages

One of the things that I love the most about our Wandering DMs project is that we've had the happy accident of assembling a crack D&D research team from among our patrons and followers. Maybe the best? When we gather together for any Sunday afternoon show, we can usually get questions about the history of the D&D game, for any edition, answered live in a couple seconds flat with a citation down to the page and paragraph. It's pretty amazing.

In this vein, when we were prepping for our show a few weeks back on Sweep Attacks, my initial impression was that they'd basically died out after 1E AD&D. To be clear: I'm talking about the ability of classed fighters to get a large number of attacks against very weak opponents -- traditionally 1 hit die or less. (Since 1E didn't have a label for it, many different names have proliferated: Sweep, Cleave, Heroic Fray, Combat Dominance, Fighting the Unskilled, etc.... see the video for more.) In conversations in that show and afterward, it's turned out -- to my great surprise -- that some form of the rule has been in the core books of every single numbered edition.

Amazing. And I'd have never known that without the generous help of our viewers. Because of that community spirit, I think I can say this is first "Through the Ages" post that covers every edition from 0E to 5E. Thanks, everyone!

### Chainmail Fantasy

HEROES (and Anti-heroes): Included in this class are certain well-known knights, leaders of army contingents, and similar men. They have the fighting ability of four figures...

SUPER HEROES: Few and far between, these fellows are one-man armies! (Particularly when armed with magical weaponry.) They act as Hero-types in all cases, except they are about twice as powerful...

In the transition from normal Chainmail mass-combat, to the individual scale Fantasy combat, the basic implementation of high-powered fighters is simple: they just roll more attack dice. Noting that the Chainmail system is entirely d6-based, in a fight of equal-class normal units, each figure rolls a d6 and any "6" kills a figure. In this same situation, a Hero rolls 4 dice, and a Superhero rolls 8 dice. Elegant, yes? Of course, when D&D evolved from this system, 4th-level fighters were called Heroes and 8th-level fighters titled Superheroes.

Now, there's a totally separate system added on for when Heroes fight fantastic monsters, in which only a single dice-roll was thrown against some target number on 2d6. Thus began the legacy of a distinctly different attack mode against basic-level types vs. higher-level opponents.

It bears noting that in the introduction to the Fantasy rules, Gygax writes that:

Man-sized figures include: ghouls, heroes (including anti-heroes and super-heroes of the "Conan" type)... (p. 25)

And then near the end of these rules, under "Combination Figures", he observes:

There are certain natural, although rare, combinations. A good example of this is Moorcock's anti-heroish "Eric of Melnibone," who combines the attributes of the Hero-type with wizardry, and wields a magic sword in the balance! (p. 35)

Which gives some helpful literary references for exactly what Gygax had in mind for these mechanics.

### Original D&D

Finding the rule in OD&D is unexpectedly tricky, to the extent that it eluded me for several years. There's this in the Monsters & Treasures book:

Attack/Defense capabilities versus normal men are simply a matter of allowing one roll as a man-type for every hit die, with any bonuses being given to only one of the attacks, i.e. a Troll would attack six times, once with a +3 added to the die roll. (Combat is detailed in Vol. III.) (Vol-2, p. 5)
That's basically the same as the mechanic in Chainmail Fantasy -- but arguably only given for monsters. (Some but not all monsters in Chainmail worked that way: ogres, trolls, giants, etc.) Plus I've definitely never seen anyone run classic D&D that way for monsters. But, here we find it more explicitly in the D&D FAQ from the Strategic Review #2 (by Gygax in Summer 1975, one year after D&D's debut), in a combat example where a Hero fights ten Orcs:

Assume the following dice score by the Hero. Note that he is allowed one attack for each of his combat levels as the ratio of one Orc vs. the Hero is 1:4, so this is treated as normal (non-fantastic) melee, as is any combat where the score of one side is a base 1 hit die or less. Hero: 19; 01; 16; 09. Two out of four blows struck... (TSR #2, p. 3)

And in addition, it's somewhat cryptically given as an essential basis for the system in Gygax's Swords & Spells 1:10 scale mass combat rules for D&D another year after that -- given on page 1, in the second paragraph of the Introduction:

At the scale of these rules a single man can be represented by a single figure on the table. So if one opponent has a lone hero (4th level fighting man) facing several figures of men-at-arms (or orcs or similar 1 hit die creatures), an actual melee can take place. The hero will inflict .40 of the damage shown for a 4th level creature on the combat tables and sustain damage until sufficient hits are scored upon the figure to kill the hero. Similarly, if a 12th level fighter is involved he will score 1.2 times the damage shown and so on. (S&S, p. 1)

Again, it's not entirely clear here, but I have marked in the margin of my copy there so I don't forget any more -- Why would a 4th level fighter get 0.40 damage multiplier in this situation? If the tables are designed for 1:10 scale play (they are; you can check the math), and it's a "lone hero", then shouldn't they only get 0.10 of the listed damage? Ah, but the solution is: they're getting a multiplier to attacks equal to their level (4), exactly as in the FAQ example. And likewise the 12th-level fighter is getting 0.10 × 12 = 1.2 damage multiplier for the same reason. Puzzle solved.

Note that in both the FAQ and the Swords & Spells text, the attack mode is applicable to "1 hit die creatures", with an explicit example of it being used against Orcs. This sometimes unsettles players of later editions, where the benefit threshold was reduced to a lower value (see below).

Another thing we might observe, from the 12th-level example above, is the assumption of something like theater-of-the-mind combat happening here. If we required immediate adjacency of man-to-man scale figures for attacks (something required in later editions; see further below), then there's no way that a 12th-level fighter could be adjacent to 12 enemies all at once, and thus get a multiplier of 12 attacks every round. It's more likely there's an implied walk-and-chop-and-walk-and-chop going on here.

In conclusion (although I resisted it for quite some time), given that the rule is clearly in Chainmail, in the OD&D FAQ and supplementary materials, as well as in the later 1E AD&D, I'm now convinced that Gygax's intent was to have this rule consistently present throughout all those versions of the game.

Note: This [the standard fighter attacks-per-melee-round table] excludes melee combat with monsters (q.v.) of less than one hit die (d8) and non-exceptional (0 level) humans and semi-humans, i.e. all creatures with less than one eight-sided hit die. All of these creatures entitle a fighter to attack once for each of his or her experience levels (See COMBAT). (PHB p. 25)

In 1E, the rule is explicitly given as a core mechanic (although still easy to miss, buried as a footnote to a table at the bottom of the page after Rangers). It's applicable to any member of the Fighter class, including all of its sub-classes (so: Fighters, Paladins, Rangers; and later, Barbarians from Unearthed Arcana). And as alluded to earlier, a critical lowering of the threshold has occurred: no longer "1 hit die creatures", but here, strictly "less than one hit die". So the ability is usable against, say, Goblins, but not the Orcs used as the canonical example in OD&D material.

Occasionally there's some interpretation made here that, in terms of battling man-types, this represents fighters gaining an advantage over completely untrained combatants (hapless peasants), as opposed to trained soldiers. But, by the rules in the 1E DMG, mercenary soldiers also fall into this category -- including, for example, archers, pikes, and heavy horsemen:

Note that regular soldiers are 0 level men-at-arms with 4-7 hit points each. (DMG p. 30).

It should also be pointed out that near the end of this era (and overlapping with the next), TSR licensed the Advanced D&D brand to SSI to make their well-regarded Gold Box video games, and throughout those games this ability of the Fighter classes was referenced onscreen by the shorthand label, "Sweep Attacks". Players of those popular games are thus likely to remember the ability by that name.

As an option, a warrior fighting creatures with less than one Hit Die (1-1 or lower) can make a number of attacks equal to his level (i.e., a 7th-level fighter can make seven attacks). These attacks are handled in order of initiative. (DMG, p. 57)

Here's the same mechanic in 2E AD&D, now given as an optional rule, appearing only in the DMG. Again, it's distressingly easy to miss it, because it's tucked in at the end of a section titled, "Multiple Attacks and Initiative", and still not given any memorable label. Otherwise, it's identical to the mechanic seen in 1E (a fairly common situation for this ruleset).

