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 [link]. 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%

Monday, April 16, 2018

In Praise of Carl Sargent

I'm a big fan of Carl Sargent's work for D&D. In the mid-1980's to 1990's he worked for both Games Workshop and TSR. At GW he worked on the Fighting Fantasy books (under the pseudonym Keith Martin). At TSR, he worked on numerous setting/adventure books for Greyhawk, such as the From the Ashes boxed set (something of an attempt to resurrect Greyhawk after it was razed in Greyhawk Wars), Iuz the Evil, The City of Skulls, and the Night Below boxed mega-adventure. He also wrote PC2, Top Ballista, and co-wrote GAZ 13 The Shadow Elves, for the BECMI D&D line.

I find that Sargent's work is, without fail, incredibly careful, thoughtful, detailed, and with near encyclopedic awareness of the prior game literature (e.g., whether working in the campaign world of Greyhawk or the Known World or whatever). He also has a real streak of imagination. For example, I recently read PC2 Top Ballista, which is a fanciful and attractive product (I would not want to write it off as a total joke, as one might from the title and cover). I honestly enjoyed the rocket-powered flying city, skygnomes with a biplane aerial academy, and the great library with its centuries-old undead floating-head librarian (get it?) armed with silence and death spells. At the same time, he presents alternative rules for falling clearly based on real-world speed/times, some obvious research into early biplane fighters, etc.

I might guess that Sargent's legacy for D&D is unfortunately constrained by having worked in a very conservative era for TSR: in the shadow of Gygax's departure, in an artistic contraction from the culture wars of the 80's, with very restrictive design dictates that ultimately wanted all the products to be PG-rated at best. His 165-page source book for the Great Kingdom, Ivid the Undying, was cancelled by TSR circa 1993 and never published (although later released as a free download online).

My general instinct is that Carl Sargent is a writer very much after my own heart. I would have liked to see what he'd create for D&D in a less restrictive context.

However, here's the surprising thing that I just learned: Sargent also held a PhD in parapsychology, and was quite a major figure in experiments claiming to show evidence for psi-powers, remote sensing, ESP, etc. He appears in the Encyclopedia of Pseudoscience. His experiments claimed among the highest effect sizes for remote-sensing, until scientist Susan Blackmore visited his lab in the 90's and pointed out numerous violations of protocol (actually terminating her own prior belief in the paranormal). Sargent left the field after that, and at the moment I can't find any information on what he's done since then.

The one additional kick is that I can't help but note that Top Ballista (1989) is riddled with lots of ESP-type powers and counter-powers. Perhaps even better, he features a new equipment item for the tinker/mechanic skygnomes, the Skyhook Set, "essential for best use of the Machine Building skill... an old gnome saying is 'a good gnome needs naught but skyhooks'". Then in Susan Blackmore's essay on his work (2001), she cites the philosopher Daniel Dennett as asserting of the parapsychologists: "they are looking for 'skyhooks' rather than 'cranes.'". Weird echoes in a crazy world. Maybe some actual belief in the supernatural is of benefit to a fantasy game writer.

Carl Sargent, we miss you!


