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!


  1. >NA = scaleFactor × level / EHD
    This seems off, I think? The one example I know of that hints at the authorial intent of the cryptic
    >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[...]
    is AD&D's random encounter tables, where the "level of the monster" seems to be the "monster level" (as per the table, albeit expanded to I-X in AD&D) and the increase in number is a fairly simple +100%/level.
    e.g. the by-the-book Kobolds would appear 1x on L1, 2x on L2; hobgoblins 1x on L1-2, 2X on L3; Wraiths 1x on L1-4, 2x on L5, up to 4x on L7.

    This does make lower dungeon levels exceptionally deadly, but OD&D seems somewhat built on the assumption that you'll just have a dozen or so levels. I don't know if a sole Fighter facing four Purple Worms on L10 is the intended result, but AD&D still has you face one with an additional "attendant monster" (or you could face 40d4+20 (120) kobolds, or 20d4 (50) hobgoblins, or six seven-headed hydras -- there's no limit for when low-HD monsters stop appearing).
    Then again, AD&D doesn't have the rule for multiplying monster numbers by ROUNDUP($partySize / 3).

    In any case, the main difference between your ruling and AD&D's is that the latter increases the number of high-level monsters more (and also goes by Monster Level rather than hit dice).

    Incidentally, Arneson's system in The First Fantasy Campaign is entirely different and not that useful for puzzling this out. The OD&D number of monsters seems to be Gygax attempting to simplify stuff and failing to give solid examples, from what I can tell?

    1. I agree that we're missing a concrete example in OD&D. In fact, the minimal notes there seem a bit slapdash and not fully formed.

      So I have made an interpretive call; actually using monster level (1-6) for scaling would make for mostly gruesome massacres, esp. since the power level of level 6 monsters varies so widely (unbounded above). The one thing I've done on that page of my OD&D copy (Vol-3, p. 11) is to scratch out the word "level" (in "level of the monster") and write in "EHD" in its place, which makes for a rational way of dealing with that issue.

  2. See this is why it is important to have hirelings/followers. Some extra fodder for the monsters, but a smaller cut of XP/Treasure (or none if they don't survive) :) Win Win!

    1. I would think so. I'm a little stumped at why my current players have declined to do that (see: The Master's Monastery posts).

    2. I have to agree with that. I recently took two PCs into the Caves of Chaos (a Magic-User with one hit point and a Fighting-Man with two), so of course they hired five mercenaries to help them.
      They returned to the Keep with just two mercenaries, if I remember right, but more importantly they themselves were still alive and well despite having minimal hit points.

      Of course, OD&D BTB makes hirelings cost-prohibitive for a first adventure ("100 Gold Pieces would be required to tempt a human into service") and my reading of the text is that men-at-arms require an Armorer and an Armorer requires a stronghold.
      And, of course, even if you don't need a stronghold there's a weekly 100-600GP cost to find recruits in the first place. Again, "cost-prohibitive for a first adventure".

    3. Pretty much yes; there's (as always) a lot of room for interpretation there. For me, I assert that 0-level mercenary soldiers just won't ever go in a dungeon. For the ad cost of leveled hirelings, I interpret it as a choice of the PC; e.g., each 100 value gets 1d3 1st-level prospects to be interviewed. So that puts it barely in the range of new adventurers if they pool their extra money, maybe. (Not super feasible, but barely possible.)

    4. Wouldn't any character count against the number appearing formula?

      If so, then excess henchmen or hirelings just bring down more monsters on you without contributing much combat power. Hirelings naturally become useless much deeper than level 2... Henchmen are more useful longer assuming they lag only a level or two behind.

      If straphangers don't increase monster numbers appearing, then it is plausible for a team of two fighters to hire dozens of hirelings to clear the dungeon with them... And somehow a platoon of infantry attracts no more monster attention than two PCs.

      I think it's very reasonable to count any adventurer against the number appearing formula. Maybe allow one "free" straphanger per three pcs for torch bearing duties, or allow fighters a free squire as a class feature.

    5. The way I figure it, you probably want hirelings for the lower levels anyway simply because there's so much treasure. The average treasure horde on level 13+ has 17,500 gold pieces; that's six people's worth of encumbrance, or twenty people if you just go with backpack+2xLarge Sacks.
      (Incidentally, this is also why you pay the hired help a fixed sum rather than a percentage.)
      Or, well, you pay 20GP for a 2+1HD Mule with a 3,500GP maximum load.

      Also, well, you probably want to have someone holding the torch (or stick of Continual Light) for you so you can free up your hands. This is less of an issue if you've already got a Magic-User with nothing better to do, but in a Fighting-Man party like these tests assume?

      There's also the more sinister aspect of mercs, which is the thing where you don't need to outrun the 15/30 Spectre, you only need to outrun the mercenary. This is probably negative to your Loyalty scores if public, though, so beware.

    6. Chris: You have a fair point. Admittedly in my real table game, I don't scale monsters by party size (at least: after estimating the number of players before writing an encounter location), so my thoughts in the comment above somewhat had crossed-wires. Maybe hirelings should count in the monster formula. Or maybe an interpretation should be made where they don't count, or for half, or somesuch, by the Vol-3 logic.