Sunday, July 30, 2017

Further Obvious Thoughts on Wilderness

My prep for Dungeons and Discourse continues.  Also, I had lunch with one of my ACKS stalwarts a week or two ago, and have been re-reading some old posts (particularly this one) and some thoughts came up.

Topology - Jayquaying is considered important in dungeons, but not something you hear about much in the wilderness.  This is because the wilderness is "open" by default - you don't have to take any particular measures to provide multiple paths through it.  On the other hand, this abundance of paths can also be boring.  An inverse of jayquaying for the wilderness to restrict available paths probably makes sense.  Quayjaying, if you will.  Hard quayjaying is limiting available paths by impassable obstacles, soft quayjaying is limiting it by obstacles which are expensive to traverse.

Traps - Thinking about the resource game in dungeons, it's true that zap traps and trivial encounters aren't interactive or particularly exciting, but they perform an important function - putting chip damage on the party to keep them under resource pressure.  Seems workable in wilderness too - as simple as "if you sleep in the mountains above the treeline, all party-members take 1d3 points of damage from exposure unless you can find a cave", "every time you traverse a glacier hex, there's a 1 in x chance a crevasse opens beneath a random 1d4 party members, save vs paralysis or take 3d6 falling damage", or "if you sleep in a swamp, there's a 1 in n chance that your rations spoil".  In addition to grinding down party resources and providing tension, this helps make Land Surveying actually useful.

Specials - If you look at the dungeon-stocking guidelines, 25% of rooms have a "unique" or special contents.  Like traps, this is something I've largely neglected in my wildernesses to date, despite having quite a few ideas for this sort of thing.  25% may be high for a sensible wilderness, particularly a large one - 25% means that every hex has like 1.5 "unique" neighbors, which is very dense.  14-16% would mean that on average every hex would have a "unique" neighbor, which is still high but probably more reasonable.

Treasure - One persistent complaint about wilderness adventuring is "there's not enough treasure per game-time compared to dungeoneering."  Fair enough.  One way to boost this somewhat is unguarded treasure.  30% of trapped rooms have treasure in a dungeon; a reasonable parallel would be for a "trap" hex like crevassing glacier to have treasure at the bottom of a crevasse.  Likewise, 15% of "empty" dungeon rooms have treasure; no reason empty wilderness shouldn't, either.  Maybe it's a natural resource like rare wood or exposed metal ore; maybe it's actual treasure buried in a barrow mound that isn't haunted for once.  I expect you'd have to search a hex to find it, but that's OK - creates a resource tradeoff, time and rations for a chance of treasure.  This also provides endpoints for treasure maps.

Dungeons - Sometimes I think about abandoning the quest to figure out the wilderness game and just run dungeons all the way up.  Generally I don't like using dungeons at high levels because giants need a lot of calories and it stops making any sort of sense, but supernatural monsters are a reasonable solution to this objection (and wards can also explain why they're not out terrorizing the countryside).  Matt noted that dungeons do get old, and that he thinks this is not a great solution.  Reflecting further on this, the correct solution is fairly obvious - I need to put dungeons in my wilderness.  This is, of course, exactly what the damn manual suggests, but I've been too lazy for it in the past, in large part because the wilderness prep effort has been heavy as a result of large wildernesses with very dense lairs.  But, having figured those out, prep effort declines.  Dungeons provide high-treasure targets out in the wilderness, as well as a break from worrying about rations and overland movement and such.  Looking at page 235 of ACKS core, it suggests 3 large dungeons (6-10 sessions each), 10 small dungeons (1-2 sessions each), and 17 lairs for a 30x40-hex wilderness.  For a 10x10 wilderness, that's about a 25% chance of a large dungeon, an 84% chance of a small dungeon, and 1.5 lairs; lower density than I really want.  Given that historically I've gotten 6-8 sessions out of most of my 3-level, 60ish-room dungeons, I assume that what I'm building is on the low end of "large".  I could probably get 1-2 sessions out of a single-level 20-30 room dungeon, and could comfortably put three of those in a 10x10 microsandbox in about six hours of prep effort.  Then you drop rumors and these become places that players have to go find (as Alexis says - if you tell the players precisely where something is, they will go directly there.  If you tell them vaguely where it is, they will go everywhere.  And I want them to go everywhere if at all possible, because that's efficient use of my prep effort).

Homesteads - I was skimming Renegade Crowns the other day, and its system generates quite a few homesteads out in the wilderness.  Think Beorn and Craster.  These present a great, ambiguous opportunity.  If your players meet orcs, the first instinct is to fight them.  But if they meet hillfolk, it's hard to tell whether they're normal and friendly or cannibal cultists until you agree to join them for dinner.  If it works out, they're potentially great allies against beastmen, and at the very least a "safe and sanitary" place to rest and recover resources.  Homesteads might fall under a more general category of "oasis" features where replenishment of certain resources is possible; Rivendell's another example.

Level range - An observation I mentioned to Matt is that just as 1st level, 2nd level, and post-3rd level dungeoncrawling are all very different, it's possible that 5th, 6th, and 7th+ level wilderness adventuring are very different, with lower levels being much more resource-constrained and dangerous.  Got me wondering if maybe launching a wilderness game closer to 7th wouldn't be a bad idea.

On further reflection, I think that even if I executed successfully on all of these ideas, in an unmapped borderlands microsandbox with limited lair density, some route-blocking topology, "trap" hexes, unguarded treasure, an abundance of special features, three dungeons, and a smattering of homesteads, that would still be somewhat unsatisfactory.  Better than my previous wilderness efforts, and pretty close to my first ACKS dungeon, but still merely an open world rather than a living world.  The folks I've been talking to here seem big into Dungeon World and fronts and clocks lately, but I think something more up my alley would be "build a big list of NPCs who might do something that the players might care about, along with some Renegade Crowns-style internal conflicts between NPCs.  Every session, roll on the list, think about what resources they have at their disposal and what they want, and then something happens."  Might be NPC-vs-NPC violence in the background, might be something aimed at the PCs if they're on that NPC's shit-list, might be a job offer from that NPC.  But something happens, because somebody wanted something in the world and they've finally gotten around to acting on it.