It also bears noting that in the 2E Combat & Tactics supplement, among the extra optional rules given, there's one called "Heroic Fray" which gives a modified mechanic: when outnumbered by 1-hit-die types, fighters get double attacks, plus one more if holding a shield. I mention this because (a) it's given an official label here for the first time, which some players used thereafter, and (b) possibly because of that nifty label it sticks in people's mind, and some folks think that's the only place it appeared in 2E. (The OSR Hyperborea game calls the attack mode "Heroic Fighting", probably as an homage.)

### 3E D&D

CLEAVE  [General] You can follow through with powerful blows. Prerequisites: Str 13+, Power Attack. Benefit: If you deal a creature enough damage to make it drop (typically by dropping it to below 0 hit points, killing it, etc.), you get an immediate, extra melee attack against another creature in the immediate vicinity... (PHB p. 80)

GREAT CLEAVE  [General]
You can wield a melee weapon with such power that you can strike multiple times when you fell your foes. Prerequisites: Str 13+, Power Attack, Cleave, base attack bonus +4 or higher. Benefit: As Cleave, except that you have no limit to the number of times you can use it per round. (PHB p. 82)

3E D&D introduced the concept of "Feats": special powers that may be chosen as characters advance in level. Fighters get additional, bonus Feats (more than any other class), and the two listed above are on their Bonus Feat applicable list. That said, not every Fighter gets they power; they must make a deliberate choice to pick up the ability. At the earliest, a Fighter might have Cleave at 1st level, and Great Cleave by (you guessed it) 4th level.

Most of us interpret this as a reworking of the rule from earlier editions; if a Fighter (with the Feat) battles very weak creatures, then they're likely to get a chain of attacks that puts many of them down. And many of us prefer the continuity of this mechanic -- unlike in 1E, where there's a huge quantum collapse between fighting "up-to-7-hp" creatures vs. "up-to-8-hp" creatures, the benefit here will more smoothly be usable against 2 HD or 3 HD creatures, just less frequently.

In addition, there's another high-level Feat in these rules called Whirlwind Attack which gives one melee attack against each adjacent opponent in a round, which I think would be equally eligible for the "heir to sweep attacks" title. But in hindsight it's the Cleave terminology which got the most mind-share (e.g., note the title of this blog, and see more below).

### 4E D&D

Cleave | Fighter Attack 1
You hit one enemy, then cleave into another.
At-Will | Martial, Weapon
Standard Action | Melee weapon
Target: One creature | Attack: Strength vs. AC
Hit: 1[W] + Strength modifier damage, and an enemy adjacent to you takes damage equal to your Strength modifier. Increase damage to 2[W] + Strength modifier at 21st level. (PHB p. 77)

Sweeping Blow | Fighter Attack 3
You put all your strength into a single mighty swing that strikes many enemies at once.
Encounter | Martial, Weapon
Standard Action | Close burst 1
Target: Each enemy in burst you can see | Attack: Strength vs. AC
Weapon: If you’re wielding an axe, a flail, a heavy blade, or a pick, you gain a bonus to the attack roll equal to one-half your Strength modifier.
Hit: 1[W] + Strength modifier damage. (PHB p. 79)

Surprised to see me covering 4E (I think for the very first time)? Yeah, me too. Again, thanks to the wonderful WDMs helpers to lead me here.

In the 4E rules, if you don't know, every character class gets a menagerie of powers to pick from, about as deep as the wizard's spell list. In the Fighter's case they're called "Exploits". Note that the very first Fighter Exploit listed in the book is that "Cleave" ability. If chosen, this can be used every round at will; it provides the ability to make a normal hit against one target, and then get some more damage, equal to the Strength bonus, against a second adjacent enemy. At first blush, that may not seem like much, but recall: 4E has a rule for "Minions" where low-level types are all assumed to have 1 hit point by default. So in this use-case that Cleave ability is basically always a 2nd free kill. (Thanks, Ash!)

And the next thing that strikes my eye is the 3rd-level power "Sweeping Blow". Of course, the name of this exploit hearkens back to those AD&D Gold Box games. Note the attack type is given as "Close burst 1", which means that the attack effect is applied to every target immediately adjacent to the Fighter in question. To me, that seems like the closest analog to the original ability. (And the ability in the AD&D Gold Box games also required adjacency, as characters were portrayed miniature-style on a grid.)