Saturday, April 14, 2018

The Master's Monastery, Ep. 3

Apru 7-8, 4729.
  • Personae: Brother Maccus (Human Ftr2), Long Tim (Hobbit Ftr2), Aslak the Unclean (Dwarf Wiz2), Tia Birdfoot (Elf Wiz1/Thf3). The party pays living expenses for the past 3 weeks, deletes any rations on record, buys two new potions of healing from the local witch, and then proceeds to the monastery ruins. 
  • Descending into the cellars beneath the ruin, Tim notes in the entry chamber that the pile of bones and skins seems larger than last time. The group skirts the wall to avoid it.
  • Eagerly proceed to the bandits lair, where the chief and servant boys were trapped to their doom in panic room (storage crates stacked over trap door). Distressed to discover that they have chopped their way out with an axe, writing "I will return a**holes" on the wall on chalk. Aslak adds "Wangs" to the graffitti. Open the inner trap door and a stone-weight of iron balls pour out on their heads: 4 points of damage to Aslak & Maccus. Treasure is gone.
  • Listen at a nearby door and hear dastardly goblins within in. Break open the door; Aslak casts sleep and 5 of 6 goblins hit the floor; Maccus cleaves the last one in twain with a sword. No treasure found.
  • Twenty feet later, at an intersection, Tia's keen ears detect more goblins, possibly lying in wait, to the west. Party goes south instead to a goblin storage room piled high with boxes, barrels, and sacks; no exit to be seen. At this point the half-dozen goblins cut off the intersection, and throw darts at them; all miss. Aslak charms the largest goblin (whose language he speaks); Maccus and Tim charge into the front row of spears and chop down two goblins. Morale for the others breaks, and they retreat to their guard chamber.
  • Charmed goblin, Ambros, is interrogated and says the goblins have a treasure chest, trapped with darts, unless the proper key is used. Also informs them that further east there are "giant goblins" (bugbears), which concerns party. Looking down the west corridor, they see overturned tables and beds, goblin-spears, and goblins warning them off. Party calls out to turn over treasure; reaction dice say cowed goblins comply. They push out chest and throw the key. Inside: 2,000 cp and 50 gp. Party loads up sacks with treasure, tells Ambros to rejoin friends and murder any bandits if they show up again.
  • Return to village. Treasure split up. Long Tim levels up to 3rd (Swordsman). Tia throws celebration; sets tradition of leveled-up member being forced to eat bowl of garlic and then down a quart of wine. Discussion of whether only one clove of garlic, or one per level. In interest of time, Maccus and Aslak drink healing potions so as to return next day.
  • Return to dungeon and corridors further west. First corridor finds flickering red light to south. Proceeding, look in half-dozen cells on each side; barred windows with an old corpse in each shackled to wall. In end room: a table with two skeletons in chainmail, slumped in chairs, and a fist-sized glowing red gem! 
  • Party suspects trap. Maccus notes doors to cells are unlocked; Aslak pounds spikes in to shut them. Takes pole and pokes gem which rolls off table; dead skeleton guards begin cackling hysterically; unshackling and pounding sounds from behind. Party grabs gem and runs, but Maccus is slow. Rolls for animate corpses to force open doors; 3 succeed, cutting off Maccus from rest of party. First one is stout and takes distressing punishment; dagger stuck in skull, arrow shot through throat, and two magic missile spells before he goes down. Another lurches through door but Maccus cuts that down with one stroke. Party escapes. Gem found to be clear glass with magic light that flickers red.
  • Further east, party sneaks past pair of wood-store chambers with many giant fire beetles. Enter large storage hall with mostly empty and smashed crates along walls, stretching to south. Exit via side door to west.
  • First small room: Pile of smashed wood, wood and walls stained reddish up to waist height. Second room: A 10' wooden vat with brass pipe through south wall. Following pipe: A room with 5' depressed floor, a few inches of filthy water within. Aslak steps through to look around next corner. Surprised to find himself trapped by giant acid amoeba, his boots already disintegrating off his feet! Party jumps to rescue, Maccus tries but fails to pull him out. Chops with daggers and swords, lantern fire applied to no effect. Aslak gruesomely consumed by the ooze, skin and flesh sliding off his bones. Tim finally chops the thing to death, but his sword disintegrates into fragments in the slimy mass.
  • Party proceeds past room with several old empty barrels. Enters large L-shaped chamber with many old barrels in wall racks, mostly broken and empty. Turns corner to find many nests in the barrels; 3 stirges appear. New dwarf shows up: Jam Falcon, "Hey, watch out for those stirges!"; throws dagger, bit by stirge for 6 points, immediately dies. Swordsmen chop two down; 5 more fly out to attack. Party runs and succeeds at slamming door shut to cut them off.
  • New dwarf shows up: Banjo Saskin. Conveniently brings spare sword for Long Tim. Group proceeds back to storage chamber, finds three doors in lower part of large chamber (east, south, and west). Listening at central door, succeed at hearing normally quiet bugbear voices. Try to force open door, Maccus fails initial roll. Group runs to westernmost door and bursts into same room that way, catching bugbears ambushing first door by surprise. Banjo charms bugbear in center of room (DM note: winds of magic say this is a one-time occurrence). Group mass-fires attacks at bugbear near door to no effect; he twists and dodges, several arrows sunk in door. Smashes Maccus in armored leg with large spiked mace; rather frail Maccus reduced to 1 hit point. Bugbear at other side of room throwing spears. Charmed compatriot attacks him, misses. Maccus, Tim, and Tia finally fell first bugbear. Tia hides behind boxes for backstab. Tim and Maccus cut down the remaining one.
  • Treasure chest found; searching for traps, skittering sound within. Charmed bugbear interrogated; what is it? Pet giant centipede. Any way to prevent it from coming out? No, it always jumps out tries to bite the opener. Bugbear opens chest and giant poisonous centipede indeed jumps and furiously bites neck, arms, ears, etc; thick-skinned bugbear laughs it off and offers party to pet it. Party declines and takes treasure instead; 1,000 sp and 100 gp. Bugbear ordered to stay and kill any human bandits he sees.
  • Back at village, party splits treasure and XP. Brother Maccus becomes 3rd level (Swordsman). Arranges room at inn to rest & recover, as he will require 4 weeks to heal from his fractured leg and other injuries.

Friday, April 13, 2018

Improv and RPGs at Paul's Gameblog

In which a sharp lesson is delivered about inviting Yours Truly to be a player in one's game:

Monday, April 9, 2018

Monster & Treasure Assessment

The goal of the D&D game is, in some sense, revolves around the monsters and treasure. We defeat monsters, and accumulate their treasure. These are precisely the two things that generate XP in classic D&D.

The goal of this blog, as is perhaps obvious, is generally to analyze the system present in Original D&D. However, at its essential root, we are forced to admit the following (despite what appears to be a system of well-defined tables and the like): the quantification of both monsters and treasure in Original D&D is ultimately by DM fiat. In some sense, there is really no well-defined system for either of these subjects in the books. Let’s take a closer look.