Wednesday, July 12, 2017

Player-Controlled XP Allocation

A friend of mine asked me to give a talk on DMing, so I've been writing and rewriting endless cycles of notes on that.  One theme that I know I want to hit is putting players mostly-in-control of the difficulty of the combat that they face, by giving them free rein to scout the dungeon and avoid dangerous monsters.  Another theme is that really strong play often requires submission of the individual party member to the interests of the party - the wizard has to hold on to his one spell carefully rather than using it early for personal satisfaction, the thief has to expose himself to substantial personal risk in order to find traps so that they don't kill anyone (or everyone) else, and fighters are sometimes called upon to die for the party so that everyone else can live.  Clerics, of course, are clerics, and have always operated been expected to operate "in service" to the party as a whole.

But when you take these two ideas, players collectively in control of their destiny and subordination of the individual to the party, and combine them with XP for treasure, a funny possibility arises.

Under a certain reading of the rules, you earn 1 XP per GP that you receive from the adventure.  If the party as a whole determines (by vote, say) that some player failed to contribute and to pull their weight, by (say) fleeing from combat, the party as a whole need not allocate any GP from the treasure to that player, and hence he will earn little XP - just the monster XP portion, which is around 20% of XP on most adventures.  A persistent problem player who regularly earns 20% XP will eventually end up about 2 levels behind the rest of the party.  A player allocated only half a share of gold will tend to end up one level behind.  This is, obviously, not a form of censure that should be used lightly, but it is one that should be considered.  I suspect that, as with PC death, this is not something that needs to happen often for it to modify player behavior substantially.  The knowledge that it is a possibility encourages cooperation.

The reverse also applies - if you have a new player join a group and he's playing a class that you really need, the party can allocate greater than a share to him.  If someone's fighter died in a heroic rearguard action to cover the party's retreat and now they're playing a henchman and a level behind, you can allocate them greater than a share until they come up to level parity.  The trivial, common case is that a PC is 10 XP from leveling with standard shares, and a tiny reallocation might push them across a threshold.

Unfortunately, henchmen complicate this XP allocation scheme, for one because they receive an odd share size, and for two because traditionally they receive their shares straight from the party pool, but if a player receives an odd-sized share, do his henchmen too?  In the case of a problem player, it seems reasonable to dock his henchmen as well; in the case of a hero player, it seems reasonable to award his henchmen extra as well.  But this all complicates the accounting, or raises again the specter of "the pay for your henchmen should come out of your share of the treasure", which I suspect most sensible parties will reject on the grounds that a player with many henchmen is of great value to the party as a whole.

At the end of the day, one of the interesting facets of this game not present in more modern editions is that it is in many ways an experiment in small-scale self-governance, civics, and organizational behavior.  And yes, the gaming community seems to have settled on very regular norms regarding the allocation of treasure and XP, but one of the joys of transgressive/retrogressive gaming, allowing things like PvP and uneven allocation of treasure, is an opportunity to reinvent those norms (with good stories and object lessons about why we have those norms), or to arrive at new and strange norms.  And isn't that what the OSR is all about?  Rolling back the clock and seeing the other possibilities that could have been, not merely in the rules of the game, but in the rules of the group?

Wednesday, July 5, 2017

ACKS Melee Offense Analysis

At long last, I've figured out the computational tools needed to do the analysis of ACKS' fighter offense system.  For small cases (d6 damage vs d8 orc HP) it's easy enough to do by hand / in head, but for a long time I was sort of stuck on the big cases (d10+6 two-handed sword vs 4d8+2 ogre HP).  Getting expected values is easy, but as we saw with Weapon Focus and backstab, variance is actually super-important to get right.  The sensible way to do this with a modern computer would've been to just enumerate all 41,000 possible outcomes.  Instead in the shower I figured out generating functions (again...  they came up twice during my undergrad), which express those sort of probability distributions as big polynomials that you multiply.  This may or may not be more efficient, but it was certainly more entertaining.

In any case, on to the main event: probability that an attack will hit and kill an enemy of a given type from full HP.  A pure "killing power" analysis.  By expected damage output * survivability, sword-and-board is superior.  I'm curious if this analysis with kill probabilities and cleaving will highlight cases where two-handers and two-weapon fighters are competitive.  Additionally, I'm interesting in looking at kill probabilities on backstab.  So we're going to consider a couple of different "builds" at 1st, 3rd, 6th, and 9th levels:

  • Sword-and-board fighter
  • Two-hander fighter
  • Two-weapon fighter
  • Two-hander assassin, backstabbing
  • Thief with one-handed weapon in both hands, backstabbing
  • Explorer doing archery (we often hear that explorers are "very strong", and I'm curious how much of that is raw combat power vs special abilities)

At first level, the builds look something like:
  • Sword-and-board: Str 16, FS: Shield, plate and shield (AC8), THAC0 8+, damage 1d6+3
  • Two-hander: Str 16, FS: Two-handed, plate (AC6), THAC0 8+, damage 1d10+4
  • Two-weapon: Str 16, FS: Two-weapons, plate (AC6), THAC0 6+, damage 1d6+3
  • Assassin: Str 13 Dex 13, probably Skulking, THAC0 5+, damage 1d10x2+2
  • Thief: Str 9 Dex 16, Weapon Finesse, THAC0 4+, damage 1d8x2
  • Explorer: Str 13 Dex 13, Precise Shooting, arbalest, THAC0 8+, damage 1d8+1
Here are the probabilities each of these PCs has of hitting and one-shot killing each of the following types of monsters (taking into account that the monster's HD are actually rolled rather than just taking the average for hit points):

pc kobold goblin morlock orc hobgoblin gnoll lizardman bugbear ogre hill giant
sword and board 0.5500 0.4583 0.4750 0.3958 0.3438 0.1359 0.0973 0.0185 0.0010 0.0000
two-hander 0.5500 0.4917 0.5550 0.4625 0.4375 0.2637 0.2250 0.0839 0.0141 0.0000
two-weapon 0.6500 0.5500 0.5542 0.4750 0.4125 0.1661 0.1189 0.0226 0.0013 0.0000
assassin 0.7000 0.6283 0.6938 0.6013 0.5769 0.4341 0.4050 0.2701 0.1224 0.0016
thief 0.7031 0.6125 0.6500 0.5688 0.5250 0.3453 0.3047 0.1425 0.0343 0.0001
explorer 0.4984 0.3958 0.4031 0.3359 0.2813 0.1055 0.0738 0.0138 0.0008 0.0000