There are other powers at higher levels which expand on this ability: "Come and Get It" (7th level), "Shift the Battlefield" (9th), "Thicket of Blades" (same), "Vorpal Tornado" (17th), "Devastation's Wake" (19th), "Warrior's Urging" (23rd), "Cruel Reaper" (27th), etc. -- these work in a similar "burst" fashion, and add on effects like allowing the Fighter to move between attacks, to pull more enemies into their burst, to add conditions like more damage or paralysis, and so forth. But I feel like "Sweeping Blow" is the basis for this system (the first available "burst" attack).

### 5E D&D

Cleaving through Creatures

If your player characters regularly fight hordes of lower-level monsters, consider using this optional rule to help speed up such fights.

When a melee attack reduces an undamaged creature to 0 hit points, any excess damage from that attack might carry over to another creature nearby. The attacker targets another creature within reach and, if the original attack roll can hit it, applies any remaining damage to it. If that creature was undamaged and is likewise reduced to 0 hit points, repeat this process, carrying over the remaining damage until there are no valid targets, or until the damage carried over fails to reduce an undamaged creature to 0 hit points. (DMG p. 272)

In 5E, the status of this rule somewhat reverts back to that of 2E; it's only an optional rule, but if utilized, then every Fighter in the game has it by default -- well actually, every character has it by default here, even non-Fighter-types; but my point is that PCs don't pick it from a list of options as in 3E or 4E.

Other than that, the mechanic is quite different from early editions. 5E tends to be amenable to giving PCs two attacks per round, maybe three at most; but tries really hard to otherwise limit the number of attacks or rolls made in a turn. In that light, the possible multiple-hits are all adjudicated off a single d20 attack roll, and spreads out a damage roll only to creatures that are all insta-kills. There's an echo of the 4E version of the Cleave Exploit here (as well as other higher-level powers).

Note that the option seems to be reserved only for "player characters". That's not generally a clause you'd find in a rule from classic editions, and Gygax (at least in his writings, e.g., around saving throws or critical hits) would frequently emphasize giving monsters a fair-shake, i.e., grant any general benefit that PCs get to monsters as well. In any case, this flips one possible reading of OD&D Vol-2, where monsters get the benefit and PCs don't.

### Basic D&D Line

Let's not forgot that through the 1980's and into the 1990's there was a parallel ruleset, the "Basic D&D" line, being published alongside the flagship Advanced D&D line. This includes the Holmes Basic, Moldvay/Cook B/X sets, and Mentzer's BECMI line. All of those were boxed sets that could be sold in mainline department and toy stores, whereas the AD&D rulebook line was all hardcover gaming books, generally for specialty stores (broadly speaking). The Basic line, I think, is concurrent with the biggest "spike" of incoming players in the D&D boom-fad circa 1980-1981. There are a few Dragon articles by Gygax around the time where you get a whiff of surprise/grief that the Basic line is far outselling his  magnum opus AD&D line.

Anyway, my point is that lots of classic D&D players started with the Basic set and are most familiar with those rules (assuming they didn't mix-and-match to the point where they can't tell the difference). Where is the cleave/sweep rule in that line?

Well, in this one case there isn't any, no matter where you look (and I've looked in all those dozen or so revised rulebooks trying to find it). Why is that? I'm not totally sure. You could say as a principle that while other editions were usually fairly generous about giving Fighters some way to get multiple attacks per round, the Basic line simply wasn't (outside of magic like haste). Maybe that's because the initial Basic set only covered levels 1-3, and such a benefit wouldn't really show up at those levels. Or maybe because Holmes was mostly just copying text directly from OD&D and its supplements -- not looking very much at Chainmail or AD&D, even for things that might be implied in Gary's mind by reference (also e.g.: dragon fear & detection abilities) -- and the one and only place the cleave/sweep rule is not given explicitly to PCs is in the OD&D LBBs.

