## Monday, September 18, 2017

### Turnbull's MonsterMark System

Following on from the discussion of systematized EHD (equivalent hit dice) last week, let's look at a much earlier attempt at the same idea. In the first three issues of White Dwarf magazine, Don Turnbull presented a measurement he called "The Monstermark System". This would be through the summer and fall of 1977, that is, exactly 40 years ago as I write this. (Thanks to Stephen Lewis for the tip-off to these articles!)

In the third article in the series, Turnbull writes:
Although it has been said by quite a few D&D addicts that the Greyhawk system of experience points, which is based on monsters' hit dice, is too stingy I don't think this is something which can be considered in isolation...  So, circuitously, back to experience points. In my view they are intended to reflect risk. A character gets experience for meleeing with a monster because there is a finite, non-zero, risk that he will be killed or at least suffer wounds which could contribute to his eventual death. He gets experience for gold because he has taken risks to grab it... He should not, however, get experience for finding a magic sword or that seven-spell scroll since these things will assist him in getting experience by other means... Since the whole point of the Monstermark is to measure the risk inherent in tackling a particular monster, experience points should bear a linear relationship to M...
I fully agree with those observations, and my motivation for EHD is exactly the same: to provide a measure of risk, from of which we can support a simple, linear calculation for experience points. We both assume a protagonist fighter with a fixed armor type, shield, and a sword; we both give the fighter one attack per round. Now, the basis of his system is this: for the default fighter, compute the expected amount of damage he would expect to take fighting the monster (assuming the combat never ended from the fighter's death). In this case, the calculation is done by first computing the number of rounds the monster would expect to live (D); and then multiplying that by the expected damage per round (analogous to the DPS -- damage-per-second -- statistics in MOORPGs) for an overall aggression level (A). In the first article, Turnbull presents it like this:

This seems like a solid, undeniably valid base measure of monster risk level. As long as the monster has no special abilities. Which is, as you know, almost none of them. As soon as a monster has special abilities, then Turnbull is forced to step out of the methodical expected-value analysis and revert back to a purely discretionary set of multipliers, hoping to estimate the power of various abilities, to get the final MonsterMark score (M). As he writes, "All this is very subjective and I would be surprised not to meet with different views, but the following bonus relationships seem to give results which instinctively 'feel' right:"

Now, if you take nothing at all but one thing away from this blog, I hope that it's this: these kinds of a la carte scoring systems for game entities are always a lost cause.The inter-relationships of different abilities and powers are too complicated to be encapsulated in such a system; the true acid test can only be made by systematic playtesting (which is very hard).

Consider a few short counterexamples -- A giant rat given magic-to-hit defense is effectively unbeatable by the PCs it normally fights; but a very old red dragon, given the same ability, would have little effect against its high-level opponents (surely wielding magic weapons already). If ghouls have possibly paralyzing attacks, then it makes a huge difference if they have one attack for 1d6 damage, versus three attacks for 1d2 damage (even with nearly the same expected damage). Centipedes and carrion crawlers, with a base damage of zero, even with poison or paralysis, would generate a product that is still zero by this multiplicative system. And so on and so forth.

Nevertheless, Turnbull pushes forward with the tools he has, first presenting a table of basic humanoids without special abilities (of which there's really only a half-dozen), and then separate tables for various other categories of monsters from OD&D, the Greyhawk supplement, and a few magazine articles current at the time. For a few examples of his M scores: orcs get 2.2, ogres 29.9, trolls 158.4, and red dragons 675.5 (by comparison, I give those creatures EHD values, respectively, of 1, 4, 9, and 32; and no, I don't think that going into decimals here is a great idea). Ultimately he recommends giving XP of 10 times his M score, which is generally about double the low Greyhawk XP awards for these sample creatures (whereas I still prefer 100 times the EHD level, in the spirit of Vol-1).

There are 73 monsters for which Turnbull & I both are willing to give measurements. Consider the correlation between our assessments:

That's not very close at all. The data points are scattered all over the place, not close to any regular relationship; knowing one measure only allows you to predict about 50% of the variation in the other measure. On average, Turnbull's Monstermarks are about 20 times what I find for EHD levels, but that doesn't tell us much. He assumes plate armor for fighters whereas I assume chain (for reasons given last week), but that can't explain the low correlation either. Let's look at some specific cases for why this is.

The most obvious problem for Turnbull is this: The Monstermark system cannot handle area effect abilities at all. His model tries to do accounting on the hit points from breath weapons (in the 2nd article), but he steadfastly assumes just a single deathless fighter in melee against a given monster; so, if a red dragon breathes fire, then only damage to that one fighter is accounted. But that doesn't reflect the true risk or utility of area-effect weapons like that; our PCs don't adventure in solitude but in groups of some size. The examples of dragon combat in both OD&D and AD&D show three PCs being incinerated at once from a single breath attack; so the damage/risk multiplier should really be at least several times higher than Turnbull counts. Likewise, petrification weapons get no distinction for delivery by touch or wide-area gaze -- the cockatrice (touch), medusa (gaze), and basilisk (both!) each get an identical 2.5 multiplier for their abilities. This alone probably accounts for a massive skewing in many of his scores, downward from the true risk level. In contrast, my Monster Metrics program runs up to 64 opposition fighters simultaneously against any given monster, and they suffer appropriately from area or gaze weapons.

Some examples where the Monstermarks seem clearly too low:
• Basilisk (EHD 25, MM 128), with its combined touch-and-gaze petrification, which only gets the same multiplier as a cockatrice does.
• Medusa (EHD 13, MM 56), likewise with her area-effect gaze petrification.
• Carrion Crawler (EHD 14, MM 120); as noted above, the multiplication system from zero damage should come out to zero, so I think he just made this up from whole cloth (note the round number).
• Harpy (EHD 9, MM 22), with her mass charm song ability, shouldn't be weaker than an ogre.
Another rather egregious issue is this, although it affects only two creatures: Summoning abilities are entirely left out of the accounting. As noted before, we find these abilities to be among the most potent in the game! But the Monstermark system actually overlooks them entirely, giving no bonus at all for them.
• Vampire (EHD 39, MM 440), given no summoning abilities.
• Treant (EHD 33, MM 420), which actually appears in Turnbull's first table of "simple human-type monsters" without any special abilities, and yet its tree-controlling ability allows it to effectively triple its own brute strength. (As an aside, consider a vampires-vs-treants scenario, in which we find two of the most powerful opposition monsters in the game due to their parallel summoning abilities.)
Meanwhile, there are some other monsters with nothing but brute strength that appear too highly scored -- like the Fire Lizard (EHD 14, MM 758), and Hydra with 10 heads (EHD 18, MM 707) -- but I think that this is only an artifact of the special ability monsters being relatively too low. Also, the Mind Flayer's score seems ridiculous (EHD 20, MM 700), granted that he doesn't even note its mind blast power, and was probably again just a raw guess (another suspiciously round number).

Now, there are two other cases that literally jumped off the chart above, such that I felt compelled to remove them as outliers -- and on inspection they are rather obviously in error. These were:
• Roper (EHD 16, MM 3,750). This is clearly a mistake. Turnbull notes the creature in part 2, p. 15: "These calculations make the Ropers the most fearsome beasts we have met so far; I don't recall ever meeting them down a dungeon, and I devoutly hope I never will." The problem, if I'm reading his attack notation correctly, is that he's applied the Roper's 5d4 damage factor -- which should be just for its mouth -- to every single one of its 6 ranged tentacle attacks. That really would be horrifying! While the Roper is a tough customer, it obviously shouldn't be worth the same as 5 or 6 Red Dragons; that doesn't pass any kind of sanity check.
• Flesh Golem (EHD 21, MM 1,920). In this case, the problem is that Turnbull shows a radically different AC for the monster than I see in the books: My copy of Sup-I (with correction sheet) gives it AC 9, as does the AD&D Monster Manual. Turnbull shows it has having an AC of -1, which is obviously the diametrical opposite. I'm not sure where he got that from, maybe from a wild guess before the Sup-I correction sheet was available to fill in that statistic?
There were some other things I had to leave out of the analysis, such as those other golems and elementals that are hit by only +2 or better magic weapons, which have undefined EHD in my model. Turnbull gives medium and large elementals a score of 1,000-2,000, stone golems nearly 13,000, and iron golems just shy of 33,000 (but again their ACs are treated as much harder than in the rulebooks, namely AC -3 and -5, so there are multiple reasons to leave them out of our comparison).