What's interesting here is that the break-even point for two-handed weapons is 2HD monsters.  Looking back at the Nonlinear Effectiveness of AC, the AC8 sword-and-board fighter is about 1.5x as survivable as the AC6 two-hander against low THAC0s, while against 2HD gnolls, the two-hander is twice as likely to instantly-kill (and be able to cleave) as the sword-and-board fighter, which means that's about where it starts to become a good proposition - if you kill them twice as fast and take 1.5x as much damage, you're going to end up taking only 75% as much damage as a sword-and-board party.  When you factor in cleaving, as the sum of a geometric series (0.26 + 0.26^2 + 0.26^3 + ...), the two-hander fighter actually kills 0.36 gnolls per turn in expectation, while the sword-and-board fighter kills 0.16 gnolls per turn.  Meanwhile, two-weapon fighting is the most effective against low-HP foes where you're THAC0-bound, but only marginally more effective against bigger opponents than sword-and-board.  Granted: this analysis doesn't take into account the initiative penalty for using two-handed weapons.

Another conclusion here is that backstab is tremendous.  A 1st-level assassin with a claymore has a 1 in 8 chance of insta-killing an ogre with a backstab.  That's way higher than I expected.

Let's look at third level:
  • Sword and board: Str 16, FS: shield and combat reflexes I guess, THAC0 7+, dmg 1d6+4
  • Two-hander: Str 16, FS: two-handed and combat reflexes, THAC0 7+, dmg 1d10+5
  • Two-weapon: Str 16, FS: two-weapon and combat reflexes, THAC0 5+, dmg 1d6+4
  • Assassin: Str 13 Dex 13, probably Skulking, THAC0 4+, damage 1d10x2+3
  • Thief: Str 9 Dex 16, Weapon Finesse, THAC0 3+, damage 1d8x2
  • Explorer: Str 13 Dex 13, arbalest, probably precise shooting twice, THAC0 7+, damage 1d8+2
Here are the kill probabilities:


pc kobold goblin morlock orc hobgoblin gnoll lizardman bugbear ogre hill giant
sword and board 0.6000 0.5347 0.5688 0.4813 0.4354 0.1992 0.1510 0.0340 0.0026 0.0000
two-hander 0.6000 0.5500 0.6256 0.5294 0.5088 0.3344 0.2930 0.1226 0.0241 0.0000
two-weapon 0.7000 0.6319 0.6563 0.5688 0.5146 0.2391 0.1813 0.0408 0.0031 0.0000
assassin 0.7500 0.6883 0.7600 0.6650 0.6475 0.5007 0.4702 0.3250 0.1587 0.0026
thief 0.7500 0.6563 0.6906 0.6094 0.5625 0.3719 0.3281 0.1535 0.0369 0.0001
explorer 0.5813 0.4813 0.4977 0.4211 0.3695 0.1582 0.1172 0.0256 0.0019 0.0000


With that one extra point of fighter damage bonus at 3rd, the balance on the gnoll between the sword-and-board and the two-hander has shifted dramatically, to only a 50% advantage for the two-hander, making sword-and-board and two-handed competitive against 2HD opponents.  But now two-handed fighting has a 2:1 advantage over sword-and-board against lizardmen (makes sense; they're 2+1 HD, both fighters gained one point of damage, so now the ratio should be pretty similar to the 2HD case without the extra point of damage).  Almost everyone is THAC0-bound against kobolds, and the extra point of fighter damage bonus brought the assassin's odds of one-shotting an ogre up to 16% on the backstab, about 1 in 6.  Two-weapon fighting doesn't look competitive from these numbers, but when you start looking at cleaves, it's actually quite a bit better than the other fighting styles against weak humanoids.  A 63% kill chance against goblins means that in expectation, a two-weapon fighter kills 1.7 goblins per round in expectation, while a 53% kill chance for a sword-and-board fighter nets you 1.13 goblins per round.  That's right around where two-weapon fighting starts to pay off compared to sword-and-shield; you're two-thirds as survivable, but you're 3/2 as deadly, so it balances out.  Against morlocks and orcs, the two-handed fighter's damage is more important than the two-weapon fighter's THAC0 (for now).

At sixth level, things start to get interesting.  We're going to start adding magic weapons and armor (possibly a pessimistic assumption - it's not that unusual for 3rd level PC fighters to have swords +1), and thieves and assassins get their x3 backstab.

  • Sword-and-board: Str 16, FS: Shield, Combat Reflexes, Command, sword +1 and shield +1, plate +1, THAC0 4+, damage 1d6+6
  • Two-hander: Str 16, FS: two-handed, Combat Reflexes, Command, two-handed sword +1, plate +1, THAC0 4+, damage 1d10+7
  • Two-weapon: Str 16, FS: two-weapon, Combat Reflexes, Command, sword +1 in each hand and plate +1, THAC0 1+, damage 1d6+6
  • Assassin: Str 13 Dex 13, Skulking, Combat Reflexes, two-handed sword +1, THAC0 2+, 1d10x3+5
  • Thief: Dex 16, Weapon Finesse, Skulking, sword +1 in both hands, THAC0 1+, 1d8x3+1
  • Explorer: Str 13 Dex 13, Precise Shooting, Precise Shooting, Command, longbow +1, THAC0 4+, 1d6+3

pc kobold goblin morlock orc hobgoblin gnoll lizardman bugbear ogre hill giant
sword and board 0.7500 0.7000 0.7833 0.6854 0.6563 0.3910 0.3250 0.1009 0.0122 0.0000
two-hander 0.7500 0.7000 0.8000 0.7000 0.6913 0.5281 0.4845 0.2497 0.0657 0.0002
two-weapon 0.9000 0.8500 0.9302 0.8323 0.7969 0.4813 0.4000 0.1242 0.0150 0.0000
assassin 0.8500 0.8000 0.9000 0.8000 0.7900 0.6867 0.6680 0.5619 0.4250 0.0725
thief 0.9000 0.8146 0.8758 0.7836 0.7570 0.6000 0.5672 0.4166 0.2368 0.0071
explorer 0.7500 0.6417 0.6333 0.5542 0.4813 0.1964 0.1405 0.0267 0.0015 0.0000

