Monday, July 9, 2018

Dyson's Delve at Paul's Gameblog

Nothing new from me at the moment: go check out Paul's Gameblog to see what I was doing over the long holiday weekend. (Updates as Paul adds more posts this week.)

Monday, July 2, 2018

How Tall is that Humanoid?

Let's look at all the height-values explicitly given for monsters in OD&D Vol-2 (there aren't that many; mostly just giant types) for some kind of pattern.

We assume the following: Hit dice are related to strength. And strength is related to cross-sectional area of the body. (This is certainly true for simple physical systems, where compressive strength is a function of area. It is broadly true in muscle physiology. However, it varies between individuals of a species based on gender, training, etc.)

Below we map the hit dice of various OD&D Vol-2 creatures to the square of their stated height (i.e., something proportional to their cross-sectional area). We include Men as a known quantity from the real world (taking 5' 8" as the mean height of medieval men). Also, we exclude Fire Giants as a rather obvious outlier (they are given proportions that are notably dwarfish, likely an allusion to the deformed god Hephaestus and many other mythological smiths/craftsmen).

Of course, we do not expect that these game values were set up with any kind of mechanical system in mind (on the other hand, it's pretty intuitive that strength and size should be increasing together). That said, we do find that a regression on these values gives a 96% coefficient of determination; a good match.

So if we want to invert this and use it as a rule-of-thumb, given that hit dice are given for every monster and height is usually not, we could say roughly that height (in feet) = √(27.71 HD) = 5.3 √HD5√HD.

Let's spot-check a few simple values. For Men (HD 1), our rough estimate would give 5√1 = 5×1 = 5 feet. For Ogres, we get 5√4 = 5×2 =10 feet (whereas the book says they "range from 7 to 10 feet in height"). For Stone Giants, we get 5√9 = 5×3 =15 feet (precisely the book figure). And so forth; it seems to work pretty well for creatures with man-like proportions.

For more serpentine creatures (like Tolkien-style dragons), we might say they have double the length given by this formula. In fact, we can check against the only other creature with a stated length in Vol-2: the Purple Worm, of which it is said that "some reach a length of 50 feet". Assume this is for the largest of the species, i.e., 6 pips per hit die, so 15 × 6 = 90 hit points. This equates to standard monster hit dice of 90 / 3.5 = 25. And our rule-of-thumb would estimate the corresponding serpent length as 2×5√25 = 2×5×5 = 50 feet. Well, isn't that nice.

Bonus: How Heavy is that Humanoid? This happened to come up (half-jokingly) in our game last weekend. Spring-boarding off the above, this needs to be proportional to the cube of the square-root of hit dice, that is, HD^(3/2) = HD^1.5. For the coefficient (multiplier), we back-calculate from information on the Corpulence Index (CI): We find that one can very roughly use weight (in pounds) = 100 × HD^1.5. For a somewhat better estimate, use 120 as the multiplier. For a value in stone-weight, use 8 as the multiplier. (Compare to "How Heavy is My Giant?" in Dragon #13, which relates height to weight but not hit dice.)

Saturday, June 30, 2018

The Master's Monastery, Ep. 6

Juno 30, 4729.
  • Continuing personae: Long Tim (Hobbit Ftr3), Brother Maccus (Human Ftr3). After the dreadful encounter with ghouls last time, other new PCs need introduction.
  • New PCs: Aslak Jam Saskin (Elf Ftr2/Wiz1), a peddler of holy water and haunted by the spirits of earlier dead dwarven wizards; Dusteg Bronzehide (Dwarf Thf3), a trap-searching expert. Interesting side note: The party Strength scores are now 15, 17, 17, and 18; this is assessed as "Darwin having written OD&D".
  • Aslak JS makes use of the rule to "send[s] messengers to whatever place the desired character type would be found (elf-land, dwarf-land, etc.)" (Vol-1, p. 12), specifically elf-land, putting out a call to hire brave (but hopefully cheap and not-so-wise) elven adventurers. Three show up and two are hired after haggling on price and treasure shares (100 or 150 sp up front, and 1/8 each of all treasure); Tamar the Miller (Elf Ftr1/Wiz1; chain, war hammer) and Yulia the Ape (Elf Ftr1/Wiz1; chain, silver dagger, Str +1).
  • Brother Maccus makes use of the "Rumors, Information, and Legends" rule (Vol-3, p. 23) on two evenings at the inn; pays out 90 sp and gets two tidbits: (1) the hexagonal chamber in the dungeon is to be feared; (2) there is a powerful necromancer in the woods not far to the north. After some debate and purchase of healing potions, the group decides to return to the monastery dungeon and seek the priceless fire opal once more.
  • Into the pit; skirting the entry bone-mound, to the large empty ceremonial chamber. There, the secret door is closed and the makeshift steps gone. The group returns to the wood store in the dungeon, gets more logs, and recreates the climbing apparatus. Through the raised secret door into the crypt section. 
  • Look into the crypt-chambers to the immediate east and south; looking carefully for more lurking/hidden ghouls. Find hundreds of more bodies and skeletons in niches along all the walls; no exits and no obvious treasures, acting with utmost caution, the group backs out and searches elsewhere.
  • Passing through the alcove guard post, the party is surprised that 8 animated skeletons destroyed earlier have been replaced; combat is once again engaged. This goes fairly well, with the bulked-up party chopping down skeletons left and right with swords, polearms, and halberds. It is over in less than a minute, a pile of shattered bones beneath their feet. 
  • Further south, off a smaller hallway to the west, a very old and locked, heavy oak door; silence behind it. Dusteg tries to pick the lock but it seems jammed. The three strongest members line up to kick it down together; this works, and the door snaps inward. Within: a single stone sarcophagus. Dusteg enters to search the walls. At this, the lid scrapes open and a hideous figure stands up; clearly dead, black leathery skin, hairless skull, old robe and gold medallion, fairly crackling with foul energy. A mummy? Dusteg runs and with Tamar slams the door shut; the creature within pulls on the door, almost beating their combined strength. The others back up 20 feet and pull out missile weapons. The two let go of the door and duck and run; the rest launch arrows and bolts which all shatter helplessly against the creature's hide. The thing launches at the plate-armored Maccus, rolling poorly; chalkboard-sound of nails gouging his shield.
  • Everyone flees, running back up the long northern hallway. Maccus is slower than the rest, and the creature keeps pace; gets an attack at +2 and no shield; lashing at his ankles, again fails to connect. Rounding two corners, rolls are made to see if the creature follows (Vol-3, p. 2); these fail, the monster returns to its lair, and the party catches its breath.
  • With few options, the party returns south; looks at the door which is shut but clearly no longer locked. Further south, small tunnels; to the east a dead end. To the west a small dead-end room with sarcophogus; this has merely a long-dead body and no treasure. A bit further south another likewise. Now time for a wandering monster check: this comes up "6" so something comes down the dead-end tunnel at the party; another roll indicates it is this same weapon-immune undead creature (which the DM just added to the encounter table after the PCs released it). Long Tim spots it as others are searching for secrets and everyone gasps.
  • Aslak JS fires an arrow at the creature's gold medallion, but the shot goes wide. Tamar tries to hit it with her war hammer and this does nothing. Dusteg throws his silver dagger and connects; the creature recoils, silvery burning smoke wafting from the wound! Tim misses the medallion with his hobbit's two-handed sword. Maccus drops his sword with a clang, grabbing for the embedded silver dagger (success) and tries to hit with it (fails). Yulia also strikes with her silver dagger (the only other such weapon the party has), but also misses. The creature lashes out randomly; strikes Yulia for 4 points and drains her Wizard-class level permanently.
  • Aslak casts protection from evil. Tamar casts magic missile and the creature takes full damage. Dusteg throws a normal dagger; hits it in the black eyeball, but it gets spit out with no effect. Tim severs the medallion, it falls off, but this also has no effect. Maccus connects with the silver dagger and the thing weakens. The undead misses its next attack; around the table again, mostly with no effect; and then Maccus finally gets position and finishes it off, twisting the dagger deeply in its dead-again chest, silver smoke billowing into the air. The group pick up its gold medallion and silver bracelets and give a healing potion to Yulia.
  • Party decide to return to the village and sell this loot and recover. Split up 178 sp and 410 XP each (or 118 sp and 205 XP for the hirelings). Long Tim advances to 4th level; succeeds in mastering the ability to double-strike with a melee weapon.
  • The next day, the party decide to explore the nearby northern woods for the necromancer of note, one "Akharis the Astonishing". It rains but the group take some rations and head off anyway. After a half-day's march, into the trackless woods; the encounter roll "6". A short distance ahead they are spotted by 3 giant snakes (20' long each) wrapped around an ancient, withered tree. The snakes slither down to attack, and most of the party uses various hiding powers to disappear in the bushes. Brother Maccus is left standing alone with no such special abilities. He looks (success) for a thick cluster of downed trees where only one snake can get through at a time, and stands at that point. The first giant snake slithers through and bites his shield; a miss. The whole group launch attacks, cutting and stabbing it multiple times. It bites Maccus' leg and starts coiling around him; before it can crush him it is finished off, but the next is upon them. Again Maccus is bit and wrapped; and again the thing is split up. The third is likewise attacked and defeated. Beyond the tree, the party spots a wide and deep ravine and on the mesa beyond, an a tall tower surrounded by trees. Having no obvious way (or time) to cross, they return to the village.
  • Open questions: Can the party contact the necromancer, and will he/she/it be happy to see them? Does the party have any way to defeat the ghouls and find the fire opal in the dungeon -- if it exists at all? With Long Tim having reached maximum level as a Hobbit fighter, is there any way to cheat the rules, say, by training with a stronger or higher-level fighter? We shall see.