I asked Frank Mentzer about the status of the "sweep attack" type mechanic in his games on Facebook, and he kindly replied:

So Frank is (1) quite intentional about the rule status, (2) faithfully applies it in an AD&D game, (3) doesn't like it, and (4) tends to be sensitive about monsters getting equitable rule benefits compared to players (likewise as noted for Gygax above).

As an aside, you really have to hunt in Basic/BECMI to find any way for PCs to get multiple attacks without magic. There's a loosely suggested rule in Cook Expert (p. X8), pending release of a future Companion rule set, that Fighters might get a 2nd attack starting at 20th level (and more at 25th and 30th; maximum 4 attacks per round). But that rule is not part of the Companion rules when Mentzer finally publishes it.

What Mentzer's Companion Rules set (for PC levels 15-25) does have is the following. Fighters who have sworn fealty to another ruler (either to serve as a wandering Paladin/Knight/Avenger, or as a ruler in a feudal network) get this combat option:

Multiple Attacks: The character gains this ability at 12th level. Demi-humans gain this ability at certain XP levels, as given in the class descriptions. If the character can hit an opponent with a Hit roll of 2 (calculated including all adjustments), he may make 2 attacks each combat round. At level 24 and higher, he may make 3 attacks; at level 36, he may make 4 attacks each round. This applies to ideal circumstances, and the character may use movement or some other action instead of an extra swing. (Player's Companion, p. 18)

I suppose if you squint really hard, this ability -- only usable if the PC basically auto-hits the target -- kind of has whispers of a more-attacks-against-very-weak-enemies concept? But of course it's based on armor, not hit dice or hit points, and the number of attacks given is still really very small. (Compare: In Swords & Spells a 12th-level fighter can get a multiplier of 12 to attacks; here it's just 2.) It does echo Cook's earlier proposal in that it has a top-level limit of 4 attacks per round.

Up in the Master's Rules (for levels 26-36), there's an option where the DM might just let a character get one extra attack by wielding a second weapon in the off-hand, at a -4 penalty and loss of one mastery/specialization level there. And there's also an added piece of specialty equipment: a shield with one of various attached weapons (horn/knife/sword), which permits one extra attack per round with it. (Frank is really stingy with the extra attacks.)

### Conclusions

I've been focusing on this lately because (1) honestly I overlooked this rule in my OD&D games for a long time, and (b) I now think it's the single most essential mechanical difference between the Basic and Advanced D&D lines from the 80's.

In Original and Advanced D&D, the standard monster numbers appearing (by default for wilderness encounters per the texts there) zoomed up into the hundreds for humanoids like men, kobolds, goblins, orcs, hobgoblins, dwarves, gnomes, and elves -- all types that were originally 1 base hit die. Anything else only had numbers up to 20 or 30 at most. There's fairly good statistical evidence that was done as a balancing factor in light of high-level fighters putting down many such targets per round. In fact, we're told that Arneson specifically used the listed numbers appearing as the trigger for fighter cleave/sweep attacks -- if the numbers were in the hundreds, then fighters got their turbo-attacks.

On the other hand, in the BX/BECMI line, where the cleave/sweep rule is absent, then the designers (starting with Moldvay/Cook) were compelled to radically reduce the humanoid numbers appearing. This averaged by a cut of roughly 1/10th from the O/AD&D wilderness numbers (a division factor of from 3 to 13 depending on type). The most numerous monsters are goblins and orcs, who may appear in an outdoor band of up to 60. (Note that Holmes dodged this by not listing any standard numbers in his stock monster list; and the Expert rules have some text notes that camps of men, et. al., may be in larger OD&D-scale numbers.)

Anyway, players who switch between the Basic and Advanced games (and it was very common to mishmash the rulebooks together in play) are likely to be the most surprised by the sudden appearance or disappearance of the critical cleave/sweep rule. In our video discussion (at top), this was true for me & Paul, with me coming from more Advanced play, and Paul having more Basic line experience.

But it's a core part of how combat and encounters were structured in the root of the game back in O/AD&D, and that legacy is so strong and deep, that indeed it has appeared in some form in every edition since, up to the current day (Basic offshoot excepted).

For my games going forward, I do need to make a decision for my brand of OD&D games: Incorporate the sweep/cleave rule for fighters, or some variant, or do some radical surgery on balancing encounter numbers (like the cuts done in B/X)? Which form do you like best?