At this point, almost everyone is THAC0-bound on goblins, the gap in effectiveness between two-hander and sword-and-board against 1HD foes has practically vanished, fighters start having a small chance to one-shot ogres, bugbears are the new 2:1 advantage zone for two-hander fighters, and assassins now have a 7% chance of one-shotting a hill giant on the backstab.  x3 backstab damage produces a sharp increase in thief and assassin lethality, most noticeable against ogres, where the assassin's odds of a kill are almost triple what they were at 3rd level.  The two-weapon fighter starts to see big increases in effectiveness against 1HD opponents, killing 4.8 orcs per turn in expectation vs the sword-and-board fighter's 2.2.  Unfortunately, the addition of magic armor and shield has raised the sword-and-board fighter's AC to 10 (and the other fighters' ACs to 7), which means he's around four times as survivable against 1HD foes as the other fighters.  Against ogres, though, he's less than twice as survivable as a two-hander fighter, and against bugbears he's twice as survivable while the two-hander is three times as deadly once cleaving is taken into account (0.33 bugbears slain per turn vs 0.11 bugbears per turn), leaving the advantage with the two-hander.  Explorer gains mostly from accuracy increases, because he swapped his arbalest for a magic longbow, which kept his expected damage flat.

9th level:
  • Sword and board: Str 16, FS: shield, combat reflexes, command, ???, shield +2, sword +2, plate +2, THAC0 1+, damage 1d6+8
  • Two-hander: Str 16, FS: two-handed, combat reflexes, command, ???, two-handed sword +2, plate +2, THAC0 1+, damage 1d10+9
  • Two-weapon: Str 16, FS: two-weapon, combat reflexes, command, ???, two sword +2, plate +2, THAC0 -3+, damage 1d6+8
  • Assassin: Str 13 Dex 13, ???, two-handed sword +2, THAC0 -2+, 1d10x4+7
  • Thief: Dex 16, Weapon Finesse, ???, sword +2, THAC0 -2+, 1d8x4+2
  • Explorer: Str 13 Dex 13, Precise Shooting x2, Command, ???, longbow +2, THAC0 1+, 1d6+4

pc kobold goblin morlock orc hobgoblin gnoll lizardman bugbear ogre hill giant
sword and board 0.9000 0.8500 0.9500 0.8500 0.8500 0.6271 0.5583 0.2307 0.0411 0.0000
two-hander 0.9000 0.8500 0.9500 0.8500 0.8500 0.7300 0.6950 0.4313 0.1466 0.0007
two-weapon 0.9500 0.9500 0.9500 0.9500 0.9500 0.7447 0.6630 0.2740 0.0488 0.0000
assassin 0.9500 0.9500 0.9500 0.9500 0.9500 0.9263 0.9144 0.8275 0.7005 0.3045
thief 0.9500 0.9500 0.9203 0.9203 0.9055 0.8146 0.7867 0.6531 0.4898 0.0792
explorer 0.9000 0.8264 0.8313 0.7438 0.6729 0.3188 0.2417 0.0544 0.0041 0.0000

At this point, it's pretty clear that the fighter's just not scaling like he used to.  The two-hander fighter is up to a 1 in 7 chance of one-shotting an ogre... right where an assassin backstab was at 3rd level.  It's true that with cleaving he's 4x as deadly against ogres as a sword-and-board fighter, but the sword-and-board is up to AC 12 (with the other fighters at AC8), making him more than twice as survivable against ogres.  Even high-level fighters who aren't playing the spear-charge or giant strength damage multiplication game just aren't going to cleave up ogres.  That's OK, but you have to be aware of it.  The assassin, on the other hand, can kill two and a third ogres in the surprise round (in expectation).  Lethality is now very high across the board against 1HD foes.  The two-weapon fighter is going to hit his cleave cap of 10 against hobgoblins and orcs most rounds, while the sword-and-board fighter kills 5.6 per round on average and is three times as survivable, making him the winner against those target.  The two-weapon fighter is competitive with the two-hander against 2HD foes, but remains weaker against 3-4 HD opponents.

I think that's about as far as I'm going to go with this analysis.  I suppose another thing to consider at this point is how these stats translate into mass combat.  The sword-and-board fighter gets one company-scale attack at 1+, and his AC 12 means that most massed units need a 20 to hit him, even on a charge.  The two-hander fighter also gets only one attack at company-scale at THAC0 1+, and his AC of 8 means that massed units hit him on 18+ before disorder or charging.  The two-weapon fighter gets one attack at -3+, and also has an AC of 8.  So overall, I feel like the shield guy is strongest in company-scale mass combat; the damage advantages of the two-hander are abstracted away, and the -3+ THAC0 represents only a small increase in to-hit probability when you're attacking AC4 massed noobs in chainmail.

Overall, I believe this analysis supports the conclusion that across the level range, sword-and-shield tends to be the strongest fighting style for fighters.  Two-hander fighters are competitive or superior in killing power * durability against 2HD opponents in the low- and mid-levels, while two-weapon fighters are competitive against large numbers of 1HD opponents in a brief window in the mid-levels, but overall, sword-and-shield is strong by default.  While cleaving presents another exploitable nonlinearity, where high kill probabilities lead to very large expected bodycounts per round, it requires both high THAC0 and high damage output, is capped by level, and it's hard to get the required high kill probabilities against 3+HD foes with just the straight fighter damage bonus + magic weapon damage bonus (as opposed to multipliers like polearm charges, giant strength, and backstab).