Monday, June 25, 2018

Expected Backstory Poll Results

Back in February, on the Facebook AD&D group, I asked a poll on the following question: "About how many pages of backstory is expected for a new AD&D 1st-level character in games you play?"

To be clear, this is not a question I would ever think to ask on my own. (Another poster previously asked, "How can I write the required 8 pages of backstory for my new character", or something like that, which generated a lot of interest.) As it turns out, this seems to be the most controversial/viral thing I've ever asked there: it generated 493 votes and 128 follow-up comments to date, with fiery opinions in all directions. Here's the original as it appeared on Facebook (out-of-order, and with vote totals of 100+ not visible):

Here's a possibly more useful version, with a table and chart in numerical order:

As you can see, the most popular choice by far was "zero pages" (by default, what I would have answered, the thought never even naturally occurring to me) with about 60% of the votes cast; but "one page" was also popular, with about 20% of the votes -- even more popular than a "half page", with 13% of the votes. On the other hand, while almost no one picked options in the range of 5 or 10 pages, ten people picked either "20 pages" or "More" (2% of the total voters), and were likely to post a comment justifying this stance (and so triggering counter-comments from the no-backstory camp).

Disclosure: There is a possibility that a few people picked "More" (i.e., more than 20 pages expected) accidentally, as by default Facebook only shows the top 5 options in a poll until one clicks "More Options...", that is, the options for 5-10-20 pages would be initially not visible.

In statistical practice, it is sometimes said that bimodal (or multi-modal) results like these indicate that one is measuring at least two disparate populations that perhaps should be separated apart in future analysis. The difference between "zero pages" and "twenty or more pages" of expected starting backstory is so startling that it does indeed seem like at least two different games are being played.

Thursday, June 21, 2018

Thousand Year Sandglass at DriveThruRPG

My good friend B.J. Johnson, a.k.a. BigFella Games, has just released what may be his RPG magnum opus: the Thousand Year Sandglass, a fantastic Arabian-themed campaign that he's developed and run -- and which I've had the great pleasure in playing -- for about 10 years now. It has what I consider to be a uniquely and creative world, with never-before seen custom class, races, spells, magic items, monsters, etc. that have all popped out of B.J.'s genius skull. Plus top-notch art by the man himself.

That probably doesn't do it justice, though. B.J. is the single most creative producer of RPG setting content that I personally know. Here's a little slice of what it's like gaming in the Thousand Year Sandglass or any of his other games: Start out and get a customized setting with custom pre-generated characters, backstories, companies, handouts, cards, counters, and custom miniatures. Play for 4 hours and every encounter is fresh and novel, and has B.J. rolling out (again) custom landscape, buildings, miniatures, music etc. -- every one hand-crafted just for the game in question. Then at the end sit back for some extra hours as he shows off the other 70% of the encounters, battlemaps, miniatures, charts, sub-systems, etc., etc. that we never encountered. It's jaw-dropping and inspiring and truly humbling.

So some of us have been encouraging him for a while to pack up these ideas and make them public -- finally, you can take a look yourself and join in our amazement! After presenting the campaign setting, it even has no fewer than 8 adventures at the back to use in your games. Officially uses Labyrinth Lord but (of course) easily compatible with any classic D&D system. It gets my highest recommendation: Check out Thousand Year Sandglass on DriveThruRPG.

(Bonus: A post just about all the custom jinni miniatures he's made over the years for the game!)

Monday, June 18, 2018

AD&D Alignment Color Wheel

An alignment color wheel for AD&D. There are many places in AD&D where colors are associated with specific alignments (e.g., 1E Manual of the Planes color pools, or in Gygax's Gord the Rogue novels), but none were systematic in the following sense: I felt that oppositional alignments should be opposite colors (a.k.a. complementary in the traditional RYB model), and that adjacent colors should be close on a color wheel, and smoothly blend with each other (as a corollary: gray must be in the middle). I don't play AD&D anymore with its 2-axis alignment system, but back in 1996 I wrote a very small computer program to smoothly blend from one point to the other, and here was the result:

Saturday, June 16, 2018

The Master's Monastery, Ep. 5

Juno 15, 4729.
  • Personae: Long Tim (Hobbit Ftr3), Tahj Birdfoot (Elf Ftr2/Wiz2), Brother Maccus (Human Fighter 3), Penrod Pulaski (Human Thf3), Banjo Saskin (Dwarf Wiz 3). A month and a half since the last adventure, all are healed fully. Upkeep is 75 sp per person; restocked on healing potions.
  • One complication: While Banjo recently achieved 3rd level through a cunning stratagem, which expands his mind to possibly memorize a 2nd-level spell, he has none such in his book. So he satisfies himself with memorizing 3 1st-level spells, and the group departs for the ruined monastery on a rainy morning.
  • Traveling through passages previously explored. Looking down one passage, known to be trapped with hideous undead in cells, sees a glowing light -- reappearing even after the fake gem was removed before. Entering the lower storage chamber, Penrod hears a creaking noise: former bugbear hideout active again?
  • Group proceed to the ruined wine cellar, formerly with a swarm of stirges that caused several deaths, last seen in flames. Entering wine cellar, smoky and acrid, a few partly-burnt stirges angrily take the air, but are quickly cut down with slings, thrown daggers, and swords.
  • Enter a small nearby room, seemingly undamaged by nearby monsters. Pick up several bottles of aged, fine whiskey (value 2,000 sp total). Maccus open a door and several sacks of grain come toppling towards him. Passing through (and after some mapping confusion), realize they're back in the goblin storeroom, the door hitherto hidden by stacked foodstuffs.
  • Explore a northern hallway that turns out to exit via a secret door back adjacent to the entry chamber.
  • Having exhausted any obvious exits, the group decide to exterminate the two wood-store chambers full of giant fire beetles. Assemble at the first, Banjo throws a spike in to disturb them, and a half-a-dozen creatures run out. With the heavily-armored Tim and Maccus in front of the passage, and others launching missile weapons, they are defeated. Banjo cuts out a glowing gland and replaces his lantern with that item.
  • The second chamber is attacked likewise; this time, Tahj casts sleep and all the strange creatures curl up in balls and get eliminated. Maccus pulls down most of the rotten wood pile; the group find and ancient heavy leather-bound sketchbook. Among the schematic notes is an apparent wooden stage construction. There is discussion and then an "Aha!" moment.
  • Group returns to the large dead-end chamber off the entrance. Taking split cord wood with them, they affix the logs into the holes in the walls for a makeshift step-ladder. Tahj and Penrod climb and search for a secret door higher up the wall. Success! A hidden button pens a panel, and the group clamber into the dry, upper tunnel.
  • Travel south; enter into a wide 20' corridor with a double row of horizontal niches on each wall; the niches are filled with ancient rotting wood coffins, bones, skulls, mixed-up bits of human remains. Maccus starts bashing skulls and chests in, but the job seems endless.
  • Travel west and south. Here, a side-room with eight skeletons posted on the walls; the skeleton animate, stepping forward with rusty swords. The fighters protect the more vulnerable members. Tahj casts a magic missile and blasts one to splinters. Daggers get thrown in eye-sockets, ripping the skulls off. Maccus finishes off the last one with a mighty sword-blow.
  • A small tunnel northwest, north, then a side branch is explored for secret doors. This disturbs a swarm of 10 giant rats that come pouring out of the wall, biting legs and feet. The party runs back from where they came.
  • Once the rats have clearly settled back in their nests, the group returns north. Finds a half-octagonal chamber with a large stone sarcophagus and 5 painted panels on the walls; various scenes of a traveling monk, monastery, reception of gifts, training with arms, slavery of peasants. Maccus pushes the lid off the sarcophagus and a giant constrictor snakes slithers out? Tries to bite Maccus, who fends it off with a shield. Banjo casts sleep, but the creature is too large to be affected by it. This catches the monster's attention and it bites Banjo, casting horrible snaky loops around him and constricting. All of the party desperately attacks the thing, slashing and cutting. Banjo gets low on hit points and the party has only a few seconds to save him before more crushing occurs. Maccus gets a last hit in; is it enough damage? No, the snake has exactly 1 hp left, and it uses its dying breath to crush the life out of poor Banjo. Penrod finishes off the filthy thing.
  • The group returns from the apparent dead-end chamber, traveling south and then a wide hallway southeast. They are joined by another dwarven wizard from the same college: Bill of  RA. Step into a chamber with more coffins and bodies in the walls; consider exits east and northeast. As they pass through, they are horribly surprised by a half-dozen ghouls, disguised as corpses, stepping silently out of the niches. Ghouls are known to spread a horrible paralyzing fever with their bite, turning a victim into another ghoul. One is behind them, cutting off the exit.
  • Surprise round: Every party member is attacked by a ghoul. First target: Bill, who takes a natural 20 for a critical: The nearby ghoul grabs and bites into his skull, instantly killing him. Next: Penrod takes a hit, misses his save, and is paralyzed; the fever racks his body, gnashing teeth, helpless. Tim and Maccus avoid attacks. Tahj takes a hit, but is immune as an elf. Initiative follows: This the party wins.
  • Tim spins and attacks with his hobbit's two-handed sword, cuts the ghoul to the rear neatly in half at the waist, its diseased innards spilling out all over the floor. Tahj takes the opportunity and runs from the room at full speed. Maccus powerfully pushes the remaining party members back into the passage, blocking the entrance with his shield. Only two ghouls can attack, and they need a natural 17 to hit. The rolls: 4 and 17. Maccus misses his save and is paralyzed. Only Tim remains, facing 5 ghouls.
  • Tim has a ghastly choice; he can only carry one of the armored, larger humans away. He grabs Maccus and fireman-carries him off. Burdened, he either has to remain visible in the main hall or take a small side tunnel that hasn't been explored yet. He takes this to get out of sight. Unfortunately: It's a dead end, and the ghouls have the chance to bottle him up and finish off almost the whole party. Rules say that semi-intelligent creatures are 50% likely to be distracted by food, e.g., Bill and Penrod. Tim's player calls the dice "high". A d6 is rolled and the result: "6". So amidst the horrible rending sounds, Tim slips back out with Maccus, rejoins Tahj, and escapes the horrible place.
  • Back at the village with only 3 survivors. Aged whiskey is sold. Each gets 666 sp and 1633 XP. Tahj advances to a 3rd-level fighter. Have we seen the last of the ill-fated members of the Dwarven College of Magic? We'll see.

Thursday, June 14, 2018

Rope Reckoning

In comments to the last post, G.B. Veras pointed to a nice web page on the economics of medieval rigging (MIT History Dept.), and asked how much rope costs in my games. The short answer to that is that by default, I just use the stock Original D&D equipment list, read as silver pieces, so: 1 sp for 50'. For things either not on the list or clearly broken, then I look to outside source like the Medieval Price List (or whatever) and convert with the interpretation that 1 sp = 1 groat (that is: 1 shilling = 3 sp). This usually comes out closer to the D&D equipment list than you'd normally expect.

Let's use G.B. Veras' cited MIT page as an exercise.
  • The page in question says that over three years or, 4,327.3 kg (9540 lbs) of rope were sold out of Bridgeport at a cost of 134 pounds sterling (including 20% transport cost).
  • We must convert that weight into a standard length, which is predicated on the standard width of our rope. This site on climbing says that something a little under 10mm (0.39 inches) is common. Then we can find that Home Depot sells a brand of manila rope that is 3/8" (0.38 inches wide), 1200 ft., at a weight of 45 pounds. (Side note: This is rated for a load limit up to 243 pounds.) 
  • 1200 ft/45 pounds is proportional to about 50 feet/2 pounds. Dividing this into the Bridgeport figure, we get 9540/2 = 4770 lengths of 50' rope. Dividing that into the price figure we get 134/4770 = 0.028 pound sterling. Then 0.028 × 20 = 0.56 shillings. Then 0.56 × 3 = 1.69 silver pieces. And if we back out the stated shipping cost, then we get 1.69 × 0.8 = 1.35 sp. So once again I'd say that's "close enough" to the book D&D prices, if we read them in terms of silver pieces/groat coinage (namely: 1 in this example).
  • A side issue is that the weight of the example 50' rope is only 2 pounds, which is less than half the weight currently specified in the OED rules supplement (specifically: 1/3 stone, that is, 14 × 1/3 = 4.6 pounds; whereas the AD&D DMG specifies 75 coins = 7.5 pounds). Presumably that's okay in OED if we assume the number is inflated for overall bulk/awkwardness in carrying it.
Thanks to G.B. Veras for the data and the interesting exercise!

Monday, June 11, 2018

On Pulleys

Only on the Hotspot: A post about how pulleys work. I've made at least one really bad call in-game about them previously. So here's my homework-atonement.

I've got a house rule in OED  that provides a small chance for a rope to break in any critical situation. My players totally hate it! (That said: I relaxed it a bit recently.) In dealing with this, sometime in the last year or two one of my players asked if they could purchase a pulley mechanism. I said, "I don't think that's available as medieval technology". Whoo-boy, was that super wrong. (If you have a mechanical engineering background you probably knew that.)
  • Pulleys have been in use since antiquity. Archimedes in the 3rd century BC studied it as one of the three most basic machines (lever, pulley, screw). Heron of Alexandria in the 1st century AD included it in his list of five basic machines (lever, windlass, pulley, wedge, screw), and described crane mechanisms using several pulleys. Renaissance scientists identified it as one of the six "simple machines".
  • Specifically in the medieval period, pulleys were used to hoist materials when building castles. Later drawbridge mechanisms used pulleys. They are part of the mechanism for a trebuchet. Some crossbows incorporated pulleys for cocking as early as the 13th or 14th century. On sailing ships they are referred to as block and tackle (although I couldn't confirm the earliest date of such use).
  • How much should one cost? Looking at the Medieval Price List, we can compare them to a vise, which seems like a machine of comparable sophistication (a large screw, basically). In the early 16th century this is documented at 13s 4d, or about 40 silver pieces in our silver-standard conversion of 1s = 3 sp groats. (In D&D book inflationary money, that might be 40 gp.) Note that if used for climbing or hauling, PCs would still need to find a solid structure to hang one on.

Monday, June 4, 2018

Underworld Overhaul, Pt. 6: Revised Monster Determination

For your consideration: A revision to the OD&D system for underworld monster determinations. We suggest using this in place of the tables on Vol-3, p. 10-11:

Click here for PDF version.