Monster Numbers

The guidance on populating dungeons is in OD&D Vol-3, “The Underworld & Wilderness Adventures”. The subsection, “Distribution of Monsters and Treasure” is near the start of the book. For the moment, let’s just focus on its advice regarding monster quantity. It says (p. 6):

The monster(s) can be selected by use of the Monster Determination & Level of Monster Matrix which is given later in this booklet. The number of monsters is best determined by the level being considered and the kind of monster inhabiting the room or space. The Monster Table from Volume II can be most helpful here.

Note the second sentence here: it is essentially just a call for DM’s to make a subjective judgment call (no real system quantification). We might then look to the third sentence and direction to the Vol-2 “Number Appearing” statistics, but Vol-2 itself contraindicates such usage for dungeon encounters; the footnote there says, “Referee's option: Increase or decrease according to party concerned (used primarily only for out-door encounters)” (p. 4). So then we might attempt to follow the first sentence above, and refer to the Vol-3 random monster determination section (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.

Now the advice in the first sentence here fundamentally makes no sense as a balancing principle. If Orcs are the same individual strength as some other 1st-level monster – Spiders, for one example – then you simply cannot have the former appear in large numbers, and the latter in isolation, and have them both represent the same level of danger. But the rest of the advice here does synchronize and basically repeat comments elsewhere in important ways (ways which one might not expect, judging from later published adventures). To wit: (1) The number of monsters should be scaled to however many PC adventurers show up (as in the footnote in Vol-2, p. 4). (2) The number of monsters is ultimately up to the DM’s discretion, with no “hard and fast rule” one way or the other (echoing Vol-3, p. 6).

Treasure Value

Now we turn to the other half of the adventuring and XP equation: treasure. First of all we must dissect the fact that OD&D has two competing treasure tables: one in Vol-2, p. 22 (the “Treasure Types” table), and the second in Vol-3, p. 7 (no title, but the first column is denoted “Level Beneath Surface”). To cut to the heart of the matter: all evidence is that the former is for wilderness adventures, and the latter for dungeon adventures (that being in the “THE UNDERWORLD”, subsection “Distribution of Monsters and Treasure”). The clearest statement comes from the AD&D Monster Manual, which we consider to be continuous and a clarification of OD&D rules (p. 5):

TREASURE TYPE... it must be stated that treasure types are based upon the occurrence of a mean number of monsters as indicated by the number appearing and adjustments detailed in the explanatory material particular to the monster in question. Adjustment downwards should always be made for instances where a few monsters are encountered. Similarly, a minor adjustment upwards might be called for if the actual number of monsters encountered is greatly in excess of the mean. The use of treasure type to determine the treasure guarded by a creature in a dungeon is not generally recommended.

This specification is in line with the somewhat more cryptic advice on monster “Number Appearing”  in Vol-2, above (“used primarily only for out-door encounters”). We conclude that the entire Vol-2 system of monster numbers, in-lair %, and treasure types, is for use only in the outdoor wilderness setting. Another point of evidence comes from the D&D Monster & Treasure Assortment product, for use in keying dungeons only (introduction, 1st paragraph), which was produced by a school-aged Ernie Gygax rolling on that Underworld treasure table in Vol-3, and not by monster Treasure Types (Ernie remembers it was in the LBBs, per message on Facebook 2/19/18, but not the exact table – although we can logically deduce it was from Vol-3, because that’s the only one keyed to dungeon level as is M&TA). A third point of evidence is in Strategic Review #1 (1975), p. 4: the solo-dungeon system specifies treasure with monsters as "According to the type indicated in D&D, Vol. III for 'Outdoor Adventures' with pro rata adjustment for relative numbers." (A little scrambled, because treasure types are in Vol-2, and here they are in fact being used in the dungeon; but the intent seems clear that by design treasure types are for outdoor adventures, and also scaled by monster numbers, as in the later MM.) In AD&D, the dungeon treasure table is missing from the core DMG text (excepting perhaps one in Appendix A), so a pure AD&D player can be forgiven for not knowing where there was any positive rule for dungeon treasure.

At any rate, the dungeon treasure concepts are in that critical OD&D Vol-3 subsection. The “Level Beneath the Surface” table provides a way to randomize silver, gold, gems/jewelry, and magic based on the dungeon level – but this is indicated only for secondary, random fill-ins. The main advice comes a few paragraphs before that (p. 6):

The determination of just where monsters should be placed, and whether or not they will be guarding treasure, and how much of the latter if they are guarding something, can become burdensome when faced with several levels to do at one time. 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. Once these have been secreted in out-of-the-way locations, a random distribution using a six-sided die can be made...

So the foundational process is really this stage in which the DM must “thoughtfully place” the most important (largest?) treasures... and apparently this could be anything, as no further quantification of this advice is given. In fact, consider the following: in the random determination method, the vast majority of the treasure value is in the very rare, very high-value gems and jewelry. Compared to the overall “average” treasure there, any treasure with gems has double the expected value; and any treasure with jewelry has about ×20 the expected value. So if we take the quoted advice above in the most literal sense, then Gygax is recommending that the foundational DM-placed treasures represent anywhere between ×2 and ×20, or more, in gold value compared to the treasure that appear in the random table. It could legitimately be almost anything and still be in line with the rules-as-written.