Other conclusions: I was slightly surprised as how much better assassins were at backstab than the thief.  d10 weapons make a lot of difference when you're multiplying them I guess.  If there's one other conclusion to this besides "shield fighters generally good, other fighting styles situational but not totally useless forever", it is that assassin backstab is very good.  On the other hand, explorer didn't perform all that well.  Part of that is that I of phoned it in on his proficiencies (Fighting Style: Missile would've been a better choice, for example), but it's also just an issue with ranged weapons - no str bonus to damage, low base damage, and no magic weapon bonus to damage (in the absence of magic ammunition, which is scarce and expendable).  On the other hand, ranged is qualitatively different in ways that make up for its low damage.  Finally, cleaving seems to work basically as intended in ACKS - I recall reading (probably on the Autarch blog) that cleaving was intended to mimic a rule from Chainmail or OD&D that high-level fighters could outright kill a number of 1HD opponents per round equal to their level.  9th level fighters (except for two-weapon fighters) don't quite manage that, getting around 6 instead of 9 kills per round, but they do still lay waste to weak opponents and it doesn't change their performance all that much against strong opponents.

I suspect that there are two ways to use two-hander fighters.  One is full-offense polearm bumrush, with two-handed "victory or death" as the party doctrine.  The other, more reasonable thing, is to put polearm berserkers in the second row of the phalanx.  Being in the second row masks the penalties from berserkergang, and it gives them the THAC0 of a two-weapon fighter with the damage of a two-hander fighter.  If the front-line collapses, they'll hold morale while the rest of the party retreats.  Great use for a henchman.  Between fights, if the front line is chewed up, you can give them a shield and spear and yeah, they don't have the fighting style, but they're probably OK for one or two fights as a stopgap on the way out of the dungeon.

Oh, and the third way to use two-handed weapons: Thrassians.

Limitations: obviously, as stated at the beginning, this was about killing power and cleaving.  It totally neglects teamwork and multiple fighters stacking damage on the same target.  Given that sword-and-board expected damage output per attack is around 66% of the two-hander's across the level range, this probably works against sword-and-board in this style of analysis.  Also, this analysis neglected polearm and lance charges, which I suspect are a really important part of fighter play in the mid-levels against tough opponents.  Finally, my assumptions about the availability of magic items may not be representative.  Depending on how strictly your DM reads the treasure tables, magic two-handed swords may just not exist, which increases the superiority of the sword-and-board fighter over the two-hander fighter.  Relatedly, magic shields occur on the treasure table much more often than magic plate.  60% of rolls on the Armor table yield an uncursed magic shield, while only 45% yield uncursed magic armor.  Of those 45%, 25% are plate, so about 11% of Armor table rolls yield uncursed magic plate.  Thus, you're going to find about 5.5 times as many magic shields as suits of magic plate.  This remarkable availability of magic shields also contributes to the strength of the sword-and-board fighter.

Follow-up questions:

Is there a rock-paper-scissors thing with fighting other fighters, where two-weapon beats shield, two-handed beats two-weapon, and shield beats two-handed?

As a DM, what can you do if you want to favor one fighting style over another?  Say you have a two-hander player in your party, what can you do with your encounter design to make them feel good (if that's a thing you care about)?  Probably you include more 2HD opponents that they can cleave but that your sword-and-boards can't.  If you have a two-weapon guy, include high-AC 1HD opponents, where their high to-hit lets them cleave and their lower damage doesn't hurt them.

How do these fighters look on horseback?  Two-weapon loses out.  Two-hander can use a polearm instead of a lance to keep his proficiency bonus, or go shield and lance and be inferior to the shield-fighter.  Shield can use a lance one-handed to get d10 doubled damage while keeping his AC.  I think shield wins this one too...

How important is the Fighting Style proficiency?  If, say, I'm mainly a sword-and-board fighter but we're up against gnolls and I'm considering going zweihander, how much worse am I than a dedicated, FS:Two-Handed polearm fighter (one point of damage, but how much does this matter)?  If I'm a two-hander fighter but we're up against a big mob of weak opponents where shield-fighting is strong and I decide to go shield-and-sword, how much worse off am I than a dedicated shield-fighter (one point of AC, but how much does this matter)?  Sure, you could take both, but you don't get many class proficiencies and you're probably better off taking things that still work when you're in your usual fighting style.  There was a concept in some weird corners of the 3.x sphere of the "toolbox fighter", who spent his feats on things that were useful across a wide range of weapons, carried around a whole armory, and switched to whatever weapon was good at the moment.  In general, Weapon Specialization was so strong that they didn't see much play (but they were more viable in Trailblazer).  The question: how strong is a "toolbox fighter" in ACKS?

How does everyone's favorite front-liner at 1st level, the armored war dog, compare to actual fighters?

How much do ability scores matter to fighting style choice?  It's worth noting that a 16 Str provides to-hit and damage benefits comparable to both two-weapon fighting and two-handed fighting at the same time.  Is the dominant strategy different for low-Str henchman fighters?  Is the dominant strategy different at Str 18?  What about fighters with Dex bonuses?  Is the dominant fighting style strategy different with Berserkergang's to-hit or Fighting Fury's damage bonuses (interesting because most of the time, to-hit and damage bonuses go together, like magic weapons, Str bonus, bless, and bardsong)?  What about for clerics without fighter damage bonus?

Actually working out expected kills per round instead of probability of a kill - it's straightforward, but I'm way over my weekly tolerance for pasting tables into blogger.  Also, adding in initiative - I think this should be straightforward with the method I've been using.  Roll initiative for both sides, roll attacks and damage for both sides, and then check both init and HP totals.  Multi-round analysis could be tricky, but worth pursuing.