Saturday, June 2, 2018

Target 20 at OD&D Discussion

Over at the OD&D Discussion Proboard, user Piper started a poll on people's preferred AC/combat mechanic, specifically: OD&D RAW Tables, Swords & Wizardry Ascending AC Conversions, or OED Target 20. I'm intrigued by the results so far. Thanks to Piper for thinking to survey that!

Thursday, May 31, 2018

Dragon Metrics By Age

Following up on Monday's post, I thought it might be nice to look at the Equivalent Hit Dice (EHDs) for Dragons, broken down by separate age categories. (In the OED Monster Database, for brevity, I have only color breakdowns, and assume ages are set by a random 1d6 method). This also includes all the different enumerations for Hydras. Power-curve ASCII graphs can be seen here. Enjoy,

Monday, May 28, 2018

Harmonic Hit Dice

I recently made a change to how the MonsterMetrics program estimates monster Equivalent Hit Dice (EHDs), so as to make it more transparent and flexible; this slightly changed some of the monster EHD values (mostly for higher-level monsters). I think there’s an interesting mathematical lesson here – I learned a few things – so I think it worthwhile to lay that out here.

Consider the basis for how MonsterMetrics does its job (recently clarified in the code). We want to measure monster potency over a wide range of possible PC levels. So for each level 1-12, we compute the number of fighters that comes closest to an even fight against that monster (that is, closest to a 50% chance of either side winning; this itself entails a binary search across each possible number of fighters 1-64, or the inverse, with possibly hundreds or thousands of simulated combats at each possible number to assess the chance of victory on each side). This generates an array I call Equated Fighters (EF); and each element therein is multiplied by the level-index to generate a value called the Equated Fighters Hit Dice (EFHD).

Example: Consider the standard Ogre. We find that one is fairly matched against 2 Veterans/Warriors, 1 Swordsman/Hero/Swashbuckler, ½ Myrmidon/Champion/Superhero/Lord (that is, 2 ogres against one Superhero is fair), and so forth. So we have an Equivalent Fighter array that looks like this: EF [2.0, 2.0, 1.0, 1.0, 1.0, 0.5, 0.5, 0.5, 0.5, 0.3, 0.3, 0.3]. Multiplying each value by its associated level gives us the Equivalent Fighter Hit Dice; spot-checking a few simple values, we see that an Ogre is symmetrically worth 4 HD of Warriors (2 × 2HD each), or 4 HD of Heroes (1 × 4HD each), or 4 HD of Superheroes (½ × 8HD each), etc. Not to say that every point is exactly the same; due to the discrete nature of the matchups, there is a bit of a sawtooth artifact in the values. In total we have this array for the Ogre: EFHD [2.0, 4.0, 3.0, 4.0, 5.0, 3.0, 3.5, 4.0, 4.5, 3.3, 3.7, 4.0], and this is shown pictorially below.

Now, given that we want to present a single number to represent “monster power”, the question is, what metric do we use to crunch those numbers down to a unitary value? Granted that the EFHDs in the example above are approximately the same, this is good news for the overall idea of making a single, summary value in the first place; that is, in the graph above, they all fall roughly along a horizontal line. This is generally true for most monsters, but not all. Monsters with save-or-die abilities that short-circuit PC hit points have EFHDs that trend upward (positive slope); while monsters with area-attacks that can kill lots of low-level fighters have EFHDs that trend downwards (negative slope).

Previously I was computing an overall monster Equivalent Hit Dice (EHD) by taking the arithmetic mean of the EFHD values. That's an obvious choice, but one that has notable limitations; the arithmetic mean is sensitive to outliers, so if a monster is unusually dangerous versus PCs of one specific level, then the EHD can be wildly biased in that direction. As an extreme case, some monsters can actually face off against an infinite number of 1st-level attackers – e.g., Golems and Elementals are hit only by +2 or better magic weapons, which mere Veterans will not have – and in such a case, the mean of the EFHDs itself becomes infinite. As a result, I was forced to mark those monsters as having undefined EHDs (asterisks in the OED Monster Database).

So: Here’s where the change comes in. What other options do we have for computing an average (measure of center) of the EFHDs? The median could be considered – it’s less sensitive to outliers, but would suffer the same fate if, in theory, half of the PC levels had infinite EF’s (it has a 50% breakdown point). Instead, the silver bullet seems to be the harmonic mean, that is, the reciprocal of the average of the reciprocal EFHDs. The neat thing here is that the harmonic mean actually has no problem handling infinite values (with the understanding that 1/∞ = 0). It’s dominated by a multiple of the minimum value (see here), so the only way the harmonic mean can become infinite is if every single EFHD value is infinite (that is, the monster would be unbeatable by PCs of any level; in which case we can interpret the non-real EHD as communicating the fact that awarding XP is a non-consideration).

If the EFHD values are all equal, which is approximately true for most monsters, then the harmonic mean is exactly the same as the arithmetic mean – so we won’t get wholesale changes in our EHD values. For example: The Ogre above has an EFHD harmonic mean of about 3.5; so I set the EHD value to 4, the same as before (and the same as its actual hit dice, which is nice). On the other hand, the harmonic mean is always lesser than or equal to the arithmetic mean, so in some cases, for high-level monsters with skewed power curves, the suggested EHD was reduced by a few pips. For example: The Red Dragon presented the most extreme case of this, in which its EHD dropped from 32 to 27 (a 5-point difference). I think that this bias in the downward direction may be reasonable for a few reasons: (a) it emphasizes the most likely use-case of opposition PCs (that is: the most effective PC level), and (b) it suggests that accounting for magic spells and the like may reduce the overall danger level of such monsters.

Most importantly, this change in methodology allowed us to fill in the previously-missing EHD values for monsters like Golems and Elementals (the tricky cases mentioned above). The most dangerous monster by this metric is now seen to be the Iron Golem from D&D Supplement I, with a devastating EHD value of 104! (All other monsters top out at around 40 EHD: c.f., the Stone Golem at 41, Large Earth Elemental at 39, Vampire at 38, etc.). This allowed me to cut the number of monsters with "undefined" EHDs by more than half (adding 14 monster types to the list); those that are left are those with copious spell-like abilities (lich, titan, beholder, etc.), are invulnerable to any fighter weapons (oozes), or have attacks that don’t actually kill people (rust monster).

A bunch of stuff got updated to follow along with this method of using the harmonic mean on EFHD values. See the code on GitHub. In particular, the module received new command-line switches: -e to see the Equated Fighters array, -d to see the Equated Fighters Hit Dice Array, and -g to see the latter graphed as ASCII text. I uploaded the output for all monster evaluations and graphs (at 5 units per step on the y-axis). The OED Monster Database has been updated, and so has the Monster EHD Listing (including sorting by both name and EHD value). And more to come next week.

Thanks to CUNY/Kingsborough Professor of Mathematics Nataniel Greene for suggestions that clarified my problem and led me in this direction.

Monday, May 21, 2018

Underworld Overhaul, Pt. 5: Dungeon vs. Monster Treasure

Throughout our investigation of the OD&D underworld stocking system, we've taken for granted that the treasure table in Vol-3, p. 7, with the first column titled "Level Beneath Surface" -- what I call the "dungeon treasure" table -- is indeed the standard in use for treasures in the dungeon. We have many points of evidence that the Vol-2, p. 22, "Treasure Types" table is for use only in wilderness adventures. However, here we entertain the thought: what if we used monster-keyed treasure types in the dungeon anyway?

There is an undeniable attraction to that idea. In particular, the treasure types system seems to give a certain "flavor" or preference to the treasures commonly found with different types of monsters. For example: Men (Type A) have large amounts of treasure and prisoners. Dwarves (Type G) have large amounts of gold, and reject any baser metals. Dragons (Type H) have overwhelmingly huge piles of treasure. Rocs (Type I) may have gems but can't collect coins. (Note the extreme specificity of those latter types; the monsters I just named are the only ones keyed to those treasure types.) On the other hand, a great many monsters are entirely lacking any keyed treasure type; e.g., skeletons/zombies, most fliers, extradimensional creatures, oozes, insects, and animals.