In conclusion, while the motivations are exactly the same, the scores that Turnbull & I come up with a radically different, effectively incommensurable. (If you want the full data, my Monster Database from last week has Turnbull's MonsterMarks entered in hidden column Q.) Of course: while Turnbull's instinct was noble, he didn't have the immense computing power all around us to simulate playtests the way we can today. Now, maybe someone will come back to critique my work in another 40 years -- someone who has access to a complete game engine with all the special abilities, full wizard spell selection, mixed-class PC party simulator, and hard Artificial Intelligence to optimize the best tactical choices on each side -- and in that light my suggestions might look totally naive. We can only hope for such continuity and progress.

## Saturday, September 16, 2017

### Saturday Software: Monster Metrics v.103

Previously, we've looked at the output of my "Monster Metrics" program (a branch off the "Arena" codebase), which simulates thousands of fighters in combat against specified monsters, so as to gauge their physical power level in terms of Equivalent Hit Dice (EHD). Last Monday, I presented the OED Monster Database, including pretty much every monster in OD&D and the first few supplements, which served as a platform to comprehensively assess every monster's EHD. Of course, the program needs to get updated every time a monster with a new special ability is added, so here is the current codebase with a few comments.

First, I added a couple command-line options which you see below if you want to play around with them.

 Usage: MonsterMetrics [monster] [options] By default, measures all monsters in MonsterDatabase file. Skips any monsters marked as having undefinable EHD (*) If monster is named, measures that monster at increased fidelity. Options include: -a armor worn by opposing fighters: =l, c, or p (default Chain) -b chance for magic weapon bonus per level (default =15) -f number of fights per point in search space (default =100) -r display only monsters with revised EHD from database -u display any unknown special abilities in database 

For each monster, the program runs through fighters of level 1 to 12 and does a binary search at each level for the number of such fighters which provide the closest to a fair fight (i.e., 50/50 chance of either side winning). Each step in the search runs 100 fights by default to determine the winning percentage (which you can adjust with the -f switch above for greater fidelity and slower running time, if you wish). Then a total EHD is assessed across all levels by computing the weighted total $$EHD = (\sum_{n = 1}^N n \cdot f(n))/N$$, where $$f(n)$$ is the fair number of fighters at level $$n$$ in the table above, and $$N$$ is the maximum level considered (in this case, $$N = 12$$). Note that this is likely different from "best fighter level to provide a fair fight", in that special abilities that can wipe out an army of of 1st-level fighters, but are impotent against high-level fighters, do get accounted here.

Every fighter in the simulated combat gets a sword, shield, and chain mail. One might ask, "Why chain mail by default, when most fighters after 1st level will be wearing plate?". But the thing is, I wanted the EHD ratings to actually be scaled to units of monster hit dice, e.g., the number of orcs that a monster is really worth, and those low-monster like humanoids all have chain-like armor (goblins/orcs AC 6, gnolls/ogres AC 5, trolls/giants AC 4), so we want to keep the simulation in that scale without adjusting other factors. Doing it this way, the EHD for those low-level types (lacking any special abilities) does in fact match their normal HD (orcs 1, gnolls 2, bugbears 3, ogres 4, etc.). If we switched the default fighter armor to plate, then that would devalue the monster risk, and even the simple monsters would see their EHD fail to synch up with their HD (in that case: gnolls 1, bugbears 2, ogres 3, etc.).

The next important consideration is: what level of magic weapon to give each fighter? Previously, I just assumed a +1 magic sword for every fighter, so as to not make creatures hit by magic totally invulnerable. But we will really don't want fixed bonuses like that (or fixed bonuses by level), because it creates singularity dropoffs between level or steps of bonus (e.g., makes the protection of lycanthropes and gargoyles totally useless, even to 1st-level fighters). So in this version I switched that to a probabilistic factor of 15% per level to get an extra magic boost, and also a silver dagger as a backup weapon. Having tried several levels between 5% (as seen in Vol-2) and 25% (as suggested by some comments online), I found that 15% overall gave the best match to the prior version, while giving a reasonable boost to lycanthropes, etc. And that's also what I do in my OED house rules, giving a 1-in-6 chance per level for a magic boost to characters created at higher levels.

Now, that leaves another problem, namely that any monster hit only by +2 magic or better weapons (e.g., golems or elementals in Sup-I) is totally invulnerable to 1st-level fighters, who can theoretically only have at best a +1 bonus. This means that the number of 1st-level fighters, and thus our EHD clculation, becomes technically infinite. That is: in these cases our model simply fails.

It's for reasons like this that the OED Monster Database shows an asterisk (*) under EHD for some very exotic monsters, to note that the EHD is effectively undefined in our current model. More generally, this is done for any creatures with wizard-like spell capability that isn't implemented in the program (triton, titan, lich, lammasu, gold dragon, beholder), creatures hit only by +2 or better magic weapons (golems, elementals), and creatures totally immune to blows from weapons (various oozes).

So that's the skinny on what the program is now doing under the hood, and why the Monster Database appears the way it does. Note that the included data file MonsterDatabase.csv is an exact duplicate of the Monster Database from Monday (just in CSV format so it can be read in by the software). Hopefully this makes it easy to investigate or add other monster in the future when we need them.

## Monday, September 11, 2017

### OED Monster Database

One of the places that OD&D can be most successfully criticized is in its presentation of the monster listing. In many places in the original work key details are missing, contradictory, or left to the DM (e.g., all of the normal and giant animals that appear in the encounter charts). As of the first supplement, one had to look in at least four different places for all of a monster's information: (1) the main table (HD, AC, MV, etc.), (2) the alternative attacks/damage listing, (3) the alignment category, and (4) the main text description, each of which appeared in different far-flung sections, even different books for one monster. The overall situation is what motivated release of the Monster Manual as the first hardcover book, which compiled all the statistics from OD&D monsters in one place, before any other volumes of the AD&D rules.

Below you'll find the OED Monster Database, a compilation I've made over the years for OD&D monster statistics, in line with my OED games and house rules. This gives me a convenient one-stop resource for OD&D monster statistics when I'm writing other material. One might ask: Why not just use the Monster Manual? One reason is that I very much like to stick with the original d6-based hit dice, attacks, and damage, as found in the LBBs (i.e., we do not recognize the alternative monster hits starting in Supplement I). Moreover, here are other reasons why I think this exercise was worthwhile:
1. Provides a consolidated listing of OD&D-style monster statistics.
2. Creates automatic summary stat blocks for insertion to adventures (see sheet 2).
3. Software can provide data-integrity checks for monster records.
4. Software also assesses "equivalent hit dice" valuations for encounter balancing and XP awards.
5. Forced me to think through any ambiguous adjudication cases in code (this prompted many "rules archeology" investigations and margin notes that you see on this blog).
Generally I've compiled everything I could find from OD&D Vol-2, Sup-I, land creatures from Sup-II, and TSR (The Strategic Review) No. 1 and 2 -- for a total of 147 monsters. Not included are aquatic monsters from Sup-II, demons from Sup-III, or deities from Sup-IV. For things like giant animals I turned to the Monster Manual and back-ported the information there, translating variant damage into units of d6's as we would normally expect/prefer.

Among the things you'll see is that any kind of special ability is given a keyword (and optionally one numerical parameter) for readability by my "Monster Metrics" program (more on that this Saturday); hopefully a knowledgeable DM can parse what those notes mean. The third-to-last column shows the EHD (equivalent hit dice) as determined by that program. A number of monsters are fundamentally outside the ability of my model to determine EHD, and so indicated by an asterisk (*). These would include monsters with expansive wizard-type spell ability or need spells to defeat -- for example: oozes with weapon immunity, or elementals/golems hit only by +2 or better magic weapons.