What are some of your rules-of-thumb for quantifying the “most important treasures” and monsters in an OD&D dungeon?

Thursday, April 5, 2018

Cubical Dice Through the Ages

Small joke here: not a true "Through the Ages" post looking at various editions of D&D, but rather an actual academic study by professor Jelmer Eerkens on the changing shape, size, and design of cubical dice from antiquity to the modern day. Fascinating stuff. From the abstract:
Cubic dice were brought by the Romans to the Low Countries, and are found in small numbers at many archaeological sites dating to the last 2000 years. We report on a systematic analysis of 110 well-dated dice from the Netherlands, showing that shape, pip configuration, and pip style changed significantly for bone and antler dice from the Roman to the recent historical period. Dice predating 650 CE are highly variable in all attributes, those dating between 1100 and 1450 are highly standardized, and those post-dating 1450 CE are standardized for some attributes, such as symmetry and configuration, but variable for others, such as material type. There is also a major shift from “sevens” to “primes” and back to “sevens” pip configuration across these temporal windows, and pip style was simplified over time from a dot-ring-ring pattern to simple dots.
(Hat tip: Jon Miller.)

Monday, April 2, 2018

On the Clock

For your consideration: I've fallen into a thing with wandering monster checks in my recent games, that I've never seen anyone else do. I broadly assume that adventurers are exploring a dungeon in real-time (however long they take to decide and interact with me), and time the wandering monster checks with my watch, every 15 minutes. In fact, I'll even tell the players exactly how much time to the next check on occasion. Checks themselves are rolled in the open; standard 1 in 6 chance. (Checks are waived while in combat mode; this can be adjusted to taste, but I like the simplicity.)

The reason I'm doing this is to combat my own cognitive biases about perception of time as the DM. We're all familiar with the advice that if the action drags, the DM can start rolling dice as a random encounter threat (possibly real or vacuous) to hasten the action. For example, DMG p. 97 cautions about a "boring session", and suggests, "Mocking their over-cautious behavior as near cowardice, rolling huge handfuls of dice... might suffice."

But the problem with that is that the DM's perception of "boring" may not be exactly the same as the players'. If the players are deeply engaged with strategizing and planning, or character role-playing if that's what they like, or whatever, then perhaps that's not so bad a thing after all. While I want to be hospitable and support all of that, I'm just a bit suspicious that my own sense of time might be different while I'm not on the critical path of the action. And I don't want to prioritize my own sense of what the pace should be over everyone else's.

So, keeping the wandering checks (such that there's a legitimate pressure to use time wisely and proceed forward at some positive pace), but putting them on a strict clock (so as to make the pacing objective and not tainted by the DM's sense of time), seems to feel very nice right at the moment. This is a very "gamey" strategy, in line with my tendency to make almost all dice rolls in the open, to try to make the mechanics as transparent as possible, etc., and likely not suited for "deep narrative storytelling" type style. But if you're reading this blog, that latter description probably doesn't apply to you anyway. Consider it for a session and tell us how it feels.

