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.)

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!

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.

Edit 7/24/18: This particular format turned out to be a pain to maintain and has been removed. Please see the full OED Monster spreadsheet that contains all the most-up-to-date EHD estimations (as well as having them now inserted into the automatically generated stat blocks):

Monster Database at OED Games

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!

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.

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