### XP Awards by EHD

Let's consider XP awards for a minute. My preference is to award XP by simply multiplying HD by 100 (and this is supported by evidence of a fundamentally linear relationship between risk and HD). Of course, this method from OD&D Vol-1 overlooks the value of special abilities. Sup-I introduced a variant XP table, and a secondary column to award bonuses for special abilities (which was of course carried forward into later editions like Holmes, B/X, AD&D, etc.). But in most of these works the DM still needs to make a subjective decision about what abilities warrant this bonus -- and I would argue in many cases it vastly undervalues some very nasty abilities (esp. on creatures with low HD).

There's a much easier way to do this, without any new tablature required or DM subjectivity, by just assigning a revised hit die value for XP purposes, which I've taken to calling "equivalent hit dice" (EHD). I gauge this with my Monster Metrics program by running several thousand fighters of different levels at each monster until we can determine a "fair" fight in each case. But the core of this idea (as simple as it is) predates the Sup-I and later variant XP charts, appearing first (briefly) in The Strategic Review, Vol. 1, No. 2 (Summer 1975), p. 4:
For purposes of experience determination the level, of the monster is equivalent to its hit dice, and additional abilities add to the level in this case. A gorgon is certainly worth about 10 level factors, a balrog nut [sic] less than 12, the largest red dragon not less than 16 or 17, and so on. The referee's judgement must be used to determine such matters, but with the foregoing examples it should prove to be no difficulty.
This seems like a much more elegant way to assess the risk/reward of exotic monsters, and it's also the simplest measurement model I could construct in my software, so this is what I now include for each monster (where appropriate) in the Monster Database. Let's just briefly compare the sample evaluations from TSR #2 to what comes out of my program for EHD:

So we can see that, compared to our model, Gygax seemed to to undervalue the more exotic special abilities of monsters (in this case: petrification, immolation, and fire breath), which is consistent with his low valuation for specials in the variant Sup-I XP tables. Perhaps on closer inspection we could generously grant that Gygax's numbers correctly assess the minimum fighter level which could possibly match the creature man-to-man, but this is not an ideal metric of the danger to parties of several men of lower or higher levels.

Finally, let's look at the distribution of the EHD values currently recorded in the monster database:

Here we see that the distribution is a nice logarithmic curve, with the largest number of monsters at the lowest level (EHD 1-5), and decreasing regularly after that. (If we zoom in a bit more we'd see that the highest number of monsters are actually the level of EHD 2, outnumbering EHD 1 by a small margin.) This seems to be useful for a fantasy campaign, and nicely echo the curves we'd expect to see in demographic and economic statistics from real-world data.

That being said, here's the link to the OED Monster Database, in the ODS Open Document Spreadsheet format:

## Tuesday, September 5, 2017

### OED Fantasy Rules v1.04 Released

As many of us head back to work and school, I wanted to share the labors of some gaming work that I've done over the summer. In that spirit, I've updated my Original Edition Delta house rules to version 1.04, and made them available on the main page of the OED Games website.

If you check it out, among the main changes you'll see is that I've split off the Player's Rules from the Judge's Rules into two separate documents. This allows you to hand the short core version of the rules to interested players (the former fits on one sheet of paper, actually), and consider the slightly longer set of behind-the-screen suggestions for judges (what I personally play by) on your own. Another reason this seemed to make sense is that the player's rules seem to have become pretty stable in the last few years of playtesting, while the judge's rules are still somewhat in flux (in fact, at the end you'll see a short list of planned still-to-come future expansions).

The other big formatting change is that I've started adding extensive endnotes to all the rules, citing classic rules, outside articles and interviews, pulp literature, and blog posts where these ideas germinated and got tossed around -- along with various difficult points considered, "proud nails", and so forth. The hope is that this helps others ("gaming archeologists", as Prof. L. Schwarz calls us) to track down where these ideas came from more quickly, help them get a grip on the various issues being balanced, and save others time from re-doing the same scholarly research over and over again. (Of course, just ignore the section at the end if that's not your bag.)

As for the game rules themselves, you'll find some very-small edits to the Player's Rules, like a slightly streamlined presentation of the weapon and encumbrance mechanics. The Judge's Rules has a lot more new stuff, like consolidations of the research on player statistics, monster metrics, exploration, combat, and rewards that we've seen here on the blog (and some more besides). I've tried to go through and share most of the copious margin-notes that I have in my copies of the OD&D LBBs, that no one has ever seen before. There's also a new Player Aid Card and even a promotional flyer (under Add-Ons) if you want to share the drama with others.

Hope that's helpful to some of your games! As always, thoughtful feedback and comments on what you see are warmly welcomed here. Hope everyone has a safe and rewarding season coming up.

## Thursday, August 31, 2017

### Gygax on Slings

Earlier this year, I had a post inspired by some scholarly research that said, perhaps counter-intuitively, that slings were at least as powerful a missile weapon as bows, and perhaps moreso -- although the amount of training required for slings was far more extensive and difficult than that needed for later types. I just realized that, like many other topics, Gygax was far out ahead of this one, with a two-page article on exactly that subject in the last Strategic Review, Vol. II, No. 2 (April 1976). He writes:
With great practice the slinger could achieve respectable accuracy — perhaps as excellent as that performed by a well-trained bowman. So on the counts of range and effectiveness the sling was at least the equal to the ancient bow (and just as equal to the medieval bow too), but it was somewhat slower in its rate of fire. Perhaps the telling factor regarding the sling was usage. While it was known by most peoples, few really specialized in its use. Because, like the bow, it required constant training and practice to use effectively, certain peoples constantly supplied most of the slingers to ancient armies — notably the Rhodians and Balaerics. As so many more peoples used the bow, it is natural that the latter would be more commonly found. Also, while it is possible to train troops to the use of the bow so as to make them at least passable archers within a reasonable period of time, the sling (as do the longbow and composite horsebow) requires familiarity and training from youth. Perhaps the disadvantages of slower rate of fire, fewer users, and long training for accuracy eventually caused the sling to be completely displaced by the bow in the Middle Ages, but it certainly wasn’t due to that weapon’s ineffectiveness against the armor of that period. Had slingers been available during the medieval period their ability to employ the shield, their ability to function in wet weather, and the relative ease of procuring or manufacturing missiles (as opposed to arrows or quarrels) would have made them popular contingents until plate armor came into fashion again in the Fourteenth Century. It is worth noting that the Spaniards who encountered the sling in America found this Incan weapon but little inferior to their own arquebuses, that it could hurl a missile which would kill a horse with a single blow, and these slung stones could shatter a sword at 30 yards.
In short, he agrees with all of our recent scholarship except on the issue of slings also possibly being as fast or faster in fire rate than bows (which is reflected in his AD&D rule that gives slings half the rate of bows). He even includes the following illustration, with the caption, "ASSYRIAN SLINGERS, swinging their slings parallel to their bodies, stand behind the archers in this drawing based on a relief from Nineveh showing one of the campaigns of Sennacherib (704-681 B.C) Their place in battle suggests that they outranged archers.":

## Monday, August 28, 2017

### Testing unbalanced dice in water

I've written about how to use standard statistical procedures to test for unfair dice a few times in the past (one, two, three, four). As noted in the last of those linked articles, for a d20 this probably involves some hundreds of dice-rolls at a minimum to get a test of sufficient power.

Here's a clever and much faster way of doing a check for unbalanced dice. This is from a video sent to me a while back by reader Ro Annis. Get a bowl of water, pour salt in to increase the buoyancy factor, and throw your dice in. If they repeatedly and consistently spin up the same face, then that die is obviously unbalanced. Like the second die in the video here.