Saturday, March 31, 2018

The Master's Monastery, Ep. 2

Mars 15, 4729.
  • Two weeks elapsed. Brother Marcus (human fighter with low constitution), still convalescing from sprained wrist in last adventure. Bawk Grueber (human fighter) retired. Tia Birdfoot (elven thief/wizard), in parts unknown.
  • Adventure group of 4: Long Tim (hobbit fighter), Tahj Birdfoot (elven fighter/wizard), Aslak the Unclean (dwarven wizard), Penrod Pulaski (human thief). Everyone buys a potion of healing from local witch with money from last adventure. Group considers but declines advertising for hired help.
  • Travel to the monastery, enter the main cathedral, mostly open, grassy. Search presbytery at end with raised platform. Attacked by stirges flying down from high remnant of ceiling. Party mostly specializes in ranged weapons; various arrows and daggers shot. 3 of party are struck by stirges. Tahj is hit for critical, 96% result: "larynx punctured"; no speaking or spellcasting.
  • Long Tim shoots the stirge out of Tahj's neck with a perfectly-placed arrow (triple damage critical, 15 points). Others manage to wrestle out stirges and snap their necks. Tahj drinks her potion of healing; larynx magically heals. 
  • Enter a side room, stumble upon two giant pony-sized hogs hungrily emptying out buckets of grain by old statue of stern man in robes. They leap to the attack; Tim takes vicious charge directly in breastplate; Tahj casts sleep and one saves (the other slumbering). Tim scores a mighty attack with his normal sword used double-handed (8 points), the others surround and stab it to death.
  • Stairs discovered. Lantern lit, the group descends.
  • Entry room with webs. Group carefully and quickly edges along the wall and out a side corridor.
  • Past a door, party gains a partial map, decide to follow it.
  • Map leads to large, totally empty room. Party search for secret doors or traps but find nothing. Decide to backtrack.
  • Party attacked by cat-sized, poisonous arachnid. Manages to bite both Aslak and Penrod; each of their saves vs. instant death is the exact number needed to survive. Nonetheless each take significant wounds before the thing is dispatched. Some small treasure found.
  • East and north lead to the edge of the presumed map space and two doors. Hear indistinct voices to the west. Open door, see lit room some 60' distant. Consider sending thief to creep in, but then Tahj shot by crossbow bolt (glances off armor). Aslak casts charm person, target fails save, beckoned to approach. Other men heard calling after him. Made to say he is going to latrine; another man follows, saying it isn't safe. Party lurks on other side of door; as men exit, Penrod grabs second man from behind, covering mouth, backstab is fatal.
  • Charmed man, Franz, questioned by new best friends. Explains general banditry principles; and hunt for legendary gemstone. Plans hatched. Franz calls down corridor, says Oskar (actually dead) has fallen and needs carry to bed. Three men exit without shields and almost surprised. Penrod gets caught behind door as it slams open. Franz attacks former friends. Tim takes glancing blow off iron helmet. Various daggers and arrows cut down the bandits and they slouch to the earth. Penrod loots bodies of a few silver pieces.
  • Problem: Franz tells group that his sergeant, with pay chest and two aides, is holed up in "panic room" nearby. Considered stratagems: (1) have Franz lure them out, saying other bandits encountered with treasure, (2) set fire to inner door, (3) spike door shut and siege them into submission, (4) saw through door and pay chest on other side, etc. Plan (1) attempted; sergeant opens door for Franz to enter and consult, then kills him (reaction roll: 3 out of 12, "Hostile reaction").
  • Aslak tries plan (2), spikes inner door shut. Various and sundry threats delivered in both directions. Drives a spike through into pay chest. A few silver coins spill out. Spikes hole bigger, hoping to grab mass of cash. Chest removed, Aslak jumps away as sword thrust through hole. Various other threats in both directions. Claim that party has 20 fighting men and 5 wizards not found credible per dice.
  • Party backtracks into bunk room, piling multiple heavy crates against outer door, sealing it shut. Plan is to return in some weeks after sergeant and aides starved to death.
  • Nearby tool room found; amidst junk, workable saw and drill found. Also chest: trap found, wire connected to scythe hanging on wall overhead. Wire cut safely, but chest found empty (after various searching for secrets).
  • Long eastern corridor explored. Wood store (rotting logs, worms, moths, etc.) discovered with giant glowing beetle; bypassed. Second wood store found; beetles here attack on sight. Tim cracks open first beetle with one blow, but 5 more scuttle up out of wood pile. "We don't want to fight an endless number of increasingly aggressive beetles", says Aslak. Party runs away (all at full 12" movement, faster than beetles, so automatic escape). 
  • Party looks down two other southern corridors on way to exit. Numerous doors found. Listen at one; goblin voices heard (Aslak knowing the tongue).
  • Party returns to village with little new cash, but several combats. 450 XP, 25 silver pieces each.

Monday, March 26, 2018

Point-Buy Systems Considered Harmful

A few weeks ago in "Sarge's Advice", there was a pair of questions (#8-9) on possibly pricing out individual attributes for a unit, such as movement, hit dice, armor, and morale. I feel like that bears on one of the main themes of this blog -- but when I went looking for a link to a post on exactly that point, I couldn't find any. Here I'll try to rectify that; my main thesis is this:

Game systems that price out individual attributes for figures, on an à la carte basis, are always inherently broken.

So: don't do that. (You'll see in my response Monday that I resisted approaching that idea.) Here are the top three examples that come to my mind:
  1. The Monstermark System for OD&D (in White Dwarf #1-3)
  2. "Creating New Character Classes" in 2E AD&D (DMG, Ch. 3)
  3. "Calculating Magic Item Gold Piece Values" in 3E D&D (DMG, Ch. 8)
You can probably identify others; and not just in D&D, of course. All of these systems were inherently broken and, to my knowledge, no one uses them anymore (they simply didn't stand the test of time). The 3E system probably stands out as the most poisonous of the lot, because at least the other examples had the grace to mark themselves as "Optional", but the 3E system did not. (OMG the rivers of blood that flowed over that topic on ENWorld back in the day, as every player thought themselves immensely clever for seeing that they could make a 2,000 gp infinite-healing magic item.) Now that I think of it, back in the day I also built a robot character in a Champions campaign this way that also completely broke that game.

The basic problem with any of these systems is that there's probably some synergy between two or more attributes that the designer didn't/couldn't observe, that allows constructing an overly-powerful figure when combined. And also: Some number of attributes that overlap redundantly, so that paying points for one becomes a waste as it doesn't have any benefit in the face of the other attribute. Or: The attributes are situational in nature, such that for the same price on one type of figure the ability is useless, while on another type of figure it is overwhelming. Here's what I wrote regarding the Monstermark system (the one I most recently dealt with in detail):
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.
Granted that we shouldn't engage in point-buy attribute systems (because they are always broken, we therefore have this corollary:

The acid test is gameplay.