(And phew, thanks for reading all that. There's been a lot of editions at this point!)

## Saturday, May 22, 2021

### Book of War Test Units for May

We're continuing with our Book of War Playtests on the Wandering DMs channel Saturday nights. And we're getting some great feedback from our viewers and patrons. Here's the current list of units in play after a few recent refinements. Recent changes include the following:

• We're not showing the big flying units at this time (eagle riders, griffon riders, wyvern riders). We've found in recent playtests that the aerial movement is hard to adjudicate over other units and terrain, the very high costs are stretching the system to the limit, and there's a question about whether it makes sense at all for the presumed flyers fighting in formation. They may return later as a special option or maybe solo figure types.
• The Goblin Wolf Riders had their movement bumped up from 12" to 18". There's an interesting range of variations for wolves in classic D&D, actually: e.g., Chainmail says they're as Medium Horse (18"), unless mounted by Goblins, at which point they're as Heavy (12"). Note that other mounted types don't show a difference in their D&D natural movement and when mounted as cavalry. I've been convinced by patron seeker that it's a bit more interesting to have them at the higher base D&D move rate of 18" (as seen in B/X, AD&D MM, etc.), so we'll be testing them at that rate.
• I granted an extra morale bonus to the Men Elite Foot, largely because they stuck out awkwardly on the list with no special abilities at all, and it echoes the classic Chainmail/D&D trope of knights having extraordinary morale.
• And I got the formerly hidden column listing presumed figure Width in view (by abbreviating some of the column headers), for what that's worth. Note there's some advantage to a small unit figure, because you can pack in more melee attacks against an enemy in the same space, and reduce incoming melee attacks the same way (by a little bit). E.g.: It goes towards justifying why light-foot Goblins and Orcs are at the same price, even though Goblins are slower but otherwise have the same statistics. This entry is in units of a quarter-inch.

Note also if you're a Wandering DMs Patron, we're currently running a Patron's Pick option where we'll randomly pick armies from those proposed on our Discord server for the next live show. Choose wisely!

And: Any other ideas for things that should be further refined?

## Monday, May 17, 2021

### Exploding Dice Statistics

In January, after our Wandering DMs show on critical hits, someone in the patron's after-party chat (Joshua, but you knew that) suggested replacing Nat-20-triggered criticals in D&D with exploding damage dice all the time. It's not something I ever considered for D&D, but the statistical niceties of that immediately got stuck in my head. Let's look at that a little more closely. (Someone's probably already done that in the past, but as they say: "This is my blog; there are many like it, but this one is mine," or something.)

### A Formula for Exploding Dice

I wanted a simple, closed formula for the expected (average) value from rolling any variety of exploding die. Here you get some math so I can show my work.

The essential trick/insight/tactic is this: Say we want the expected value E of an exploding d6. There's a 1/6 chance of getting any of the values 1, 2, 3, 4, 5, and then at the end, a like chance to get a value of (6 + E); that is, 6 plus the average result of the same process all over again (recursively, if you will). More generally, for an n-sided die, you have a 1/n chance for each value 1, 2, 3, ... , n − 1, (n + E). Some basic algebra solves for that E:

$$E = \frac 1 n (1) + \frac 1 n (2) + ... + \frac 1 n (n+ E)$$

$$E = \frac{1 + 2 + ... + n} n + \frac 1 n E$$

$$\frac{n - 1} n E = \frac {1 + 2 + ... + n} n$$

$$E = \frac {1 + 2 + ... +n} {n - 1}$$

Note in the 3rd step we subtracted $$\frac 1 n E$$ from both sides, generating on the left-hand side a value of $$E - \frac 1 n E = \frac n n E - \frac 1 n E = \frac {n - 1} n E$$.