I can imagine a few corner-cases where this may not suffice -- like if the die is balanced by weight, but the faces are malformed so as to bias the rolls on a table. But this is a great and fast way to do a first-pass check. Thanks, Ro!

## Saturday, August 26, 2017

### Saturday Software: Giant Packs in Javascript

A few weeks back I shared my Java application for generating giant packs in Gygax's classic G1-3 adventures. Reader Random Wizard then took my code and made an online version in Javascript at his Kirith.com site. Pretty sweet!

## Thursday, August 24, 2017

### 800th Anniversary of the Battle of Dover

Today is the 800th anniversary of the Battle of Dover -- what some repute to be the first-ever use of sailed-vessel tactics in naval warfare. Break out your favorite sailing rules and have a toss to observe!

Eustace the Monk once belonged to a monastic order, but he broke his vows and became a pirate along with his brothers and friends. His early successes at this endeavor attracted many lawless men and his pirates became a menace to shipping in the English Channel. The English opponents of Eustace credited the man with "diabolical ingenuity"...

## Monday, August 21, 2017

### Exploration Movement Rates

How long would it really take to explore a dungeon or cave? I'm just talking moving through the place and roughly mapping the perimeter. Not included: Searching through chests, desks, libraries; looking for secret doors; disabling puzzles or traps; spelunking through tunnels; etc. It does presume at least being on the lookout for possibly dangerous animals or enemies. It's hard to say how you'd even be able to measure this.

Here's the best stab I can take at it so far: the U.S. National Park Service has a very nicely laid-out website for Mammoth Cave National Park in Kentucky. In particular, it details over a dozen different tours on the site, including specifics for duration, distance, and difficulty. From these we can compute the average speed on these cave tours:

Method: The first four columns above are transcribed from the NPS website; "difficulty level" is an enumeration I added for the different difficulty descriptors; and speed is calculated as expected. Side observations: The "Trog" tour is, perhaps ironically, for kids only. The "Violet City Lantern" tour uses only open-flame lanterns (no modern lights) so as to recreate the experience of exploring the caves -- and living in an underground tuberculosis hospital that was located there -- in the early 19th century. (This latter sounds like among the most interesting to me!)

Conclusions: The speeds on these tours range from a minimum of 0.2 mph to a maximum of 1.5 mph, with an average of 0.7 mph. There is effectively no correlation between difficulty level and speed (R² = 0.04). For example, the "Easy" difficulty tours include both the slowest and the fastest speeds. There is a statistically negligible trend for the more difficult tours to be a bit faster.

Can we use this as a metric to properly gauge dungeon exploration speeds? Obviously, the experiment lacks many things: They are all safely pre-mapped routes, no one is in fear of being attacked, they're being led by knowledgeable guides, etc. On the other hand: The tours all have to account for civilians in all kinds of shape, they are organizing fairly large groups, the guides are stopping for discussions and questions, they're being environmentally careful (unlike tomb-robbing adventurers), they go up-and-down through rugged cave areas (whereas dungeons are mostly level constructions), etc. I'm sure the data is biased one way or the other, but I can't tell which.

Let's look at the exploratory move rates in OD&D. First, recall that standard human walking/marching speed is around 3 mph (from whence we get the "league" unit). OD&D sets basic encumbrance levels and move rates on Vol-1, p. 15 (and these are basically copied from Chainmail), with the exploratory turn movement in Vol-3, p. 8. This latter is described as "ten minutes to move about two moves -- 120 feet for a fully armored character". In summary we get this:

So that's pretty slow; only about 1/4 mile per hour for unburdened men; or, approximately equal to the slowest (and easiest) tour at Mammoth Cave Park. Of course, AD&D reduced the rate even further, dictating not "two moves" but only a single move of 10' per inch in a 10-minute exploration turn -- that is, half again slower than the numbers in the table above (1/8 mph at the maximum). The OD&D rate is slow, while the AD&D rate is very slow.

So today I'm thinking that those movement rates are probably too slow. Consider the following: These days I'm in the habit of using half-hour exploratory "turns". That seems like about the right pace for wandering monster checks, and it's also scaled to the approximate number of encounters per game session (e.g., many tournament writing guides suggest planning on about 7 encounters in a 4-hour game slot, plus time for setup; and in my experience this is roughly accurate). If we set exploratory movement conservatively below the average Mammoth Park tour speed, at say 1/2 mph, then this conveniently converts to nearly MV (in inches) × 100 feet per half-hour. This proposed rate is shown below:

Obviously, that's roughly double the exploratory move rate given in OD&D Vol-3 (and 4 times the rate seen in AD&D). On the other hand, it's half the underworld tunnel move rate specified in module D1-3, on the order of 1 mph  (one mile per MV per day, that is, 12 miles in a day for a person with 12" move). This seems possibly about right. It also seems roughly to scale with what my players cover in real gaming time when exploring and mapping, which I like as a usable rule-of-thumb. Of course, extensive area searches, fighting encounters, etc., add to this simple movement figure. Movement through previously mapped/cleared areas can be at a rate of 5 times this (as in AD&D PHB), so around 2.5 mph, a bit less than normal walking speed.

Can you think of any better way to model dungeon exploration move rates with real-world experimental data?

## Saturday, August 19, 2017

### Saturday Survey: Dragon Breath

I've taken the opportunity to ask a few polls on the AD&D 1st Edition Facebook group. Today: Does the damage from dragon breath get reduced after the dragon takes damage?

The AD&D Monster Manual is certainly ambiguous in its statement that "The breath weapon causes damage equal to the dragon's hit points (half that amount if a saving throw is made) on each and every creature hit by the breath weapon." (p. 30, 1977). This is somewhat frustrating, because the ambiguity could be cleared up with the addition of a single word, either "current" or "maximum". Of course, the D&D Basic line (Moldvay/Mentzer/Allston) does specify "remaining number of hit points" (in boldface in Moldvay p. B34). Somewhat less well-known is the fact that the AD&D Fiend Folio dragons also specify damage by "current hit points" (entries on p. 28-29, 1981). On the other hand, the OD&D language gives a damage amount "per [hit] die", which in the most literal reading leans in the direction of being disconnected from the dragon's actual hit points.

One interesting thing is that a close reading of the texts up to 1978 seems to indicate that Gygax (et. al.) simply had no language available to distinguish between current hit points and maximal hit points for a given character. For example, here is an excerpt from the AD&D PHB section on Character Hit Points (p. 34, 1978):
Hit points can be magically restored by healing potions, cure wounds spells, rings of regeneration, or even by wish spells. However, a character's hit points can never exceed the total initially scored by hit dice, constitution bonus (or penalty) and magical devices. For example, if a character has 26 hit points at the beginning of an adventure, he or she cannot drink  a potion or be enchanted to above that number, 26 in this case.
Note the convoluted formulation "total initially scored by hit dice, constitution bonus (or penalty) and magical devices" in lieu of the shorter, modern, phrase "maximum hit points". You can search all through the MM and PHB and never find either the phrase "current hit points" or "maximum hit points". In the DMG, the phrase "maximum hit points" does appear twice, but in this context it means something totally different than the modern usage -- namely, the maximum possibly rolled, i.e., getting all of 8 pips per die (e.g., paladin's warhorse p. 18; reincarnated badger p. 44). Another example of the ambiguity of not having this linguistic distinction can be found in the discussion of Energy Draining (DMG p. 119).

Back to the topic of Dragon breath. I find that what makes this topic unusually contentious is that whatever convention one is accustomed to playing with, most players will argue that it is "obvious", perhaps mis-remembering some explicit statement in the Monster Manual making it so, and in many cases taking offense at any suggestion otherwise. (Hey, Internet, y'all.) At any rate, asking this question on the Facebook AD&D form prompted an unusually large, boisterous, and lopsided response.

So with N = 142, 84% of the respondents said "No", with only 16% saying "Yes", on the issue of whether dragon breath effect is reduced by damage on the dragon.