Saturday, July 1, 2017

ACKS: Figuring out the Barbarian

The other week I was looking at writing a Powergamer's Guide to Fighters in ACKS, in the vein of this 3.x-era gem of a book.  Ultimately the analysis I did deepened my conclusion that sword-and-board is generally optimal, but I'm not happy with the rigor of that analysis yet.  One other thing that came out of that 8000-word draft post was that I was looking at doing a rating for each fighting-type class, and I spent some quality time looking at the Player's Companion barbarian class.  I think I sort of figured out what it's supposed to do, why it doesn't do that super-well, and how to fix it.

Barbarians get d8 HD and fight as a fighter of their level, have prime reqs Str and Con, and trade a bunch of weapon proficiencies and ability to use plate away for a pretty strong stealth ability that penalizes enemy surprise rolls, a bonus to init and surprise rolls, ability to roll twice for mortal wounds and choose, and a proficiency based on land of origin, which also determines which weapons they can use.  Options include viking (Climbing, gets two-handed melee weapons), nomad (Precise Shooting, gets lance and composite bow), and tribesman (Running, gets...  pretty crappy weapons).  Unfortunately, all those Fighting Value tradeoffs mean they're at 2600 XP to 2nd level.

Between the lack of plate and the slow leveling, my players have pretty much dismissed this one.  The thing here is that compared to other fighter-variants like assassin, explorer, and spellsword, it's not really clear how barbarian is supposed to fight.  Explorer is supposed to do archery, and they have tremendous synergy built into the class so that they're good at it from 1st level (granted, Prof Tax for Precise Shooting, but that's a separate issue).  Spellsword fits naturally into a second-row spear-and-sleep in plate role right out of the gate.  Assassin's a little weirder, but it's pretty clear that you're supposed to be sneaky out front to get in the backstabs (but we rarely use them that way, because we consider plate a prerequisite for front-line).

Barbarian sends mixed messages.  The Con prime req, d8 HD, and Savage Resilience suggest that you should be out front taking the hits, but you don't have plate and party healing resources are limited, so this seems like a Bad Playstyle.  The surprise modifier suggests that you should be trying to get the drop on people, which certainly benefits from being on the front line.  The three backgrounds bring Climbing, Precise Shooting, and Running, which are not good, solid front-liner abilities.  Sure, Climbing can help you get into position to surprise people, but then you still need to capitalize on that.  Precise Shooting doesn't synergize with surprise well at all; if they're surprised, they're probably not in melee yet.  It lets you follow up surprised ranged attacks once melee is engaged, if you want to roll dedicated archer...  but then you should've been an explorer for the faster leveling, Dex prime req, and crazy-good wilderness stealth.  Running lets you close or get out, but generally combats start at pretty close distances so it's most likely going to be used for escape, which requires the rest of your party to accommodate an aisle of retreat through the phalanx (and even then, how often is that little bit of extra movement going to make the difference?).

So I think this is how barbarian's supposed to work:

  • Be in the front line
  • Enemy fails surprise about half the time because you are naturally stealthy.  You, of course, do not fail surprise much because you have Combat Reflexes
  • In the surprise round, you charge in with a spear or two-handed weapon and Ambushing and try to cleave up a bunch of guys in the surprise round and force penalized morale rolls
  • If that works, then they flee and you win
  • If that doesn't, they whale on you, Con and Savage Resilience keep you alive until the party can recover you or you can disengage.
  • If you don't get surprise, you are sad, possibly fall back into the second row.
It's sufficiently-impetuous for a barbarian.  It's sort of skirmishy, like Keegan's History of Warfare would lead us to expect of primitive peoples.  It's a much more aggressive way to play than our typical fighter, higher-risk and higher-reward; when it goes right, it's a combat-win in the surprise round, and when it goes wrong, you're out a bunch of healing.

The thing here is that Ambushing is clutch for capitalizing on those "surprise, barbarian!" moments.  And indeed, the suggested template for Barbarian has Ambushing.  The only other class proficiency which seems to me to really compete with Ambushing is Armor Training, which gives you plate and turns you into a slow-leveling fighter with Savage Resilience.  Ambushing just completes the class' natural synergy.

Which is why, if I were to redesign Barbarian, I'd get rid of the origin proficiencies, give all Barbarians Ambushing, and standardize a weapon list with: polearm, lance, spear, sword, composite or longbow (the important weapons), javelin, dagger, battle-axe, short-sword, two-handed sword or greataxe.  Possibly vary weapon list with origin, or maybe do away with origin entirely.  Then for your first-level class proficiency, you have some real options:
  • Fighting Style: Shield in combination with a spear boosts your defense after the charge - run in for d8x3, then switch to one-handed spear and draw your shield (as a free action).  Also scales nicely as magic shields become available.
  • Berserkergang lets you double-down on the ambush; if they're all dead or fleeing before they get the opportunity to attack, the AC penalty doesn't matter, and the to-hit bonus stacks up ridiculously with Charge and Ambushing (seriously, +8 to hit is a lot).  For best results, combine with polearm for d10x3.
  • Combat Reflexes or Alertness mean you're never surprised, can always capitalize when the enemy is surprised
  • Skirmishing or Running to get back out
  • Sniping if you want to do bow-ambush from the second row on surprise, then switch to polearm or spear once melee is joined (this feels like a very solid way to play a first-level barbarian)
  • FS: Two-Handed and FS: Polearm continue to be mediocre at first level - the two-handed damage bonus is small, and the polearm init bonus is outdone by Combat Reflexes 
In the wilderness, get a horse and a lance and continue to charge from ambush, then disengage for horse-archery or more charges.  In mass combat, your synergy breaks down; you can get Command and leads troops OK, but surprise doesn't really work.  You might still be able to use Ambushing in commander-duels if you bring potions of invisibility, but generally I'd expect a barbarian with typical magic gear (chainmail, shield, sword) to lose to a fighter of equivalent level with similar magic gear (plate, shield, sword) in a straight-up fight.  Maybe I'm discounting the Con bonus you probably have from the prime req, though.  Polearms get much worse at high levels because magic ones aren't on the treasure tables, and even two-handed swords are sort of DM's discretion with the sword table.  Magic spear (+ magic shield) is probably your best bet, if you can find one.

