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.

1E AD&D

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.

2E AD&D 

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 the 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).

(Now, it's possible that I may be misinterpreting those listings! Please leave a comment with a correction if you have any.)

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). Although this author might counter-argue that the balancing factor in O/AD&D is the monsters appearing in huge numbers (hundreds) if they're susceptible to sweep attacks.

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!)

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?

Book of War Units v.210521

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?

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?

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.

For the purposes of comment, criticism, scholarship, and research, here's a link to the full article. You should read it! And then leave a comment (or a piece of criticism, scholarship, or research) on your takeaways from Richard Garfield's observations here. 

Richard Garfield: Getting Lucky

Shooting at Groups

For your consideration: Here's a new rule I recently drafted for my OED House Rules to handle shooting into large groups of combatants (like into a melee, or an advancing goblin horde). I'm actually kind of delighted by it, but I fear I might be the only person willing to actually implement it.

First, recall a few things about how I run my OD&D. I use a ranged modifier of −1 per 10 feet distance, because that matches a rather large amount of research we've compiled on the blog in the past. Second, I'm working on the continuing project to dial in mass-warfare mechanics well for the Book of War game (hopefully in an upcoming 2nd edition). 

Both of these goals span the man-to-man case and huge-army cases. An aphorism I now use as foundational is: Shooting a man at a hundred yards is impossible, while shooting an army is certain success. (Practically speaking.) Previously in OED I had two different rules to handle the two different cases. The binary switchover has troubled me for a while, and raised a few reasonable questions recently. (I dare say in my head this echoed the conflict in physics between relativity and quantum mechanics.)

So I did some computer simulations and scribbled out some math (I'll spare you that here), and then realized that I could round things off to a rule I could hold easily in my head, and give a smoothly continuous switchover between the two cases. So here's what I just edited into my next draft of the OED rules. First:

Errant Shots

Errant Shots: Fumbled or random attacks into groups are assessed with a d20 roll that ignores attacker skill and range modifiers.

Like the text says, this is a mechanic that I will (and have in the past) used for a few different cases. If someone gets in a fumble situation where they attack themselves or a friend, we invoke this. (Rules where a fumble results in automatic-damage against a heavily armored ally have always ground my gears, or even a normal attack roll as if the fumbler was aiming the perfect attack against a weak spot.) Also a shot against a faraway, large group will trigger this mechanic. (Likewise: close-up an archer should be able to target a vulnerable point on the target, whereas far away this level of skill is impossible.) 

To be clear, in an "errant shot", the attacker's base attack bonus gets ignored. I would want to apply the defender's AC as usual, and I guess also any weapon-vs-armor effect, and magic as well. But to date any time this has happened for me it's just the player rolling a raw d20, and me applying the defender's AC (under the standard Target 20 resolution process). Now consider this:

Shots at Groups

Shots at Groups: Attack rolls (including range, but before AC addition) below 10 miss a man-sized target. Each adjacent man gives a 1 pip chance under 10 to trigger an errant shot against a random target in the group.

As usual, I write that with some curtness in the document. What that means is for a close group of N man-sized combatants, the DM computes 10 − N, and an attack roll from that number up to 10 indicates a shot that completely missed the individual target -- but, close enough to possibly strike someone else nearby (randomly determined, and adjudicated the with the "errant shot" rule above). Some examples:

• Say an archer shoots at an opponent in melee with a single one of their friends. Then a modified attack roll (again: including range but before target AC is considered) of exactly 9 -- no more and no less -- triggers an errant shot against the friend.
• Next, the archer shoots at a squad of 5 men-at-arms approaching angrily. In this case an attack roll of 5-9 results in an errant shot check against a random one of the men.
• Ten goblins are running together down a hallway and the shooter makes an attack. Now an attack roll of 0-9 results in an errant shot.
• A formation of 20 orcs is posted outside a cave. In this case, any modified attack roll from −10 up to 9 triggers an errant shot. 

As you can see, for very large groups at very long range, the mechanic makes it more and more likely that an errant shot against a random target will be invoked. Obviously, the DM should be encouraged to round these numbers off to convenient values -- myself, I'd probably round it to units of 1, 2, 5, 10, 20, etc. I've set it up so the lower bound is found by subtracting from 10 to make it as easy as possible. 