Expected Values

As a lead-in, it may be helpful to inspect the expected values of each of the different treasures possible. In each case this is done via the Arena code package, with the unit tests built into the appropriate code modules, which perform simple Monte Carlo simulation methods. Expected value for dungeon treasures, by level (rounded to two figures of precision):

And here the same for monster treasure types:

Note, however, that all rolled values are highly variable; in particular, the vast majority of expected value comes from the rare and high-value gems and jewelry (esp. the latter) in each case. For example: At the 1st dungeon level, 95% of treasures lack any jewelry, and such treasures have an expected value of only 90 gp. On the other hand, the 5% of 1st-level treasures that do include jewelry have a class expected value of 12,000 gp. In this perspective, we might say that the core D&D game is one of PC adventurers searching strictly for jewelry -- after about 10 treasures (at 1st level) they have a 50% chance of having secured jewelry and so leveling up; whereas any other treasure is effectively negligible. (Later levels have somewhat less variance than this, as the chance of gems/jewelry rises; but note that chance maxes out at 50%.)

We might compare the average treasure-type values seen here to the similar chart presented in Moldvay's Basic rules, p. B45 (repeated in Cook Expert, p. X43). He has overall lower expectations (about half what we see here), and yet the main treasure type table looks to have copied all the entries from OD&D, even adding new columns for electrum and platinum. This would seem to imply equal or higher value, so how can that be? Again, this is explained by the majority of value residing in the gems/jewelry. Moldvay has modified the gems table -- emphasizing chances for the lower-valued types; and even more radically restricted the jewelry -- allowing only the lowest-value category from OD&D. And hence overall lower expected values for the same treasure types.

Adventuring Demographics

Using the current Arena program, it's simple to explore using the two different treasure tables; by default the dungeon treasure system is used, while the -t switch forces use of the monster treasure types instead.

Note the following: When dungeon treasure is used, it is generated for every encounter (waived the 50% for treasure, but also not including any DM-placed high-value "important treasures"). Likewise, if monster treasure types are switched on, then we consult the type table for every encounter (waiving the "% In Lair" chance designed for wilderness adventuring). On the other hand, we honor the Monster Manual rule that monster treasure types be scaled in proportion to the average monster number appearing in the wilderness; whereas there is no such suggestion for dungeon treasures, whose distribution is thereby fixed (regardless of monster numbers). Note that since we scale monster numbers by party size, the average shares of monster treasure stay fixed for larger parties, but shares of dungeon treasure decrease for larger parties.

The following repeats (from the last few posts) the demographics from parties of size 4 adventuring in our dungeon, with monster numbers fixed in proportion to party size (no variation), using the default dungeon-treasure setting (Arena switches -n=10000 -v -z=4 -rs):

And here are the demographic results if we instead use the monster treasure types (adding the -t switch):

Conclusions: First of all, the monster treasure types generate significantly less treasure than the dungeon treasure system. This is reflected in the fact that dungeon treasure supplies about two-thirds of XP when in use; but monster treasure supplies slightly less than half. That might come as a bit of a surprise -- I think there are some misconceptions, based on impressions of the very large Dragon treasure (for example), forgetting that the vast majority of monsters in the system have little or no treasure whatsoever.

Secondly, and as a result of that, the use of the monster-treasure system would make it harder to advance in levels past the 1st. Comparing the two charts above, the monster-treasure population has roughly half the numbers at levels 3-5 (as compared to the top dungeon-treasure chart); and only about one-fifth the numbers at levels 6-7 (and in fact, the solitary 7th level character may be something of an outlier, with their excellent Dexterity and Constitution scores).

In summary: While there is some charm in the flavor of bending the rules to use monster treasure types for dungeon adventures, this results in overall less treasure, and makes things even harder on the PCs in terms of advancement opportunities (and is also more calculator-intensive, in that it requires scaling down from the table in proportion to number of monsters encountered). We would recommend sticking with the OD&D Vol-3 dungeon-treasure tables for underworld adventures.

Important Treasures

A final consideration; granted that we plan to follow the dungeon-treasure placement rules in Vol-3, it is important to recall (again) that the foundation for that system starts with the DM placing "important treasures" by fiat, prior to any random methods being used (p. 6):
It is a good idea to thoughtfully place several of the most important treasures, with or without monsterous guardians, and then switch to a random determination for the balance of the level. Naturally, the more important treasures will consist of various magical items and large amounts of wealth in the form of gems and jewelry.
So: How big should these important treasures be? (We ask, of course, because this can have a larger impact on PC survival and advancement than anything else we've analyzed in the system to date.) If we take literally the recommendation that they include "large amounts of wealth in the form of gems and jewelry", then we note the following. A dungeon-treasure including gems has an expected value of double the basic treasure; and a treasure including jewelry has an expected value of twenty times the base. So it would be legitimate to glance at the dungeon-treasure expected values above, and place special treasures (including gems/jewelry) at something like a 10-fold or 20-fold multiplier (or more) on each level. Be sure to stoutly guard such treasures with copious monsters and fiendish traps, of course!

Monday, May 14, 2018

Underworld Overhaul, Pt. 4: Monster Numbers Appearing

Here we get to an issue that's a little bit more tricky, because the advice given in the OD&D books are somewhere between ambiguous and self-contradictory: how many monsters appear in an encounter? Again I'll quote the foremost passage from Vol-3, p. 11:
Number of Wandering Monsters Appearing: If the level beneath the surface roughly corresponds with the level of the monster then the number of monsters will be based on a single creature, modified by type (that is Orcs and the like will be in groups) and the number of adventurers in the party. A party of from 1-3 would draw the basic number of monsters, 4-6 would bring about twice as many, and so on. The referee is advised to exercise his discretion in regard to exact determinations, for the number of variables is too great to make a hard and fast rule. There can be places where 300 Hobgoblins dwell...
In particular, in the first sentence, the parenthetical comment ("Orcs and the like will be in groups") makes no sense as a reasonable balancing factor; if a "single creature" at Level 1 is a reasonable challenge for some (small) party, then any multiple number of Orcs will be deadly (to say nothing of 300!).

For the following, we make the following baseline assumptions: (1) As specified in the last post, we use a formula for numbering appearing of NA = scaleFactor × level / EHD, where level = dungeon/character level (presumed equal). That is: we interpret "level of monster" in the quote above to be EHD, not the 1st to 6th level tables on the same page (contrast usage of "level [of] monster" on Vol-3 p. 11 with Vol-1 p. 18, say). (2) Standard party size is 4 characters/fighters (this seems like a common expectation; is about median for the sample party sizes in the book quote above; and seems like a reasonable balance between safety and fast advancement seen in last week's article). In the Arena code, scaleFactor is the same as party size, so 4 in this case. (3) We are simulating dungeon lair encounters, each with a roll on the dungeon treasure table (waiving the 50% chance for treasure, but also no DM-fiat high-value "important treasures"), not wandering encounters.

Granted that, Let's investigate the effect of a few different options for monster numbers appearing in the dungeon. First we repeat the demographic results from the last post; a party size of 4, and equivalent scaleFactor fixed at 4 (so, if dungeon level = EHD, monster numbers are equal to party size, and otherwise proportionally adjusted):

Now we consider if we change the "basic number" in this case, i.e., the scaleFactor, to a variable 1d6. This has an average of 3.5 (slightly less than our prior 4); in 3 cases less, in 2 cases more than our prior fixed value. (This is done by a one-line code change to Arena, so can't be directly executed via the current release application). This results in the following population:

Despite what we might have expected (with a lower average encounter size), we see here that the extra variation in the 1d6 actually makes for a significantly more dangerous campaign. Compared to the prior chart, there are only one-half or fewer fighters at the 5th, 6th, or 7th levels. Even if the PCs may be happy to sometimes fight only 2 or 3 same-level monsters, they will easily be overwhelmed sometime when they are outnumbered by 5 or 6 same-level monsters. (On the flip side, it's a bit weird to occasionally have a treasured lair with only 1 single monster.) Also, the Strength scores for the high-level fighters start to hint that the game may have turned into something of a random meat grinder, regardless of character ability, which we do not want. So let's dial down the variation a bit and look at instead rolling 1d4+1 for the scaleFactor:

Even with the same average as on a 1d6 (i.e., 3.5), this is clearly better for the PCs. Compared to the fixed scaleFactor = 4 table, there are roughly the same number of fighters at 1st to 5th level. The numbers at 6th and 7th level are reduced, but, e.g., there are over three times as many characters at 6th level as in the 1d6 experiment. And the ability score averages at high level look reasonable. And we avoid having single-monster lairs. So: This looks pretty good for dungeon lair numbers. (Side note: In each case, XP from treasure is roughly two-thirds of the total, with monsters accounting for the other one-third.)