To address some potential objections: it's true that this is a more generic conception of barbarian.  It doesn't have the origins, and it doesn't try to model three different historical societies in a single class.  I'm OK with that.  When D&D players hear barbarian, they're looking for reckless offense.  I'm OK with giving it to them.  This may not be Rage as expected, but it still plays like the barbarians we know and love.  It's also true that this barbarian class is slightly gamey; the weapon selection is strong, and the abilities synergize well.  I'm OK with that too - they pay for the weapon selection with the Fighting Value tradeoff XP, and abilities synergizing well is fine when explorer and assassin do it.

Compared to fighter, this barbarian has greater ability to end combats before they begin, but has to assume greater risks to do so.  Compared to assassin, barbarian is tougher and better able to deal with the ambush going wrong, and has stronger stealth at low levels but weaker stealth at high levels.  Compared to both of these classes, it levels more slowly.

Saturday, June 3, 2017

ACKS, Pendragon, Manors

Upcoming Heroic Fantasy Companion got me thinking about Arthurian myth, which in turn led back to Pendragon.  It's a horribly baroque system, but one interesting thing that it does is have players start with manors - very small domains.  AskHistorians puts the population of an English medieval manor at around 300, or 60 families, which under the most recent revision of the ACKS domain rules generate 300gp/mo in revenue in civilized circumstances (low garrison, but tribute to liege lord).  They also occupy about a quarter of a six-mile hex (at default "initial" civilized population density of 280 families per hex or Medieval England's population density of 250 families per hex), so you could fit four manors per hex...  which is roughly one per PC in your average party.  At 300gp/mo in revenue, you would hit 4th level before capping out on your domain threshold.  Such a manor requires a "fortress" worth 4000 gp to secure - a large stone house with some palisade walls ought to do the job.

Depending on how much ACKS domain detail you want to preserve, you could then go and do the whole percent-increase-per-month-adventuring and domain morale and all that...  or you could take the Pendragon approach, which is that a manor is a manor and it gives you some static income (maybe modified by a roll), and then you make manors your basic unit of land-tracking (with settlements handled separately).  Pick up more civilized manors by marrying rich, conquering some Saxons, or getting a land grant from the king for services rendered (a hard thing to do IRL, but an exceedingly reasonable thing to do from an RPG perspective).

An interesting property of the domain XP system that we really haven't gotten to experience is that it's almost a second form of reserve XP - if you die, your heir will (slowly) level up back to some hopefully-reasonable level on domain income.  "Slowly", of course, is the operative word - first to second level with a single manor is ~8 months for a fighter with no prime req.  Pendragon's dynastic pace (something like one adventure per year of game-time, and I would imagine about one year per session) could address this as well.  On the one hand, this creates problems with saving money and maintaining armies, but on the other hand, it also opens up a lot of room to actually get some use out of ACKS' research, hijinks, construction, troop training, aging, &c rules, which are usually squashed out by "always be adventuring".

But at some point we're really just looking at Pendragon with ACKS' combat, proficiencies, and market systems.  Hmm.

In any case, I do think that "start players with small, civilized domains and a connection to a liege of some sort" is not a bad idea.  Passive income, assisted recovery after PC death, and connection to gameworld are all good things in reasonable quantities (particularly as I swing backwards on the sandbox pendulum, towards "you know quests could actually help alleviate some of the emergent tyranny of structurelessness / informal hierarchy that we see in sandbox play").

Friday, May 12, 2017

Dirtside

I've had the 2011 Summer of Starmada on my mind lately.  There were a couple of things that made Starmada successful, I think.  One was that it was simple enough to introduce new players without too much difficulty, with many options disabled-by-default.  This allowed us to achieve a critical mass of regular players and establish a metagame.  Finally, the availability of design rules led to strong participation in the game away from the table and allowed players to play fleets representing whatever science-fiction background they came from.  Unfortunately, it was that same design system that tore the metagame apart.

Dirtside 2 shares some, but not all, of these characteristics.  It does have a design system capable of modeling a wide variety of forces, and if the rulebook were better organized it would be easy to separate into a simple core and a number of optional components.  Compared to its brother Stargrunt, its morale system is simpler, it is larger scale, and it has a greater focus on combined arms. Unfortunately, as a ground-combat wargame, it depends heavily on terrain, and it uses a weird miniatures scale (6mm "microarmor").  Also, like Stargrunt, it does not handle alien psychology very well.  Finally, it uses a really weird damage resolution system involving drawing chits from a bowl; simple enough in practice, but an annoying number of moving parts.  If you lose a damage chit, your probability distribution is going to be skewed forever.

I've had my eye on Dirtside for a long time, but it just never seemed viable, due largely to hardware.  I looked at using roll20, but roll20's support for facing is very awkward, the asymmetric DM-player model isn't a great fit for wargames, and it sort of chugs on large maps in my experience.  I considered writing a VASSAL module, but java.  Now I think I might've found the correct tool, though - Tabletop Simulator.  TTS is already widely-available to the group that I game with, and is cheaper than miniatures.  It is easy to import hexmaps into it (I've looked at just taking Google Maps screenshots, imposing a hex grid at 100 meters per hex, and dropping them in), which solves the terrain problem.  It supports the "drawing damage chits" idiom very nicely with either decks or bags.  There are already steam workshop mods for it with models from the Dawn of War games, intended for playing Epic 40k, which would be perfect for representing units (I've been looking at using NATO-standard counters instead, but for some reason NATO has no symbols for "antigrav tank" or "giant mecha".  Gotta get on that, guys).  It seems like a very good solution to the "need miniatures", "losing damage chits", and "terrain is complicated" problems (though it may introduce some new problems, like "playing against opponents face-to-face is fun, and so is standing over a big physical map".  Maybe I need a ceiling-mounted projector aimed down on to a real table for that "war room" effect...)