What other ways of writing this are there? That top sum 1 + 2 + ... + n has a name, specifically the (nth) triangle number, which could be denoted simply $$T_n$$. It's like the factorial function, but with adding instead of multiplying; and it's sequence A000217 in the Online Encyclopedia of Integer Sequences. So we could just write:

$$E = \frac {T_n} {n-1}$$

If you don't like that (and how dare you), we could use what I refer to as the Gaussian formula to replace it with more primitive operations; $$T_n = \frac {n(n+1)} 2$$. Substituting that into our formula for E, we get this version of our exploding-die expected value formula:

$$E = \frac {n(n+1)} {2(n - 1)}$$

Note that the expected value for multiple dice is this number times the number of dice; e.g., for 3d6, just compute E for n = 6 and then triple it (expectation always being a linear operator).

### A Table of Exploding Dice Values

Here you have a table of expected values for our standard mostly-Platonic dice, in both the normal-roll and exploding-roll forms. Consider the ratio column at the end, which shows the effective multiplier that exploding is giving you on average. The benefit is best for smaller dice; e.g., for a d4 you're multiplying your expectation by 1⅓, and then it goes down for larger dice. And yet this benefit doesn't flip the ordering of any dice; the benefit on d4 (which I kind of like, say, making daggers a bit more fearful) doesn't even reach the expectation for a standard (non-exploding) d6.

That said, watch out that things get weird in the edge-cases if you go off the top or bottom of this table. If you have 2- or 3-sided dice mechanics, those exploding expectations are actually the same: E(d2exp) = E(d3exp) = 3. And theoretically an exploding 1-sided would generate infinite damage! (E.g., consider the "ordinary rat" by Gygax in the AD&D MMII with that damage specifier; the standard 1st-level adventure just got a lot more dangerous.) On the other end, larger die values have a benefit ratio decreasing towards 1; in the limit for an infinite-sided die, there would be no benefit at all (uh... not that you'd need any).

Note that the ratio of exploding-to-normal damage expectation has a nice, short formula for it. (Thanks to Drew on Twitter for noticing this from the decimal values above.) This is:

$${n(n + 1) \over 2(n - 1)} \div {n+1 \over 2} = {n(n+1) \over 2(n-1)} \times {2 \over n+1}$$

$$= {n \over n-1} = {n - 1 + 1 \over n-1} = 1 + {1 \over n-1}$$

### Graphs of Exploding Dice Values

Here's the other thing that I think is really nifty about the exploding-die mechanic; the distribution becomes right-skewed (instead of uniform, or bell-shaped for multiple dice). Here's the probability distribution for an exploding 1d6 (from Troll Dice, turned on its side for more familiar presentation):

And possibly more illustrative, here's the chart for exploding 2d6 (like the damage for giants in Original D&D):

Note how that slopes off gently on the extended right-hand side. My understanding is that right-skewed distributions like this are far more common (really, the only thing) for natural or biological processes -- you have a hard lower limit (often 0 or 1), but in theory no hard upper limit (on the right), and therefore the population/sample-space spreads out in exactly this way.

In fact: The famed evolutionary biologist, Stephen Jay Gould, wrote an entire book dedicated to exactly this observation: it's called Full House: The Spread of Excellence from Plato to Darwin.

Are those compelling results? (And did you already know that?)  Would you consider using always-exploding weapon damage dice in your D&D games, instead of a Nat-20 trigger?

## Monday, May 10, 2021

### Ability Modifiers in Immortal Rules

Occasionally I gripe about the slightly unfortunate pattern of standard ability score modifiers chosen by Tom Moldvay in the B/X rules. I mean: On the one hand it's kind of fun (you can get a +3 bonus but only at the perfect score of 18). It sort of has the feeling of reflecting a bell-shaped distribution; but in so doing it actually over-amplifies the effect. (Example gripes part way through our recent Wandering DMs show on 50 Years of Chainmail). Moreover, at some point for a variety of reasons you're going to want to expand the possible ability scores to higher numbers, and then the pattern doesn't scale well. As a case study I refer to the ability modifier table from Frank Mentzer's Immortal Rules, the final boxed set in his BECMI D&D line (1986), which expands the possible ability scores from 0 to 100:

As a someone slightly spectrum-gazing, that makes me really unhappy. Note you have that 18 score with a span of just 1 pip for the +3 bonus. Then the ranges re-expand to spans of 2, 3, 4, 5, 6, 7, 8, 9 (in the category of 54-62), and then start contracting again, to spans of 8, 7, 6, 5, 5, 4, 2, 1, and 1 again (the last two for the 99 and 100 scores, of course). Here it is in chart form:

Urgh, that bimodal distribution makes me feel like I've swallowed something very bitter.