Based on this, now consider wandering monster encounters. Seems like this could be around half the size of a "lair" encounter, say: scaleFactor × 1d3. Obviously this is somewhat subjective, because these encounters don't generate treasure, are not critical to advancement, and hopefully avoided entirely by discriminating PCs (and not simulated in our program in any meaningful way). Note that in this case, with our default party size of 4, and an average wandering encounter with 2 monsters, we exactly match the guideline text in Vol-3, p. 11, repeated here:
If the level beneath the surface roughly corresponds with the level of the monster then the number of monsters will be based on a single creature... 4-6 [party size] would bring about twice as many...
In order to make this synch up, we've had to: (1) interpret "level of the monster" as meaning Equivalent Hit Dice, (2) strictly read the "based on a single creature" phrase, and (3) entirely ignore the parenthetical note about groups of Orcs, and the follow-up example of hundreds of Hobgoblins. Our construction gives "lair" encounters again twice this size, which seems to be the upper bound for what PCs can confront and survive more than a few times.

But here's a complication: We assume that encounters (esp. wandering ones) will be scaled in proportion to both party size and monster EHD on the fly, and in practice this would require a calculator for the number-crunching (and also the complete list of monster EHDs). Here's a shortcut rule-of-thumb to make that more practical on the fly, based on the average EHDs at each level. (Bunch of spreadsheet number-crunching occurred here, not shown.) Look at the revised Monster Level Matrix we're using. There are six "tiers", and for each, a die-roll of 3-4 lands on a level-column which provides a "median monster", where EHD approximately equals the dungeon level (and so, presumably character level). The number appearing can then be adjusted by where the result is to the left or right of that median 3-4 result column:

You may note that a result of "Left 2" can only ever result from a die roll of "1" on the matrix; a "Left 1" result only from a "2"; and so forth. The multiplier shown might also be used for lair encounters (recommended base 1d4+1) and so forth. For clarity, the exact number appears for each pip of the 1d3 wandering encounter roll. I've got this jotted into my copy of OD&D Vol-3, p. 11.

Final thought: In contrast to this system, broadly in synch with what's related in that key page of OD&D Vol-3, Gygax's module creations tend to be a lot more dangerous, with larger numbers of monsters than we see here (even in proportion to party size). For example, the suggested monster numbers in Mike Carr's module B1 are much less than Gary Gygax placed in module B2. Another example: The wandering monster groups in the DMG Sample Dungeon have an average EHD of about 6 total, any one of which is an existential threat to a group of only 5 1st-level PCs, as depicted in the example of play, to say nothing of the variation which allows them to regularly be up to twice that size. (If the lair groups are any larger than this, then it's hard to see how they'd even fit in the rooms indicated.)

Monday, May 7, 2018

Underworld Overhaul, Pt. 3: Character Party Size

Here we investigate the effect of party size on success in the dungeon environment, and overall adventurer demographics, assuming our core derived dungeoneering system (parts one, two). Recall that OD&D suggests in multiple places that encounters be scaled to the size of the PC party (Vol-2, p. 4; Vol-3, p. 11). Therefore, the code in Arena sets encountered monsters at a number appearing of NA = scaleFactor × level / EHD, where scaleFactor = party size, and level = the dungeon or character level, which are presumed to be identical (more on this later). Also, we are using the core Vol-3 "dungeon treasure" table (link) for rewards; while we are not placing any high value DM-fiat "important treasures", we are waiving the 50% chance for treasure (i.e., every encounter generates treasure), so maybe that roughly balances out on average. Note well: Although monster numbers, and also monster treasure types, are recommended to scale with party size, no such suggestion appears for the dungeon treasure table; so in the dungeon, treasure distribution is apparently fixed per encounter, regardless of how many PCs or how many monsters are fighting over it.

It bears saying, regarding the basic number-appearing formula, that a lower-bound of one monster is set per encounter (or, obviously, a null encounter could occur). This actually has a major side-effect if a small party runs into a high-level monster, as is permitted by the monster determination matrix. For example: Say 1 PC fighter of 8th level encounters a Purple Worm (calculated EHD 32); even against just a single such monster, the PC is overmatched by a factor of ×4, and will pretty much automatically perish if they engage in combat. A party of 2 such 8th-level fighters (total 16 levels), again versus one Purple Worm, is overmatched by a factor of ×2, and similarly is probably dead. It takes at least 4 such 8th-level fighters to have an even match against a Purple Worm in a normal fight, by our estimate. The same is true for many of the 5th- and 6th-level monsters; even if encounters are nominally scaled to party size and strength, the top-level monsters have a fundamental irreducible danger in this way that usually wipes out small parties when they meet.

Granted that, here are some experiments to look at the effect of different party sizes on resulting adventurer demographics. This is accomplished in the current Arena simulator with the switches -n=10000 -v -z=1 -rs (adjusting the party-size z value as shown below; and reducing the overall population n value if you want faster results).

Observations: The overall survivability increases monotonically with party size, as we might expect: the total number of living fighters in the tables above are, respectively: 6141, 7000, 7626, and 7881 (this out of 10,000 fighters alive prior to the last encounter). But the peak level achievement is not monotonic: at party size 1, there is a single Lord; at party size 2, an increase to 3 Lords; at party size 4, a decrease such that there are no 9th or even 8th-level fighters, with only a half-dozen at 7th-level; and at party size 8, another decrease to just a single 7th-level fighter. This is fairly easy to interpret: compared to a solo adventurer, a party of size 2 is better equipped to survive the irreducible high-level monster danger described above; but past that, the more the fixed treasure awards are divided up, the harder it is to gain levels. Likewise, we see that the ratio of XP from treasure declines with higher party size (treasure stays fixed but monsters multiply), respectively: 86%, 77%, 64%, and 47%.

Another interesting effect: At small party sizes, we see that the abilities of Strength and Dexterity are more critical for survival and advancement in level (these scores noticeably increase with level at party size 1 and 2; more need to kill fast and avoid any hits at all?). But with larger party size, this effect fades away and Constitution becomes more important (as at party size 8; more need to tank and shield the rest of the party from attacks?). Although at the highest levels the sample size is small, so this might be illusory.

Finally, a comment on age: One may note that all the fighters in our experiment are fairly youthful, almost all between 19 and 23 years. In the code, every fighter starts at age 18 (and since the year ends on the last iteration, everyone in the final list is incremented to 19), and a default of 12 fights/year is simulated (note that this synchronizes with the OED healing rule: one month to heal up fully from any fight). On the one hand, this an unrealistically large number of combats for real-world humans (compare to Roman gladiators: maybe one event per season); and on the other hand, far fewer than most PCs engage in (bolstered by magical healing and other factors). Many of us have surely observed PCs advancing levels in our games at a temporal rate that seems counter-intuitive. For the simulator, you may consider dialing down the fights/year to a more realistic level (via the f switch); for PCs, this is part of the reason I'm in favor of not accelerating natural healing, and also possibly limiting adventuring to certain seasons, say (e.g., only in the summer, or skipping over the winter, at least).

Conclusions: With the system at hand, adventurers must in some sense balance the following risk-reward calculus: bigger parties increase safety from death, but maximal rate of advancement occurs at a party size of around two. Choose wisely!

Saturday, May 5, 2018

OERAD Offering: Monster EHD Digest

R.J. Thompson over at Gamers & Grognards has newly declared today, May 5th, to be Original Edition RPG Appreciation Day (OERAD), and I think that's super cool! A great way to show our ongoing allegiance and community support for the rawest, purest of all RPG experiences. (And not just as an exercise in nostalgia; I've convinced several of my wonderful millennial friends to buy it and convert in the last few months.)