That is: once you've designed a unit, the only way to judge it's properly balanced cost in the game is to play a lot of games and assess its real, on-the-table, utility and power. This is hard. This is why, throughout this blog, you'll see me emphasizing simulating our game designs in software so that we can test the various units a few tens of millions of times before adjudicating a final price. Of course, this was not a thing that anyone could even imagine before copious computing power was at our fingertips all the time. Historically, I assume that most game design was done by creating pieces for a game, and then pricing them as a near-afterthought (e.g., Mike Mornard has made this point many times); in my game designs the structure of the pieces is only about 20% of the effort, and the other 80% is adjudicating the right price (via simulations).

Examples of systems that we've simulated in software for pricing purposes:
Blogs where we've discussed this overall issue in passing (search for "acid test");

Do you have other examples of broken à la carte point-buy game systems? Or any you think aren't broken? Discuss below.

Thursday, March 22, 2018

Paul's Gameblog: Ego Through the Ages

Over on Paul's Gameblog last month, he had a post: "Ego Through the Ages", looking at how the mechanic for magic swords overpowering your will was a moving target throughout the years (OD&D, Moldvay, AD&D, and 3E). I know I grapple with this somewhat awkward rule whenever it comes up in my OD&D games. Check out his analysis!

Monday, March 19, 2018

Healing Through the Ages

Today we look at the legacy of natural healing rules, without the benefit of magical aid. This is an issue that has a clear and dramatic trend over different editions of D&D. Was it the right one?

Medical Research

Obviously, different bodies, and different types of injuries, heal at different rates. But consider the following as a sample of non-lethal, mid-level injuries:
So the pattern is clear: For these mid-level injuries (not even talking about third-degree burns or major head wounds, etc.), the time for healing is on the order of some weeks. If you dig into the details, this can be aggravated or lengthened if the injured member is used or stressed too early in the process.

Original D&D

HEALING WOUNDS: As noted previously, energy levels can only be regained by fresh experience, but common wounds can be healed with the passage of time (or the use of magics already explained). On the first day of complete rest no hit points will be regained, but every other day thereafter one hit point will be regained until the character is completely healed. This can take a long time. (Vol-3, p. 35)
I think previously I read this as 1 hp/day (after the first), but now that I look at it more closely, it seems that I missed the key phrase "every other day", which seems to indicate an effective ½ hp/day of complete rest? (Note that Chainmail had no rules for recovery; and in fact no campaign rules or context outside the combat encounter itself.)

Basic D&D

Each day of rest and recuperation back "home" will regenerate 1 to 3 of his hit points for the next adventure. (Holmes Basic D&D, p. 7)
We can see this same rule in the Moldvay (p. B25). However, I'm unable to find any rule for natural healing in the later Mentzer (1983) or Allston (1991) rules. Was this an editorial oversight? (The piecemeal choose-your-own-adventure organization of Mentzer's Basic Players Manual makes this seem likely.) Regarding Allston, while I can't find a rule for natural healing, other passages seem to imply that it should exist (e.g., constructs "do not heal normally; magic must be used", p. 155; and regarding nonlethal combat, "he heals them through the usual means, such as a cure light wounds spell or rest", p. 267). Can anyone find a rule for natural healing over time in these books?

Another interesting place to look in this line would be Mentzer's "War Machine" rules in the Companion set. Clashes between armies in these rules result in casualty percentages, half of which are deaths, and half of which are wounded. Regarding the wounded, Mentzer writes:
If a force retreats from the field, treat all wounded killed. If a force holds the field after the battle, those wounded troops can return to action in 1d4 months. (DM's Companion, p. 15)
Now, that 1d4 month (4-16 weeks) recovery is actually a pretty good model of our real-world medical data above (where we saw 3, 6, or 12 weeks for moderate injuries). However, it's totally out-of-sync with the current or any other edition of D&D; there is no mechanic in any published D&D which would produce recoveries for normal troops at the (realistically slow) rate shown here. So while noble in intent, this highlights just one of the many ways in which Mentzer's War Machine is essentially blind and/or in contradiction with results from the normal D&D system itself.

1st Edition AD&D

For game purposes it is absolutely necessary that the character rest in order to recuperate, i.e. any combat, spell using, or similar activity does not constitute rest, so no hit points can be regained. For each day of rest a character will regain 1 hit point, up to and including 7 days. However a character with a penalty for poor constitution must deduct weekly the penalty score from his or her days of healing, i.e., a -2 for a person means that 5 hit points healing per week is maximum, and the first two days of rest will restore no hit points. After the first week of continuous rest, characters with a bonus for high constitution add the bonus score to the number of hit points they recover due to resting, i.e., the second week of rest will restore 11 (7 + 4) hit points to a fighter character with an 18 constitution. Regardless of the number of hit points a character has, 4 weeks of continuous rest will restore any character to full strength. (DMG, p. 82)
This is something like a doubling from OD&D's "every other day... one hit point" rule. (Note that the basic D&D rule from Holmes is on the order of quadrupling.) One problem that may be obvious with these starting rules is that characters with more hit points, presumably the heartier and healthier types, take longer to heal from injuries -- for very high level characters, maybe ten times as long as a normal man. Hence, I think, the addition of the last line: no matter what one's level or hit points, healing is always complete within one month. (We may or may not consider that a fully successful adjustment.)