## Monday, August 14, 2017

### Oozes Through the Ages

Gygax liked his oozes. Most of the monsters in Original D&D (Vol-2) were either creatures out of Greek myth, or else monsters from Tolkien. The ones that were new to the game itself, created by Gygax, were the "cleanup crew" of scary amoeboids: ochre jelly, black pudding, green slime, and gray ooze. I got looking at these the other day and was surprised at how vague their functioning was, and how much they varied between editions. We've pointed out before that the Black Pudding is actually one of the most powerful monsters in the original game. Let's dig a bit deeper.

### Original D&D

BLACK (or GRAY) PUDDING: Another member of the clean-up crew and nuisance monster, Black Puddings are not affected by cold. It is spread into smaller ones by chops or lightening bolts, but is killed by fire. Black Puddings dissolve wood, corrode metal at a reasonably fast rate, have no effect on stone, and cause three dice of damage to exposed flesh. If an armored character runs through a Black Pudding the monster's corrosive power will eat away the foot and leg protection of the armor so that it will fall-away next turn. Black Puddings can pass through fairly small openings, and they can travel as easily on ceilings as on floors.

One of the things I like about OD&D is that the monsters are sorted by category (all the humanoids, then all the undead, etc., usually by increasing power level). This makes it a bit easier to assess the common themes and features, and their differences, in monsters of a particular class. For space purposes I've just excerpted the Black Pudding above, the most powerful type, but you can see the others on the same or flip page in Vol-2 (p. 19-20), and they generally have the same format of description. The description specifies what kinds of attacks have effect, what kinds of materials are dissolved, and how much damage the thing does to flesh per round. Note that in OD&D, the only attacks that do damage in the system are of type fire, cold, lightning, or martial weaponry; when this was copied to future editions, it looked a bit strange, for not mentioning all the other types of damage that then existed. Here's a summary of the traits of the different oozes in OD&D, ranked in increasing level:

Note that in every case, as hit dice improve, so too do movement and armor class (monotonically). As noted, Black Pudding is the most powerful type -- immune to all attacks except fire exclusively (consider: what if you encounter one underwater?), dissolving all materials (except stonework), and doing the most damage of any creature in the game (3d6). The ochre jelly is like a half-strength pudding; vulnerable to twice the attacks (fire and cold), no effect on twice the materials (metal and stone). Gray ooze is effectively the inverse of ochre jelly; immune to the attacks that harm jelly, harmed by jelly's immunities, and reversed effect on non-stone materials (swapping wood for metal consumption). Green slime is the dumb, immobile cousin; harmed by the same attacks as jelly, and consuming all materials except stone.

Excepting the jelly, each of these types makes noise about eating away a character's metal armor, but the mechanic is left vague, possibly for each DM's adjudication on the fly. Reading the Black Pudding text above, I could imagine a whole host of possible ways of ruling on it:
• Ooze makes normal to-hit rolls.
• Ooze ignores armor for hits (always AC 9)
• Armor is corroded only on a normal hit.
• Armor is corroded on a miss (i.e., blocked by armor)
• Weapons may or may not corrode on a hit.
• Gray ooze, affected by "cuts and chops" may or may not only allow hits by swords and axes (disallowing clubs, spears, missile weapons).
What to do? So, I was looking to other editions for guidance.

### Basic D&D

Gray Ooze: This seeping horror looks like wet stone and is difficult to see. It secretes an acid which does 2d8 points of damage if the gray ooze hits bare skin. This acid will dissolve and destroy magic armor in one turn. After the first hit, the ooze will stick to its victim, automatically destroying any normal armor and doing 2d8 points of damage each round. Gray ooze cannot be harmed by cold or fire, but can be harmed by weapons and lightning.
Holmes (1978), as usual, only restates what is in OD&D, with most of its oddities still intact. The text above is from Moldvay (1981), and the new feature that he has introduced is the fact that the ooze is sticky: "After the first hit, the ooze will stick to its victim, automatically destroying any normal armor and doing 2d8 points of damage each round," which is not something I would have ever intuited from the OD&D description. However, this particular feature is not included for ochre jellies in the same text, or for black puddings in Cook's Expert rules. These descriptions remained fixed through the Mentzer and Allston editions.

BLACK PUDDING: The black pudding is a monster composed of groups of single cells. It is a scavenger/hunter found only in underground areas normally. The body structure of a black pudding  is  such that it con pass (flow) through narrow openings (such as a  1"  crack under a door). The monster travels equally well on walls or ceilings as well as floors. Its tiny mouths and saliva do 3-24 hit points of damage per melee round to exposed flesh. If the monster needs to dissolve wood in order to obtain food, it can eat away about a two inch thickness of wood equal in area to its diameter in  1  melee round. Black puddings also eat away metal with their corrosive saliva: Chainmail in 1 melee round, plate mail in 2, and an additional melee round for magical armor at a rate of 1 melee round for each plus of armor. Thus, +1 magic (plate) armor would have to be in contact with a black pudding for 3 melee rounds before it dissolved. If chopped or struck, the monster is broken into two or more parts, each able to attack...
In the AD&D Monster Manual, we get a little more info about how quickly the pudding eats armor (chain in 1 round, plate in 2 rounds... note that in OD&D the text here said "turn", which I argue meant a Chainmail-style single 1 minute of combat at the time of writing). But this doesn't help resolve the question of exactly when armor starts to corrode, or the other questions noted above. Gray ooze refers back to this text for its own armor corrosion; it suggests for the first time, "Note, however, that in the latter case the weapons striking the creature may corrode and break.", but is not explicit about when or how likely that is to occur.

The 2E descriptions show no important differences from the 1E text. The effective attacks, damage, materials consumed, and time to corrode metal are all exactly the same. No further detail is given on when to adjudicate the corrosive effects of the oozes.

### D&D 3rd Ed.

Black Pudding

Improved Grab (Ex): To use this ability, the black pudding must hit with its slam attack. If it gets a hold, it can constrict.

Acid (Ex): The pudding secretes a digestive acid that dissolves organic material and metal quickly. Any melee hit deals acid damage. The pudding’s acidic touch deals 50 points of damage per round to wood or metal objects. The opponent’s armor and clothing dissolve and become useless immediately unless they succeed at Reflex saves (DC 19). The acid can dissolve stone, dealing 20 points of damage per round of contact. A metal or wooden weapon that strikes a black pudding also dissolves immediately unless it succeeds at a Reflex save (DC 19).

Constrict (Ex): A black pudding deals automatic slam and acid damage with a successful grapple check. The opponent’s clothing and armor suffer a -4 penalty to Reflex saves against the acid.
Split (Ex): Weapons deal no damage to a black pudding. Instead the creature splits into two identical puddings, each with half the original’s hit points (round down). A pudding with only 1 hit point cannot be further split.
Now with the 3rd Edition game, we do get added information that perhaps answers the questions we've been asking since OD&D. Black pudding is given abilities of "improved grab" and "constrict" that fold its mechanic into the more general rules on grappling in the 3E system; the monster must first hit, then can hold an an opponent as long as they do not counter, but require an additional check each round to actually do damage. In this sense it is "sticky" in a way only previously seen in Moldvay's gray ooze text. Weapons explicitly need a saving throw on contact or else they, too, corrode away. In 3E, each of the oozes considered here -- black pudding, ochre jelly, and gray ooze -- all work in this fashion. (In this edition, green slime is removed from the monster list and placed in the DMG under "Organic Hazards").

### Poll Results

I asked my list of questions about ooze corrosion on the Facebook 1st Ed. AD&D group. This did not get nearly the attention that some other poll questions did (like, e.g., the question on how to adjudicate damage from dragon breath) -- seemingly this was not an issue that most people had strong opinions about. The majority choice, however, surprised me:

I say that this is surprising because -- while the group is dedicated to 1E AD&D rules, and is often downright militant about those texts' rulings -- in the case the preferred rule was the one from Moldvay's B/X (and echoed in 3E). Of the 26 respondents, most (54%) do like their puddings and oozes to be "sticky", which is not a trait suggested in either OD&D or AD&D. Only about one-quarter (27%) require the metal armor to fall off before attacking the "bare flesh". Only a single person was fond of corroding weapons that strike the ooze. No one selected any of the variant options for assessing when an ooze strikes a victim, or possibly corroding armor when failing to hit the person wearing it.