Moreover, the DM should be encouraged to invoke the errant shot rule immediately if it's clear that the shooter simply can't hit an individual man-sized target at the range in question. As a quick rule-of-thumb, if the range penalty is 10 points more than the shooter's fighter level, then they pretty much can't hit anything without a natural 20 (and you should just break to the random shot immediately).

To be completely clear, we're assuming that attack rolls that score 10 or higher are actually on-target, but are fended off by the person's armor if the final resolution (including AC) fails to indicate a hit. Note that this mechanic simulates attack values just a bit below hitting as indicating arrows zipping close by the target (the lower the roll, the further away). And it also allows you to separate out the effect of a critical-miss (natural 1), if you so choose. 

Let's momentarily consider a possibly alternative rule that comes to mind: If a shot doesn't hit, then a natural die-roll in the range from 1-N against N men triggers an errant shot (ignoring natural-1 fumbles momentarily). Seems nice. But the problem here is that it loses visibility of the range in which the shot was actually on-target but stopped by armor (which should be significant for heavily-armored figures). I suppose you could say that a roll of 1 - N (for N men) triggers an errant shot, unless the modified roll is in the range of 10 + AC to 20, in which case it was stopped by the original target's armor. But now you're tracking two different ranges instead of one, and that seems worse to me. (Plus this implies that both very high and very low rolls indicate close-to-the-target shots, while rolls in the middle indicate shots further away, which feels confusing and wrong.) So I would shy away from that alternate proposal.

Aside from all that, another thing that fairly excited me was that the same piece of math that generated this rule also spawned a really nifty rule for handling missile shots in Book of War at targets of unusual size, like solo heroes on the field -- but more on that later.

What do you think of that rule? I've used what I'm calling the "errant shot" mechanic before, but haven't tested the "shots at groups" at the table before -- but I'm pretty confident that would work for me. Would you want to try using that? Anything I could improve in the explanation?

Rumors, Information, and Legends

Original D&D has what I think is a marvelous little rule about gathering news, baked right into the core books (Vol-3, p. 23). This didn't get copied forward into any later edition, and it's at the bottom of a certain page in the DM's booklet, amidst unrelated information about hiring specialists and men-at-arms, so I think it's commonly forgotten. Here it is:

Obviously that's just loosely suggestive of the content of the news, and DMs can move in whatever direction they want with that. Reading it closely right now, I'll point out that the opening "Such activity as advertising" is referring to the immediately preceding section on advertising to hire men-at-arms and specialists ("Post notices in conspicuous places, stating the positions open and who is offering such employ; or have servitors circulate in public places, seeking such persons as are desired.") So read narrowly, the first 3 sentences seem to be thinking mostly about notable PC activity in town (maybe planning for competing groups of PCs keeping tabs on each other in a very large campaign?); and then very last sentence on legends seems to be a different thing ("to lead players into some form of activity"). 

So in my last campaign, I used this to basically drive all the action that was happening. Aside from the very opening of the campaign, there were no quests given, hiring boards, adventuring patrons, etc., unless the players first paid to gather rumors at the local tavern. So most sessions would open up with PCs going to the tavern with their current funds and gathering some new rumors this way (I charge the higher cost, 10-60 gold pieces based on a die roll; or in my silver-standard campaign, the analogous 10-60 silver pieces). I kind of like the flavor of this, of the PCs being essentially proactive in their nosing around for opportunities for loot and magic to steal from somewhere, and not an economy where "adventuring" is some kind of recognized industry. Also it kind of feels like an ante or blind payment before a hand of poker gets started.

Now, this keys into the trope that many early D&D adventure modules have, of a "list of rumors" table near the start of the adventure, which get handed out partially to PCs at the start, usually at random. (See D&D modules B1, B2, Top Secret TS001... and many retro-products like the DCC line and Rappan Athuk, etc.) Of course, the requirement for advance payment was already lost by the time published adventure modules became a thing -- and in some sense it makes sense for 1st-level characters in these cases, likely cash-constrained, to get a few for free to get started.

So I tried that same idiom in my campaign; drafting a list or lists of rumors, and dicing for which one to give out when the PCs went rumor-gathering. This attempt initially had a few problems, and I had to evolve it a bit before I got to something that seemed to work.