2nd Edition AD&D

Characters heal naturally at a rate of 1 hit point per day of rest. Rest is defined as low activity--nothing more strenuous than riding a horse or traveling from one place to another. Fighting, running in fear, lifting a heavy boulder, or any other physical activity, prevents resting, since it strains old wounds and may even reopen them.

If a character has complete bed-rest (doing nothing for an entire day), he can regain 3 hit points for the day. For each complete week of bed rest, the character can add any Constitution hit point bonus he might have to the base of 21 points (3 points per day) he regained during that week.

In both cases above, the character is assumed to be getting adequate food, water, and sleep. If these are lacking, the character does not regain any hit points that day.
Part of the transition we see here is that while OD&D demanded "complete rest" for any healing, 1st Ed. left out the word "complete", and here in 2nd Ed. the editor has taken advantage of that gap to distinguish between normal healing (1 hp/day, even on the march), and "complete bed-rest" (3 hp/day). This is now something like six times the initial healing rate we began with in OD&D. It still suffers from the healthier/longer-to-heal phenomenon (lacking the last line from 1st Ed.).

3rd Edition D&D

Natural Healing: You recover 1 hit point per character level per day of rest. For example, a 5th-level fighter recovers 5 hit points per day of rest. You may engage in light, nonstrenuous travel or activity, but any combat or spellcasting prevents you from healing that day.

If you undergo complete bed rest (doing nothing for an entire day), you recover one and one half times your character level in hit points. A 5th-level fighter recovers 7 hit points per day of bed rest.

Higher-level characters recover lost hit points faster than lower-level characters because they're tougher, and also because a given number of hit points represents a lighter wound for a higher-level character. A 5th-level fighter who has lost 10 hit points isn't seriously wounded, but a 1st-level fighter who has taken 10 points of damage is. (PHB, p. 129)
So this rule finally addresses the healthier/longer-to-heal problem, by scaling natural healing to character level. In so doing, it leaves healing at lower levels about the same (actually reduced in the case of "complete bed rest", the category being maintained from 2nd Ed), but radically increases healing at higher levels. For example, for a 6th-level character, healing is now 12 times over the OD&D baseline, or 18 times in the "complete bed rest" case.

The 3.5 rules accelerate this further:
Natural Healing: With a full night’s rest (8 hours of sleep or more), you recover 1 hit point per character level. Any significant interruption during your rest prevents you from healing that night.

If you undergo complete bed rest for an entire day and night, you recover twice your character level in hit points. (3.5 SRD)
In this revision, you don't even need a day of light work to regain hit points; it can happen in just 8 hours of time. And the "complete bed rest" is upped from ×1.5 to ×2 instead. So in this latter case it's about 24 times the healing rate seen in OD&D, for a 6th-level character.

4th Edition D&D

I don't normally go past the 3rd Edition of the game (and I've never played any such edition), but in this case the information is easily available online, and I think instructive -- it's actually a fundamental part of the 4th edition system design. Looking at a helpful blog post by MerricB on the subject:
Characters in 4E could heal themselves from a pool of healing surges – each equal to a quarter of their hit points. A typical character might have 8 of them available each day, and they were also expended by healing magic (which would provide a bonus to the healing). Whenever a character took a rest between combats, they could use healing surges to regain hit points. (Merric's Musings)
So -- in case you're not already aware of this -- in 4th Edition, characters could heal themselves effectively instantaneously, as soon as they had a minute or so breather outside of combat, for fully a quarter of their total hit points. At about 8 times a day, that's actually double their full hit points within one day, with no outside aid required; i.e., come back from a mortal injury twice every day. By my calculation for a sample 6th-level character, this represents approximately 100 times the healing rate from the OD&D basis.

5th Edition D&D

Again quoting MerricB regarding 5th edition:
Part of this idea [4th Ed. healing surges] remains in 5E, but with a couple of changes. First of all, they’re called Hit Dice, and they’re equal to the number of dice you roll to determine your hit points. Whenever you rest for an hour or more, you may expend as many Hit Dice as you like, rolling them and adding the total to your current hit points. Your constitution modifier applies to each hit die rolled.

A Short Rest is defined as being a period of 1 hour or more when you get a chance to bind wounds and generally recover. There are several abilities possessed by characters that also recharge when you take a short rest. It’s a lot longer than the time in 4E, so won’t be as frequently employed...

Long Rests and Full Healing: If you rest for eight or more hours, you get the benefit of a long rest: all your hit points are healed, and you regain half (rounded down) of your hit dice. For those who are used to AD&D, this is a major change in how the rules work. Without magic, it’d take weeks for a badly wounded fighter to get back on his feet! For those in 3E, it’s a change but they had wands of cure light wounds so it didn’t matter. For 4E players, this is less than they had, as they got all of their healing surges back! (Merric's Musings)
Note that none of this information seems to be in the free 5E basic rules release, or the SRD, so I'm taking for granted that Merric has it correct here. So, it seems like in 5th Edition, you can effectively get on the order of all your hit points back with a 1-hour rest, and then another all-your-hit-points unit back with the next 8 hours rest. That is: Similar to 4th Ed., two units of full hit points back in less than a day (although not all at once, instantly, as in 4th). So again that sounds like about 100 times the healing rate we started with in Original D&D (for a sample 6th-level character).