I do think a better solution is to pick a standard class-width which allows you to predictably extrapolate to whatever point you might desire. This could be the 2-pips per bonus bump as seen in D&D from 3rd Edition (and echoing the way skill bonuses worked all the way back to 1E OA), or it could be the 3-pip ranges that I use in OED (which in my analysis is the best reflection of OD&D bonuses -- also has the statistical nicety that it reflects the z-score of a given ability versus the 3d6 population distribution, but don't worry about that too much).

(Side note: The Immortal Rules boxed set was the only D&D product I ever got which resulted in me returning it to the store. Partly for novelties like this, and that it's largely a totally different game; PCs simply discard whatever traits they had previously, etc.)

Can you think of any better way of expanding the Moldvay B/X ability modifier table than what Mentzer came up with here?

## Monday, May 3, 2021

### Richard Garfield: Getting Lucky

Game Developer magazine was a publication for professionals in the video game industry that ran from 1994 to 2013. It was a pretty big deal at one time, with postmortem development-process analyses by developers of some of the largest games, annual surveys on salaries and tools, cutting-edge technical tips, and so forth.

My favorite article was published in the November 2006 issue, written by Richard Garfield, the creator of Magic: The Gathering. (Have I mentioned that the 2nd company I worked for, where I first met my good friend Paul, came in 2nd in a bid to make MtG Online? Maybe another time.)

This article, titled "Getting Lucky", became one of the most influential insights that affected my game development ever since. I found the argument to be completely compelling, and an invaluable call-out to a significant risk in the ways that games evolve over time. Garfield has said similar things in other interviews, videos, lectures, etc. since, but -- people of the written word as we are in these parts -- I find that this presentation he personally crafted in writing to be the clearest and starkest communication of the idea.

Many times over the years I've wanted to share a link so others could read Garfield's "Getting Lucky" -- but was always frustrated that it appeared nowhere online, and seemed to have just dropped off the planet or anyone's awareness. Finally. I'm just going to post it here, so it can be shared with others, as it so highly deserves to be.

The article's introductory section says this:

I can find a board or card game for any group of players. Game players or people who never played games, old or young, in large or small numbers, with confrontational or passive personalities—there are games out there for them all. While I weigh many factors in choosing a game, by far the most important is the amount of luck inherent to the gameplay. If the game has a lot of luck, it usually appeals to a diverse group. Games in the non-electronic world are widely varied in luck, but computer games are a different story, as very few of them allow any real chance for a beginner to win against a skilled opponent. The number of electronic games I can play with my parents, kids, wife, or friends from outside the game industry is extremely limited.

Historically, games usually evolved in such a way as to reduce the amount of luck in them. Even chess at one time had dice. The people who are in a position to modify a game are likely to be very good at it, and the sort of modifications they will be drawn toward are the ones that showcase their talents and their friends’ talents—although they, of course, are all top players.

In other words, as games evolve, they tend to become better for the experts, but not necessarily better for new or non-dedicated players. A game that illustrates this conflict is Settlers of Catan, one of the best-selling board games of recent years. The only consistent criticism I have heard leveled at it (always from dedicated gamers) is that it has too much luck. But it’s rather possible that the abundance of luck is exactly what made the game so wide-reaching.

Enlightened players, skilled or not, will appreciate luck in their games for a number of reasons. First, they can play challenging games with a much broader audience, allowing them to easily assemble a galley of players and lure their friends, who would otherwise play something else, into the game. Second, if skilled players want to experiment and try off-the-wall strategies, the more luck a game has, the more forgiving it is — after all, no one is expected to win every time. The only cost of all these terrific benefits is that skillful players must manage to swallow their pride and settle for winning a majority of the time, rather than all the time.

We gamemakers are at a special time in game history. Fifty years ago, games were made with no credit to the designers or perhaps had no designers at all, with changes being wrought by players over time. But our nascent game design community tends to comprise game experts; it’s in our best interest to examine our own instincts openly with regard to how much luck should be in a game.