### Conclusions

While OD&D/AD&D is ambiguous about adjudicating ooze armor corrosion, the editions that are explicit -- B/X for gray oozes, and 3E for all of the types -- make the oozes "sticky", effectively grappling victims automatically after the first hit; and it seems like the cultural memory of even AD&D players has incorporated this ruling. Perhaps this is the best way to rule on the creatures because, after all, a "grappling" type attack is in fact how real-world amoebas really capture their prey.

What do you think? Any other possible adjudications that I've overlooked?

## Saturday, August 12, 2017

### Saturday Software: G1-3 Giant Bag Generator

In Gygax's AD&D Dungeon Modules G1-3, there's a table for generating the contents of Giant Bags and other containers like chests, boxes, etc. It's a bit unwieldy in practice because the recommended usage is to generate between 5-20 items per bag. I've found it useful to pregenerate a number of such containers, and have cards to hand out to players during the session.

Here's a Java program to do that job for you. One run generates 10 random "packs" (so named to cover the various bag/chest situations). Each is coded with a letter A-J so you can note it in your adventure where each one comes from (if you so choose). Run on the command line and copy-paste to a word processor set up with business-card-sized labels. Or just use the sample output run below. Print, cut, and drop them on your players when their encumbrance levels least expect it.

## Thursday, August 10, 2017

### Infravision per Westworld

On the Facebook AD&D group, Gygax Jr. asserts that infravision was intended much as the vision of Yul Brenner's character from Westworld (1973):

## Monday, August 7, 2017

### Unexpected Lycanthrope Rulings

Discussions on the Facebook 1st Ed. AD&D group (which has over 8,000 registered members) resulted in a surprising observation; a very large number of players/judges there rule attacks on lycanthropes like werewolves in an unconventional fashion. In particular, lots of people give lycanthropes regenerative powers which are only foiled by silver or magic (analogous to a troll's regeneration which is only foiled by fire or acid). Considering the AD&D rule that allows creatures with at least as many hit dice as an ogre to "effectively hit" lycanthropes, I was inspired to ask a few polls there, the final one being as follows:

Note that of 45 responses there, fewer than half (21/45 = 47%) picked the top answer which I'm fairly sure is the by-the-book rule. Almost a third (14/45 = 31%) rule by fiat that the lycanthrope cannot die from any such attacks (possibly remaining comatose or in stasis until such point as they can heal like a normal creature). About one-sixth (7/45 = 16%) make the rather astounding interpretation that they take damage from such attacks, but are instantly regenerated from them. A small number (3/45 = 7%) simply ignore or house-rule that mechanic out of their games.

I was surprised by the frequency of that. Of course: some commentators are aware that they're making house-ruled modifications, while others are adamant that their interpretation (like instant regeneration) is the intended by-the-book rule. Does this match your gaming experiences? Is it truly so widespread to make alternate rulings to how lycanthropes respond to damage?

## Thursday, August 3, 2017

### Thiefly Thursday: Running & Climbing Videos

Just in case you didn't seem them in the comments under the Climbing Through the Ages discussion, here are two excellent videos you should watch of athletic activities researched in plate armor (thanks to Rando and Joshua Macy for pointing these out):

## Monday, July 31, 2017

### Spells Through the Ages Polymorph – Polymorph Matrix

We've had some extensive reflectections on the various polymorph spells in the past (link one, two). I just realized that I made a graphical matrix of abilities conferred by polymorph in editions from 0th to 3rd, but never posted it here. See below:

## Saturday, July 29, 2017

### Saturday Software: Wizard's Spell Index

I threw out a new version of the index to the AD&D Wizard's Spell Compendium on Monday. Here's a complementary piece of software to go along with that. In my standard idiom, what you'll get is a command-line Java application (JAR), associated data and source code, and a Windows batch file to run it click-wise.

In this case, the program doesn't do anything very interesting; just read the entirety of the Compendium index, do an integrity check, look for duplicate spell names, and compile lists of all the special origins and schools of magic that appear. But if you're a Java programmer then you may appreciate being able to hook into this and read, use, modify, and possibly write out a new spell index in a few lines code. (It's what I used to programatically check and reformat the index myself.)

Perhaps more immediately useful, here's also an alternate spell list that you can drop into the spellbook generator program from last week, including everything from the Wizard's Spell Compendium General Mage List -- with 1,278 spells! Note that, following that work, spells marked "C" (Common) are identical to those in the AD&D 2E PHB (which is mostly the same as in 1E), excepting spells named after some NPC (which are "U" for Uncommon); spells from other supplements are at lower frequency levels. (Rename to SpellIndex.csv to use.)

## Monday, July 24, 2017

### AD&D Wizard's Spell Compendium Index

We wrote previously about our appreciation for the AD&D Wizard's Spell Compendium, compiled by Mark Middleton, here. Although released in the years 1996-1998, it wasn't branded as "2nd Edition"; rather, the intent of the product was to be a general AD&D resource covering publications from the game any time from 1975-1995. (That said, you'll find it categorized as "2E" in most places online just because of the time frame, and the format of the spell matches 2E, e.g., ranges in units of yards by default).

The four volumes have been missing from DriveThruRPG for some time, but as of this May, the first two volumes reappeared with improved scans, OCR, and indexing. Personally, I downloaded those, along with the older copies of volumes 3-4 I had, merged them with a PDF tool, and now have a single document close to 1,200 pages in length with all the AD&D spells in one place. It's pretty sweet.

### Compiling The Index

One thing I'm not alone in searching for in the past is a digitized index of those spells to possibly use for analysis and input to software applications. James Rizza at Dragonsfoot made what seems to be the first attempt at this (here). We should be very grateful for that work (I'm pretty sure it was all manually entered, including schools, ranges, durations, material component listings, etc.), but it has a number of limitations. The most glaring is that every spell was entered multiple times, once for each school of magic to which it belongs. That runs up against the cardinal rule of database management, that is, to not duplicate the same data in multiple places -- because every copy is another opportunity for errors to creep in, fields to fall out-of-synch, etc. (and indeed they did in this case). It makes it impossible to gather vital statistics on the work, starting with simply knowing how many different spells there are. (I'm sure that was done to enable sorting by school, which was an important mechanic for 2E specialty spellcasters, but an immensely better way to do that would be to use the spreadsheet FIND function appropriately.)

So, below you'll see a version that I massively re-formatted and corrected. Where the original spreadsheet was all-caps, I put this one in title case (matching the text of the Compendium itself). I de-duplicated all of the spells and collected the schools into one field each. I separated out reversed spell names from the name field, where they were previously appended. I did the same with any special origins (like Old Empire, Red Wizards, Dragon Knights, etc.) -- except in the dozen or so cases where it was necessary to avoid duplicating another spell's name. I programmatically reformatted most of the ranges, durations, areas, with more standardized abbreviations, and shortened many of the material component listings. I deleted the extra columns for various specialty wizards which could be discovered by inspecting the schools listing (but were in many places out-of-synch). I corrected some spell name typos and missing spells. And I inserted the frequency data indicated in the Compendium Vol. 4 table for generalist mages.

We shouldn't feel surprised at errors in the original table; granted that it had 3,442 records × 24 fields/record = 82,608 total fields, even if the original author was working at 99% accuracy, we would still expect close to a thousand fields to have errors. I'm sure there's still a bunch of errors that I haven't yet caught. Feel free to send me more corrections if you find them (esp., missing spells?).