Here's my new offering for today: the OED Monster EHD Digest. It's an extract of the primary results of the Monte Carlo simulations we do here to balance our games (i.e., computer simulations of monsters vs. fighters of various levels, run a few million times each, to dial in the danger levels). Previously you'd have to hunt through the OED Monster Database spreadsheet for this information; now you can print it on a single sheet for use at the table. Use for encounter balancing if you wish, and probably more importantly, XP awards at the end of each game. Also please check out other stuff at the OED Games website while you're there. Happy OERAD. Fight on!

Edit 5/26/18: Updated with more monsters and sorted by both name and EHD value.

The Master's Monastery, Ep. 4

Maia 1, 4729.
  • Personae: Long Tim (Hobbit Ftr3), Tahj Birdfoot (Elf Ftr1/Wiz2), Tia Birdfoot (Elf Wiz1/Thf3), Penrod Pulaski (Human Thf3), Banjo Saskin (Dwarf Wiz 2), Ruff Sharktrainer (Hobbit Thf 3). Brother Maccus unavailable, still recuperating from injuries 3 weeks ago. The group buys as many healing potions as they can afford and heads to the ruined monastery. 
  • The group decides to explore the upper ruins more. Takes a stairway to an upper-floor cloister with books and scrolls. Carefully searches the works and finds a gold ring and a partial map of the cellars, most of which they have explored, but showing several additional rooms. Attacked by several animated skeletons with swords in the dead-end room. Party manages to fend them off. Banjo takes a skeleton's arm with attached sword. (Reasons he should swing this and count the skeleton as wielding the sword.)
  • Looks inside a central garden area and finds a giant plant growing 60' away, with something metallic glinting in the sunlight. The group stays at distance and Ruff shoots it with one crossbow bolt; one of the large growths on the thing explodes, firing a stream of high-projectile seeds back at him for damage. The party responds with a volley of more missiles, all rolling well and scoring hit after hit. Two more volleys of seeds fire back and the the plant slumps to the ground, killed. A silver statuette half-buried in the soil is retrieved (1,000 sp). 
  • An exterior room is explored and two giant demonic hogs spring to attack; the party defeats them easily, but avoids the other filthy droppings in the room. The next room has a sagging ceiling and a makeshift beam propping it up; Ruff checks for whether it is load-bearing, and several flakes of ceiling plaster tumble down. The group considers whether it could fit in the wall slots in mysterious dead-end the 3rd room of the cellars, but decides it is too big a turn aside.Then, a kitchen with a mounted crossbow trapped aimed out the exit; the party disarms this and moves on.
  • One of the last exterior buildings, the party goes to move through an empty room. Unfortunately, dice show that the covered trap is sticky and only gives way as the last row crosses it. Ruff makes his save and jumps aside; Banjo falls 10' and takes damage. Immediately a large squad of hobgoblins attacks from the entrance on the other side of the pit, by surprise. Tim and Tahj take sword-hits. Penrod runs from the room, trailing a rope into the pit after him. Hobgoblins get initiative again, and press the attack with swords and spears. Tia takes two spear-hits and goes down (save vs. death successful; narrowly clinging to life). Tahj casts sleep and 4 hobgoblins fall, but 6 remain. Banjo climbs out of the pit. Tahj is hit twice, one of which is a double-damage critical; damage dice rolled -- snake-eyes for a total of only 3 points, leaving her with 1 hit point; she flees from the line of melee. The two hobbits, Tim and Ruff, hold the line; 2 hobgoblins are killed. Penrod slings stones from the entryway, bloodying the larger ones at the back. Banjo successfully casts charm person on a hobgoblin. Morale for hobgoblins narrowly succeeds, and they strike more blows. Two more fall and the chief, at 1 hit point, tosses his sword and falls to his knees, begging for mercy in hobgoblinese. 
  • Tia is given several healing potions (as do Tahj and Ruff). The group try to interrogate the chief but lack any shared language, and so put him to the sword. The charmed hobgoblin, Ukt, is discovered to know Common and pressed for information. He takes them to the group lair and informs them of the large metal net trap over the other entrance, which they spring with a 10' pole. Party retrieves a silver medallion and chest of 1,000 sp. Ukt seems to have grandiose plans of raising a goblin army and overtaking the entire kingdom, and seems to see himself as the new leader of the party group. Also discover a row of cells with a human child, Phillip, frightened and cowering, held for the next meal. Party debates what to do with this unfortunate. The warlike Tim argues forcefully for strapping him to his own back and giving him a weapon to fight in that direction. Banko suggests simply releasing him to escape on his own. Other party members try to give him various playthings to cheer him: the gold ring, a drink of wine, the skeleton arm and sword, a potion bottle with a painted face, a.k.a. "Mr. Potion Bottle", allegedly a favorite toy for city children. Phillip is then locked back in his cell for "protective custody".
  • Last few rooms of the upper ruins are searched, finding nothing but ruined furnishings. Group makes it way back to the cellars/dungeon, with Ukt leading the way. 
  • Passing stealthily, the group avoids goblin and beetle lairs, and proceed to a long, cool room to the southeast of the main storage chambers. Inside find shelves of old vegetable matter and large urns. Ukt is directed to check one, at which point 4 giant centipedes spring out him! In the first round, all miss him with their poison mandibles. Ukt throws one off and cuts it in half with his scimitar. Ruff runs forward and daggers a second. Tia pierces one with her spear. And Tim fires an arrow scoring 6 points of damage, cleaving through the last centipede and also Ukt's chain mail, killing him instantly.
  • Party proceeds to the wine cellar, avoiding the pit with the ooze-monster that killed Aslak the Unclean. Enter back into the large L-shaped room with scores of broken casks and barrels, many of which are turned into nests for many horrid bat-mosquito monsters. 5 creatures fly into the air to attack; missiles and daggers mostly miss them; Tia's last spell, magic missile, partly injures one. One sticks in Banjo's backside, and falls and rolls to squish it; it dislodges and gets speared by Tia. Two fliers are cut down, but another flies up out of its nest. A few more are cut down, and then 6 more fly out, swamping the parties' attempts at attacks. The buzzing creatures dive and strike at all the party members, and now every party member has a bat-creature stuck in them and sucking blood rapidly. 
  • Becoming desperate, Penrod lights a torch and fires one of the nests. Yet more spring into the air. One is stuck deep in Tia's ear, blood spurting up and the thing lapping it greedily. One is stuck on Tim's foot and he misses it with his sword. Several are pulled out and the party runs for their lives, creatures still pierced into Penrod, Tahj, and Tia, each rapidly turning white and near death. Tim plucks the one out of Tahj and squashes it. Tia has 3 hit points and is about to take 1d3 blood-suck damage. Banjo tries and fails to grab the thing. Tia herself fails to pull it out. Damage die comes up: 3 hit points and Tia is out of points. Save vs. death: failed, and Tia sadly expires before the others can save her. Tim slashes his sword at the bloated monster and it explodes, splashing the entire party with Tia's life-blood.
  • The party retrieves Phillip and returns to the village. His well-to-do aunt, Heide, weeps with joy and rewards them with 500 sp. Total haul for the excursion: 3,500 sp, and a total of 7,000 XP (so: 700 sp and 1,400 XP for each survivor). Tahj is promoted to a 2nd-level fighter. Banjo achieves 3rd level as a wizard and looks eagerly forward to wielding a magic spell of the 2nd level on his next adventure!

Monday, April 30, 2018

Underworld Overhaul, Pt. 2: Monster Level Matrix

You can’t really use the by-the-book OD&D Monster Level Matrix (Vol-3, p. 10) to generate the level of monsters in standard encounters; it’s almost comically, ultraviolently, overkill. We’ve noted this a number of times (links one, two, three, four). Every later edition of D&D agreed that it needed to massively dial down the danger level; including Gygax in AD&D (who might have actually over-corrected in that case). Here's a look:

Original Monster Level Matrix

Observation 1: According to this table, on the 1st dungeon level, any of monster levels 1-4 can appear regularly. Based on our initial Equivalent Hit Dice (EHD) analysis (link), the average monster on this level is not 1 EHD in power; it’s actually a little over 3 EHD that our 1st-level PCs can expect for a “standard” encounter there. Any one such encounter is a deadly threat, even solo against 4 PCs, say.