A summary of our findings are shown below (for the later editions, a 6th-level character is taken as the basis):

Note that the y-axis in the chart is on a logarithmic scale (the first time I've ever had to resort to that on this blog). This clearly highlights that the overall trend shows a surprisingly regular exponential acceleration in healing with each new edition of the game, approximately following a rule of f(x) = e^(0.72x), where f(x) is the multiplier on the OD&D baseline, and x is the sequential edition ID of the game as given above. Since e^0.72 = 2.05, this shows that, roughly speaking, the natural healing rate has regularly doubled with the release of each new edition of D&D (over the half-dozen or so editions to date).

If we go back to OD&D and look at our 6th-level fighter example, say hit points of 6 × 4.5 = 27, and a healing rate of ½ hp/day, we see that this character can regain all of their hit points in 27 × 2 = 54 days ≈ 8 weeks. That's actually a fair simulation of how long it realistically takes to heal one or two deep cuts, a halfway bad burn, or a broken bone (see the top section above). The most recent editions (4th/5th), granting something like 100 times the healing rate, or recovery from 2 mortal wounds every day, can only be considered as cartoonish. (Note that the entire analysis above pretends that we keep character hit points constant over the years; if we also take into account that PC hit points were themselves getting inflated, then the multipliers would look even more ridiculous.)

Now, someone might argue that hit points don't represent real injuries, but this is a debauched interpretation seen in 4th+ edition, and doesn't square with earlier editions of the game. Yes, 4th/5th edition makes the assertion that lost hit points may not be any real injuries at all; possibly just temporary fatigue or windedness instead. But even if we look at the 3rd Edition text above, there is no such indication; lost hit points are always some kind of injury, even for high-level characters (possibly just a minor cut or bruise). Moreover, the fact that side-effects of attacks trigger on any successful hit -- e.g., poison triggers for saves, energy-draining attacks, etc. -- contradicts the idea that a hit or lost hit point may not be any injury.

So: What to do in our house rules for an OD&D game? We are sensitive to the problem that healthier (higher-level) characters take geometrically longer to heal with a fixed ½ hp/day rule (or any other fixed number of hit points per day). We could also say this: Another problem with this rule is that it's still unrealistically too fast for low-level creatures. For example: take a normal man of around 3 hit points; even the worst wound which takes him to near zero hit points will be healed fully in less than a week, only 6 days. If we want something resembling the 3-12 weeks healing time from our initial medical examples, then we would argue for slowing it down in these cases even more. (See also the Mentzer War Machine rules above for a similar intent.)

Let's say we want any character to recover from zero to full hit points in some number of weeks like this. There is little to do but subjectively pick the number of weeks that makes us happy: this number could be 3, or 6, or 12, or something like that. I'll suggest picking 4 weeks to be a bit generous, and also to sync up with the 1E AD&D rule for capping the healing time. Hence:

Characters heal one-quarter of their full hit points for each week of complete rest.

Let's say we round this up to the next whole number to be charitable in cases where a creature has less than 4 hit points (like half of normal men). It occurs to me that (Crom help me) this slightly echoes the increment regained from 4th Edition's "healing surges" -- although on a time increment of weeks instead of seconds. Also assume that this requires comfortable rest in bed with amenities -- as in, a hostel or inn at town.

If we compare to the OD&D rule, the major change is of course scaling our healing rate to the overall hit points of the character in question. For 1st-level characters, the healing rate has decreased (to about a quarter of the book rate). For a 3rd-level character with around 15 hit points, healing rate is about the same as the OD&D book rule (hey, 3rd-level again: links one, two). For a 6th-level character, the rate has approximately doubled (and so in line with the 1E text). You can extrapolate the rest, I'm sure. 

I think I can imagine someone complaining "that's too slow for our adventures!" but I actually don't think there's any legitimate justification for such a position. For example, MerricB writes above: "Without magic, it’d take weeks for a badly wounded fighter to get back on his feet!", but I don't see any fundamental reason why that's a bad thing -- merely non-cartoonish. We can, of course, simply hand-wave the weeks of recovery time in-game, just like we do for days or nights or whatever the camping pace is.

Moreover, this rate of time actually helps to solve a bunch of other problems we commonly encounter in the D&D game. Some examples: (1) The party retreats to rest overnight, and the DM is confronted with coming up with some reason why the depleted monsters don't immediately get overrun the next morning. (2) The party wants to camp in a room of the dungeon, as they can get most of their needed recovery back in just 8 hours if they can only hold the door shut. (3) Our campaigns and timelines routinely run on an overly-accelerated basis: whole adventure paths take only days in-game, and PCs advance from 1st to 20th level within the course of a single game year. Slowing down the recovery time (to a realistic basis) could serve to put the brakes on all of that, and generate campaign stories that better resemble what we read in fantasy literature. (Especially in conjunction with reduced clerical healing magic, and possibly seasonal effects like no-travel-in-winter, etc.)

Comments or modifications?