### Statistics and Conclusions

Now we can present some descriptive statistics on the overall work:

Here are the level statistics in chart form:

For the levels, note that levels 3-4 are modal; this seems to be the "natural" thing to happen if someone doesn't enforce an outside requirement on level frequency -- it's the same thing that appears in Original D&D Vol-1. And here are the frequencies in a chart:

As you may expect, the letters C, U, R, V stand for the frequencies Common, Uncommon, Rare, and Very Rare. These are only entered as they appear in the Volume 4 "General Mage Spell List" (p. 1093-1101). The implication is that the 38% of spells marked as "None" here, that is, not appearing in that list, are "Restricted" spells given only to some specialty wizard type, and presumably appearing in one of the many other tables that follow in the Compendium. It's interesting that Uncommon is the most infrequently-used frequency.

We can also dis-aggregate the spells by level and frequency on separate axes. Consider the following chart:

Looking down the depth of that 3D chart, notice that at 1st level, more of the spells are Common than any other frequency. Meanwhile, around levels 2-5 there are more spells at the Rare or Very Rare ratings (and these are approximately the same at levels 3-4). However, at levels 6-9 the spells are mostly Very Rare (and the Rare category is almost totally unused at the uppermost levels).

Finally, here are compilations of the special origins and schools of magic to be found in the database:
• Special Origins: 21 [Alhoon, Bard, Beholder, Dragon, Dragon Knight, Drow, Elf, Galeb Duhr, Ghul, Hishna, Necromancer, Neogi, Ninja, Old Empire, Paramander, Phaerimm, Pluma, Red Wizard, Savant, Witch, Wu Jen]
• Schools of Magic: 28 [Abjuration, Air, Alchemy, All, Alteration, Artifice, Charm, Chronomancy, Conjuration, Dimension, Divination, Earth, Enchantment, Evocation, Fire, Force, Geometry, Illusion, Invocation, Mentalism, Necromancy, Phantasm, Shadow, Song, Summoning, Universal, Water, Wild]

### Further Research

Among the limitations in the current index are the lack of data for setting-specific information, which are indicated in the Compendium with graphical icons next to many of the spells (e.g., Dragonlance, Dark Sun, Ravenloft, etc.; see p. 1126-1136). While the information for many specialty wizards can be parsed from the schools field (assuming no errors there?), other specialty mages appear at the end of the Compendium that would need additional field(s) to include (e.g., Deathmaster, Frost Mage, Red Wizards, Storm Mage, Witches, etc.; see p. 1137-1148). If you're generous enough with your time to add those, then do please forward it here so that we can share them.

Of course, many of us use a ruleset with different spell formatting than 2E. If I were to use a few entries here as surprise spice in my games, I'd probably convert all the ranges to either 6, 12, or 24 inches (depending on whether the listed range was closest to 60, 120, or 240 yards for a 12th-level wizard [i.e., 5, 10, or 20 yards/level]). And I'd convert durations to either 3, 6, or 12 turns (depending on whether the listed duration was closest to 1, 2, or 5 rounds per level). This is actually the conversion protocol that I generally used when analyzing spells for the 2nd edition of the Book of Spells work.

Get the revised Wizard's Spell Compendium Index at the link below!

## Saturday, July 22, 2017

### Saturday Software: Minidice

A minimalist website to roll dice. Like, really minimalist. It works on my decade-old feature phone.

Minidice.

## Monday, July 17, 2017

### Climbing Through the Ages

Climbing, by thieves and non-thieves, possibly with rope assistance, is a common dungeon, cave, and wilderness activity for explorers. It’s also one of those mundane, real-life skills that I would expect we could “dial in” correctly to our gaming ruleset. Coincidentally, just a day or two after our Rappan Athuk game, my friend Duncan posted a video of himself climbing a free-hanging rope for about 20’ in a gym, which looked pretty impressive to me. Discussion follows:

Indeed. Taking inspiration from the many climbing challenges last week, I felt obligated to investigate the rules present in classic D&D.

### OD&D

Chainmail (1971) mentions the use of ladders in the Siege rules (which are at man-to-man scale) -- 3 men can climb a ladder per turn (1 minute); defender above always gets first strike (p. 23, 25). The only direct mention of climbing in the D&D LBBs (1974) is that swimmers may climb the side of a ship to board (Vol-3, p. 31). Of the first pit trap, it is said, “it would only mean about one turn of time to clamber out, providing the character had spikes or associates to pull him out, and providing the pit wasn't one with a snap-shut door and the victim was alone.” (Vol-3, p. 5).

Of course, Sup-I (1976) introduces the Thief class with their special ability to “climb nearly sheer surfaces, upwards or downwards” (p. 4). The mechanic couldn’t be simpler: “There is a basic chance of 13% that a 1st level thief will slip and fall in climbing. With each higher level attained by the thief this chance is reduced by 1%”. As a formula, that is: 14% – L chance of slipping. Note what is not addressed: time, distance, speed, encumbrance, ability scores, or how many checks are required for a long climb.

Again, in the core rulebooks, only thieves climbing vertical surfaces is addressed. The probability is similar to OD&D, with an 85% chance of success at 1st level, a 99% at 10th, and so forth (AD&D PHB, 1978). Racial type may modify this; while Dexterity modifies most other Thief abilities, it does not do so for climbing.

The extra/errata notes in the DMG (1979) give movement and surface details for the first time (p. 19). In particular: “SLIGHTLY SLIPPERY surfaces DOUBLE chances of slipping and falling. SLIPPERY surfaces make chances of slipping and falling TEN TIMES more likely.” One interesting thing is how this mechanic makes the most sense in the context of OD&D, where percentages were given in chances to fail (see prior section); but it’s more confusing math when the percentages have been converted to a chance to succeed in the AD&D PHB (last paragraph). For example: 100% – 2 × (100% – P) for a slightly slippery surface, where P is the base chance of success. Like many AD&D rules, this was long a source of confusion to me, until I read OD&D which clarifies the conrext in which the rule was first written. And I think of this as one of many examples that to Gygax, the game was all one continuous work and not discrete, separate editions.

This latter rule is in fact exacerbated in that further down that page it is written, “Most dungeon walls will fall into the fairly rough to rough category. Some will be non-slippery, but most will be slightly slippery due to dampness and slime growth.” That is: Applied strictly, the default chance of falling is twice that apparent to players from reading the PHB.

And there’s yet another subtle-but-significant rule change between the PHB and DMG and that is: the time scale and number of rolls involved in one climb. The PHB asserts that only one roll need to be made for any climb: “It is assumed that the thief is successful until the mid point of the climb. At that point the dice are rolled to determine continued success. A score in excess of the adjusted base chance indicates the thief has slipped and fallen.” But the DMG gives a chart of move rates in “FEET PER ROUND”, in units of either 0, 3, 6, 9, 12, 18, or 24 feet per round; and then it specifies, “Be certain to check each round of vertical or horizontal movement for chance of slipping and falling”. So this page of the DMG has made climbing massively more dangerous to thieves, both generally doubling the chance to fall, and moving from a single such roll per climb to likely many.

For climbing by non-thieves, we’ll need to look outside the core rules by Gygax. For example, such rules appear in the AD&D Dungeoneer’s Survival Guide (1986). While this is past the time when Gygax departed TSR, the author Doug Niles gets instant credibility from me because of his excellent design work in the miniatures rules for AD&D Battlesystem and Star Frontiers: Knight Hawks. Like much of the book, the rules are somewhat too expansive to discuss here in full (p. 14-19), but an overview can be given.

Sheer surfaces like those detailed for thieves in the DMG simply cannot be climbed by non-thieves (p. 14). Compared to thieves, non-thieves are given a base climb chance of 40%, but this can only be applied to easier categories of climb like, “Rough, ledges... pole... tree... sloping wall... rope and wall” (p. 14-15). Bonuses per category apply, between +20% and +40%, making any of these climbs automatic for thieves. Abilities and encumbrance are not considered, but armor is: –5% for padded/studded, –15% for chain/splint/scale/banded, and complete prohibition for any characters in plate mail (p. 16). An even easier mechanic is given for characters rappelling downwards with a rope; +50% modifier and increased speed (p. 17).