Observation 2: By the 3rd level of the dungeon, monsters across the entire spectrum can be expected regularly. For example, within a half-dozen encounters, our presumably 3rd-level PCs can expect to confront one 6th-level monster, such as: an adult dragon, 10-headed hydra, vampire, balrog, or purple worm (various EHDs between 12 and 39 for these types). And there’s simply no way that a 3rd-level party can hope to regularly run into encounters with even a solo creatures of EHD in the 20’s or 30’s and expect anything other than a TPK.

You get the basic idea regarding that original Monster Level Matrix. Just to nail the issue home, here’s the demographics resulting from stocking dungeons blindly via that table. Using a data file that matches the original Monster Level Matrix, this is produced with the current Arena program using the switches -n=10000 -v -z=4 -rs (that is: a population of 10,000 men, versus monsters, in parties of 4 at a time, reporting summary statistics; with default dungeon treasure, 24 fights/year, and 50 years total time):

Note that even after the 12 million separate combats that this represents (the 10K population is constantly refreshed as adventuring men get killed off), it's almost impossible for anyone to have graduated past 6th level. Perhaps more troubling is the fact that their isn't any evidence of higher average ability scores (esp., Str, Dex, Con) at the higher levels; this is a signal that character ability is effectively a non-issue, and affords no benefit in survivability. Basically everyone is just being thrown into a big random meat-grinder.

Revised Monster Level Matrix

So what do we recommend for a replacement to that table today? Here’s a simple solution concept: Let’s say that an Nth-level party, operating on the Nth-level of the dungeon, should expect to run into monsters of Nth-EHD, on average. (Obviously, that is far from what the original matrix produces). To the extent that the Monster Level Tables partition various EHDs into coarser chunks (see last post), we’ll simply reflect the same in our new matrix: six monster level tables are synchronized with six rows in the new matrix. Each row of the matrix covers the same dungeon levels that the equivalent monster table covers in terms of EHD. In each case, the average die-roll of “3-4” should sit where the row matches the column number (i.e., where party level matches monster EHD; symmetric down the diagonal). The result is the following (as in the data file on GitHub):

If we run our Arena simulation using this new matrix (same parameters as above), then we get the following demographics for the adventurers in question:

Now, that's still a hard game; while there are more 7th- and 8th-level characters present, still no one succeeded at cracking Name level (after 50 years of adventures by the 10K population). No one can accuse us of giving away the store with this modification; arguably we could dial down the generating matrix even more than this. Note, however, that character abilities do now seem to correlate with survival, especially in the average Dexterity column here (for man-vs-man fights, we've previously seen that Strength is more fundamental). So this might represent a simple and reasonable upper bound for Monster Level Matrix difficulty. Also, if the DM regularly places "special" treasure at a steep multiplier over table-generated treasure (as sayeth the book), then advancement would be more swift than this; at least the PCs would have some chance of surviving to benefit from such treasure caches.

Still to come: Monster numbers and treasure value.

Sunday, April 29, 2018

Website Up

Reincarnation save successful! We've got and related websites and email back up and running. If you attempted to send me email within the last week, you should re-send it at this time. Apologies for any difficulties this caused.

Friday, April 27, 2018

Website Down

Unfortunately, the web server running (and also my associated email) missed its save vs. death a few days ago, and is currently awaiting a reincarnation. Hopefully we'll have a replacement up sometime this weekend. If you happened to send me an email on Tuesday, you'll need to kindly resend it when we're up again. Fight on!

Monday, April 23, 2018

Underworld Overhaul, Pt. 1: Monster Level Tables

We noted previously that numbers for monsters and treasure, in the dungeon in OD&D, were at their root determined by DM fiat. Now we'll spend a few posts trying to massage what is there into a more formal and evidence-based system.

The first part here is probably the easiest: Re-aligning the monster level tables via some underlying rule. Fortunately, we have the fairly well-justified Equivalent Hit Dice (EHD) values available from our previous Arena/Monster Metrics program, and it is relatively straightforward to turn those into a rule for distributing monsters among the 6 "monster levels" in OD&D. Based on inspection of the original book tables, comparing to our EHD values, and also balancing with various experiments in the Arena program, we propose the following as a pretty good definition (see also on GitHub):

Further below, you'll see a complete listing of underworld OD&D monsters parsed into the six levels according to this metric. Most monsters stay at the same level as they appear in the Vol-3 book (p. 1011), although there are some notable changes. Also, monsters are distributed fairly evenly across the six levels, with around 16 monsters each on average; fewer at Levels 1-2 (about 10 apiece), and more in the catch-all Level 6.

To compare to the book system, you can see an old analysis here, in which shaded rows indicate the original monster tables. The book tables have cutoffs at about EHD 1/2/3/4/6/10. But with better monster metrics, you can see in the link that 3rd level has a big problem with how few monsters it keeps under that rule. If we used that book rule to assess the current expanded monster list, then the problem would remain; only about 9 or 10 monsters at levels 2-3; and an enormous dump of 35 monsters all at level 6. So this strongly indicated that we needed to massage the book pattern a bit for a somewhat better distribution.

In the new list below, the third column in the list below also shows the kill ratio attributable to each monster within a level, based on about 2.4 million combat simulations of 4-man fighter parties assaying into a standard-type dungeon, and encountering bands of monsters at equivalent EHD values. (This was generated with the current Arena program using these command switches: -n=10000 -v -z=4 -rk.) Monsters in each level are sorted by increasing kill ratios, so that the whole list runs uniformly from lower to higher danger.

The kill-ratio organization also allows us to look for outliers at the start or end of a table, which may argue for incrementing or decrementing the EHD value of any monsters "on the bubble", so to speak, and this was done manually in a few cases. (Specifically, EHDs for the following were hand-tuned based on this analysis: Large Spider, Giant Beetle-Bombardier, Hell Hound, Harpy, Hero, Swashbuckler, Gray Ooze, and Zombie.) As one example, the Zombie (at the newly-recognized 2 HD) is inevitably going to stick out as either the strongest Level 1 monster, or the weakest Level 2 monster; we've set the EHD at 2 so it appears at Level 2 and smooths out the tables sizes a bit.

With that in mind, here are the proposed new Monster Level Tables:

#Level 1 MonstersKill %
1Giant Rat3%
2Giant Centipede4%
6Large Spider9%
9Giant Beetle, Fire13%

#Level 2 MonstersKill %
4Giant Frog7%
5Lizard Man8%
6Gray Ooze10%
7Giant Ant, Worker11%
8Giant Hog13%
9Giant Lizard15%

#Level 3 MonstersKill %
2Giant Toad3%
4Giant Tick4%
5Giant Weasel4%
6Giant Beetle, Bomb.4%
12White Ape9%

#Level 4 MonstersKill %
3Giant Snake4%
5Giant Beetle, Boring5%
6Giant Wasp5%
7Owl Bear5%
11Gelatinous Cube6%
13Giant Ant, Warrior7%
16Hell Hound15%

#Level 5 MonstersKill %
2Hydra, 6 Heads2%
4Displacer Beast3%
5Giant Beetle, Stag3%
6Giant, Stone3%
8Giant Slug6%
10Giant, Hill6%
11Giant, Frost7%
14Minotaur Lizard9%
15Invisible Stalker9%
16Giant Scorpion9%

#Level 6 MonstersKill %
2Giant Beetle, Rhino.0%
3Giant, Cloud0%
4Giant, Fire1%
5Hydra, 10 Heads1%
6Fire Lizard1%
8Umber Hulk1%
11Golem, Flesh1%
12Carrion Crawler1%
14Phase Spider2%
15Giant, Storm2%
16Dragon, White4%
17Dragon, Black4%
19Dragon, Green6%
20Dragon, Blue6%
21Mind Flayer6%
22Dragon, Red6%
23Ogre Mage6%
28Purple Worm9%