First, an early attempt had mostly "vague oracular idea-generators", that I probably yanked off an online adventure generator. The problem is that in-game I didn't own these, didn't really have a concrete idea on how to back them up, and they were usually so overwhelmingly weird and enticing that the players generally would pursue them exclusively, and not go anywhere near content I'd actually prepared. My attempts to fill in those ideas on the fly weren't that great (maybe not my forte, or I wasn't truly interested in them).

Second, after that, I started writing custom rumors about campaign locations that I had prepared. The problem here is that over a campaign, any list I'd write would get depleted relatively quickly. Do I just repeat the same rumor if it gets re-rolled on the table? Players felt deflated from that. So then I was crossing stuff off the table, and over time rolling more and more dice to get to an unused option. In either case, at some point the list would be totally used up. So then I was committing to writing a new rumor after a session to replace any that was shared, and my hand-written list started getting more and more cramped with overwritten replacements and the whole thing became totally unreadable. Ugh. 

Finally, I threw in the towel on that and decided to systematically improvise rumors about existing locations anytime they came up. This seemed to be what clicked, and I got at least a few compliments about how this felt in-game. The essential idea was this:

• Roll a random location (which already exists in the campaign).
• Roll for a true or false rumor: 2-in-6 it's false (based on the proportion seen in the B1, B2, TS001 lists).
• Improvise the delivery of some detail in that location, and who in the tavern is telling it.
• In any case, make sure that the detail given is something that will drive the action (an enticing true or false treasure, a promising strategy against some monster or trap, etc.)

So with this, I had an infinite-rumor generator that worked pretty well, and required no advance work or documentation. It also seemed that my "creative juices" flowed a lot better to fill in the rumor while my adrenaline was up mid-game, versus when I'd try to write stuff pre-game by myself at home.

What counts as a "location"? Well, you can shape that to taste (and I modified it over time). Some things I did:

• When the action is mostly focused on a megadungeon, I'd roll for a random level, and then roll for a random location on that level. Or: maybe roll for the "current" level the PCs have recently been exploring, plus the next 1 or 2 (i.e., a d3 for level). That can keep it a bit tighter to things the PCs can achieve mid-term.
• In the wilderness, roll for a numbered encounter location, and drop some tidbit about that place.
• Sometimes I would even drop information about custom game rules in use for in the campaign that the players would be unlikely to know about. (Stuff of interest here would be bulleted in advance.)
  
• Or, obviously, a combination: I think at one point I was dicing 1-3: megadungeon drop,  4-5: wilderness, 6: rules info.

This seemed very elegant to me, and it's what I'm still using today.

A couple other notes:

• On the theme of game rules that "players would be unlikely to know about", note that this Rumors rule is itself in that class. It's both (a) hidden in the DM's book, and (b) not in any edition but Original. So make sure this is communicated to your players. Personally, I hand-added it to the Basic Equipment and Costs table. Then, I let my players "discover" the extra thing in the stuff-to-buy list, which was a nice moment (obviously if your players aren't as observant as mine, modify that).
• This, combined with the monthly upkeep costs (OD&D 1% of XP per month), plus payments for healing potions, are the primary ways that extra cash gets sucked out of the PCs' pockets, and I think it worked well. Depending on success at the game, some PCs could get a nice store of jewelry, while others were begging for help at the start of each session from the richer ones (in a campaign that went up to about 6th level).
  
• Note that this is sort of the inverse of the popular "carousing" rules. My method here happens at the start of an adventure, and directs PCs to some location that's already detailed in the campaign by the DM. Carousing rules, of course, are used at the end of an adventure, and (in the vague not-owned-by-your-campaign sourcing) generate ideas for new or improvised adventures. For me, I really prefer the flow of my rumors system better. And I really don't want to be handing out hundreds of XP based on a random roll outside of an actual adventuring session. Obviously your mileage may vary, and many people really really love those carousing rules. 
• Also it differs from something like Justin Alexander's proposed Urbancrawl system, which creates a very elaborate, and very detailed, matrix of interconnecting relationships that one must work in a network to get information out of the town setting. My system here abstracts almost all of that away; I tend to make up a "character telling you this" on the fly, but you could skip even that and just say, "you hear that...".
  

Would you try something like that, or have you in the past? Tell me about your experiences!

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