Now, the movement rates are again given in units of feet-per-round, so in this aspect the DSG work looks continuous with the rule given in the DMG. However, there is a possibly subtle wrinkle to this; Niles writes, “When a non-thief character begins a climb, he must make a successful Climbing Check roll on 1d100... If a Climbing Check fails, the character can never climb that wall.” Now, read closely, this has the appearance of switching back to only one check per climb (due to the “begins a climb” language), and not rolling round-by-round as per the DMG. That makes climbing safer, although we might wonder about the last part of the rule, esp. for downward-direction climbs (maybe the most common usage in standard dungeon designs?). What happens when a character goes over the edge of a cliff on a rope and fails their check – are they just stuck there helplessly?

Consider the chart above which summarizes different types of characters climbing a rope-and-wall for 100 feet. (The percentages shown would be identical at any level.) Clearly there is a degradation in climbing chances, mostly related to the armor worn by the character. The roll indicated would only be made once; if successful, time spent climbing would be either 3 or 5 rounds by class (where allegedly 1 round = 1 minute).

### B/X Rules

In the Moldvay/Cook B/X rules (1981), only climbing rules for thieves are addressed. The chance to climb is actually identical to that back in OD&D (only translated from chance-to-fail to an equivalent chance-to-succeed). The rule stipulates, “This roll should only be made once per 100’ of climb attempted. If failed, the fall will be from halfway up the surface.” (p. B8). So: Here we again see a once-per-climb mechanic (as opposed to the AD&D DMG).

Edit: Scott Keeney points out that Moldvay does briefly mention climbing for non-thieves in his two pages of "Dungeon Mastering as a Fine Art" advice at the very end of the book (p. B60-61). In this case, it's "To perform a difficult task (such as climbing a rope or thinking of a forgotten clue), the player should roll the ability score or less on 1d20." Cook backs this up with a paragraph on Climbing in the Expert rules, suggesting a Dexterity-based check when "climbing a tree in a high wind, or climbing up a crumbling wall." (p. X51)

The subject of climbing is the very last topic in my copy of the AD&D 2E PHB (1989), just before the appendices. Broadly speaking, the rules are the same as those found in the DSG. Base success chance is again 40% for non-thieves; climbing categories are roughly the same; modifiers are slightly adjusted (e.g., +55% for rope and wall); modifiers for armor are mostly the same (exception: plate at –50%, not totally prohibited); checks are again only once at the start of a climb; the rule for quick rappelling downward is maintained; climbing is permanently barred if a character misses their roll. Modifiers for encumbrance rating are added. And another paragraph has been inserted after the table for climbing chances: “On particularly long climbs--those greater than 100 feet or requiring more than one turn (10 minutes) of climbing time--the DM may require additional checks. The frequency of these checks is for the DM to decide. Characters who fail a check could fall a very long way, so it is wise to carry ropes and tools.” (Note that Dave “Zeb” Cook was the listed author for both 2E and the D&D Expert rules, so the echo of the 100’ unit from B/X should not be too surprising.)

In summary, it looks like climbing for non-thieves got significantly more generous than in the 1E DSG. Combined with the boosts to both the rope-in-wall case that we’re considering, and the improved situation for plate, fighter in plate armor have gone from an impossible situation to an almost 50% chance to make such a climb.

### D&D 3E

Now, in the 3rd Edition PHB (2000), the formerly percentage-based rules, along with everything else, were converted to the d20-based uniform mechanic. Use of the Climb Skill (p. 64-65) is uniform for all character classes; it’s a class skill and so easily obtained by both Thief-types and Fighter-types (in fact, it’s the very first skill suggested for Fighters in their “starting package”, p. 37); so these classes might be expected to have skill points up to their level + 3 (the maximum). The skill is modified by Strength and Armor (e.g., –1 for studded leather, –5 for chain, –7 for half-plate), but not by encumbrance generally. The d20 target challenge ratings are, for example: DC 5 for a rope and wall; DC 10 for ledges; DC 15 for very rough natural rock or a tree; DC 20 for typical dungeon wall; DC 25 for overhang. DC is +5 for a slippery surface. Many modifiers are given for other situations and synergies. So it looks like, very roughly speaking, the categories of surface are approximately analogous to those first seen in the AD&D DSG.

But one aspect the re-emerges is significant: Rolls must again be made every round. “With each successful Climb check you can advance up, down, or across a slope or a wall or other steep incline (or even a ceiling with handholds) one-half your speed as miscellaneous full-round action.” In conjunction with this, a unique mechanic is that failures are not necessarily falls: “A failed Climb check means that you make no progress, and a check that fails by 5 or more means that you fall from whatever height you have already attained.”

The rule for rapid and easy downward rappelling is missing. But, a rule is added for something that I do think was overlooked in any prior editions: “Someone using a rope can haul a character upward (or lower the character) through sheer strength. Use double your maximum load... to determine how much a character can lift.”

Compare the case-study chart above to those given previously. Although the 3E requests that a check made each round of climbing (counter to the prior case studies), it is in other ways much more generous than in the DSG or even 2E. The modifiers for encumbrance are gone; the effects of armor are more significantly lessened (effectively only a –35% for plate); classes such as fighters as likely to have additional points in the skill; Strength bonuses can apply; and there is no prohibition against re-trying after the first failure. For example, Fighters in plate (–7 check) have that penalty exactly cancelled out by the 4th level (+7 skill); so while they need to roll DC 5 on a raw d20 to succeed in any round, it is impossible for them to fail by 5 and thus fall. They are in fact guaranteed success at climbing a 100' rope in about 1 minute of time (on average around 12 rounds, accounting for failed rolls; and note that 1 round = 6 seconds here).

This is, of course, the furthest possible cry from the 1E DSG where such a climb was strictly prohibited. But if a character is of lower level, or does not have maximum possible ranks in the Climb skill, then the chance of success will be lower -- and due to the multiplication rule for compound probabilities, the total chance to make the climb without a fall degenerates at a shocking rate. For example: At only one level lower (3rd), the fighter in plate will have a 5% less chance to make any particular climb roll (1 pip in 20). But then that opens up the possibility for a fall (on a natural "1"), and over the 10 Climb checks necessary in the example above, the chance for succeeding at the whole climb is only 52.4%. For a 1st level fighter with max skill the total chance is just 12.5%; and for an unskilled climber in plate, the chance becomes less than 1%! (Assuming no Strength bonus, which would move the example back in the other direction.) 1

### Poll Results

I also asked this question on the Facebook 1E AD&D group. The results were approximately 3:2 in preference of a check every round (i.e., following the official 1E DMG rule), with another group answering some form of "it depends" (often by distance or surface type).

For what it's worth, everyone whom I know personally picked "one check per climb" (offering a good case study in how your friends can be non-representational of the population at large). EGG Jr. selected "one check per round".

### Open Questions

I think that the last time I edited my OED house rules on the subject, I was primarily looking at the 3E rule for base probabilities; however; on my simplified d6 mechanic, making the climb more difficult (as in 1E) would be pretty much countered by the chance-to-fail-but-not-fall (in 3E), for about the same result.

So: Which of the above rules for climbing do you like the best? How risky should climbing be for an unskilled man, a fighter in plate mail, etc.? Do you prefer the frequency of checks to be once per climb (OD&D, B/X, 1E PHB, DSG, 2E), or once per round (1E DMG, 3E)? Should failed checks prohibit any further climbing (as in DSG, 2E), or not? What would be the best simulation of the real thing?

Finally: Anyone ever see anyone test climbing (rope, rock wall, etc.) in any kind of chain or plate armor?

1 This calculation is done by recognizing that the 4-pip window on the check in which no movement or fall occurs can be effectively ignored for this purpose, and proportionally consider the chance to fall out of 16 (with any negative modifier taken as the numerator). Thus, the chance for the 3rd level fighter in plate to avoid any fall is (1 – 1/16)^10 = 0.524; at 1st level it's (1 – 3/16)^10 =0.125; unskilled it's (1 – 7/16)^10 = 0.003. Also checked by computer simulation.