The "poorly-organized rulebook" problem remains, however.  The rulebook is also not OCR'd, which is pretty annoying.  These two facts combined lead me to the conclusion that maybe I should transcribe / rewrite the rulebook, cutting it up into independent modules like Starmada had:

  • Core / Armor
    • general sequence of play, units, objectives
    • armored vehicle (tracked, wheeled, GEV, grav, mechs) movement
    • big index of combat actions, direct fire, guided missiles, damage resolution
  • Infantry
  • Artillery
  • Aerospace (I'm conflicted about VTOLs; most of the time they play like armor, but then they're also vulnerable to air defense)
  • Engineering (mines, fires and smoke, bridgelaying, ...)
  • Optional Stuff (oversized vehicles, experimental rules for drones and aliens, ???)
  • Vehicle Design and Points
It's already mostly organized like this.  The problem is that (for example) infantry movement is in the movement section with armored vehicles, rather than in the infantry section, and chit validity for artillery fire is in the direct fire chit validity table rather than the artillery chapter.  That's fine for a reference, but bad when you're first learning the game.  It's (only) a 60-page rulebook, so cutting it up and figuring it out is less work than learning all the quirks of an RPG, probably.  Combined with making tokens in TTS and a unit design spreadsheet (though there is already an online vehicle design tool, but it doesn't really support houseruling), it should be a reasonable, but not overwhelming, prep effort.

Saturday, May 6, 2017

Rations, Starvation, and Morale: Addendum

So I was skimming Domains at War: Campaigns, and lo, on page 58 there were more rules for the effects of being out of supplies, which I missed in my previous collection of starvation rules:

Troops who are insufficiently supplied lose 1 hit point per day and suffer a cumulative -1 to attack throws and damage rolls. Furthermore, they lose the ability to heal wounds normally, though magic will still work. If troops eat enough food for a day, they regain the ability to heal, recover 1 hit point lost to hunger, and reduce by 1 any penalties to attack throws and damage rolls. Thus, troops that receive rations every other day (or half rations daily) can function almost indefinitely.
However, even if an army physically survives a lack of supply, it may not survive psychologically. Each week a unit is partially or completely unsupplied counts as a calamity and the unit must make a loyalty roll.
If an army has enough supplies to feed some of its units, but not all, the army's leader must choose which units to supply. The supplied units do not suffer any penalties, nor do they need to make weekly morale checks. However, the unsupplied units suffer an additional -1 penalty to their loyalty rolls, as it is evident that they are being left to starve while others feed.
So that's a fair bit harsher than the rules from the core book - no two-day grace period (though that would be consistent with having no water, rather than just no food), and accumulating to-hit and damage penalties.  The morale rolls seem more reasonable than punitive, though depending on circumstances it may still make sense for a starving unit to stick with its PC leaders exactly long enough to get home out of the wilderness.  They do fill a hole I predicted in effects of starvation on morale, though, which is nice.

Tuesday, April 25, 2017

Rations, Starvation, and Healing

Historically, my players have been very afraid of running out of food in the wilderness.  This seems like a pretty reasonable concern.  For ready reference, here is a summary of the scattered RAW on rations and foraging and such, as well as a discussion of some implications and potential houserules.

From page 94:
Each day, characters must consume food and drink weighing a total of one stone.  This assumes 2lb of food and 1 gallon (8lb) of water.  Failure to consume enough food does not significantly affect a character for the first two days, after which he loses 1 hit point per day.  Furthermore, at that point the character loses the ability to heal wounds normally, though magic will still work.  Eating enough food for a day (over the course of about a day, not all at once) restores the ability to heal, and the character will recover at the normal rate.
Inadequate water affects characters more swiftly; after a single day without water, the character loses 1d4 hit points, and will lose an additional 1d4 hit points per day thereafter; healing ability is lost when the first die of damage is rolled.
When in the wilderness, characters can hunt or forage for food.  Foraging for food is an activity that can be accomplished without hindering travel by gathering fruits, nuts, and vegetables. For each day of travel while foraging, a character should attempt a proficiency throw of 18+ on a d20. A successful result indicates that sufficient food for 1d6 man-sized creatures has been acquired.
Hunting succeeds on a proficiency throw of 14+ and indicates that sufficient food for 2d6 man-sized creatures has been acquired. However, hunting must be engaged in as the sole activity for a day with no traveling possible. In addition, there will be one wandering monster check, from the table appropriate to the terrain, while the group is hunting.
Characters with the Survival proficiency gain a +4 bonus on their proficiency throws to hunt and forage. 
From 96:
While on sea adventures, characters must consume food and water as described under Wilderness Adventures, above. Rowers must consume 3 gallons of water per day rather than the standard 1 gallon, so their supplies have an encumbrance of 3 stone per day. Standard rations are perishable and inedible after one week, so on long sea voyages most characters will eat iron rations. After one month at sea eating iron rations (that is, without eating fresh fruit, onions, or potatoes), characters begin to suffer from scurvy. Characters with scurvy lose 1 point of Str and Con each week. If either ability scores zero, the character dies. A scurvy-stricken character regains 3 points of Str and Con each week he eats fresh food.
Characters can fish if the ship is becalmed or otherwise anchored. For each day of fishing, each character may attempt a proficiency throw of 14+ (gaining a +4 bonus if the have the Survival proficiency). A successful result indicates that food enough for 2d6 man-sized creatures has been caught. 
The description of the Survival proficiency, on page 64:
The character is an expert in hunting small game, gathering fruits and vegetables, and finding water and shelter. The character forages enough food to feed himself automatically, even when on the move, so long as he is in a fairly fertile area. If he is trying to supply more than one person, he must make a proficiency throw (as described in Wilderness Adventures), but gains a +4 bonus to the roll.
Page 46 notes that iron rations last spoil after two months in the wilderness, or a week in the dungeon, while standard rations last a week in the wilderness or a day in the dungeon.  Iron rations cost 1-6gp per week, while standard rations cost 3sp-3gp/week (a rather weird range).

A final thing to note in all of this is ACKS' natural healing rate.  Per page 105, "For each full day of complete rest in reasonably sanitary conditions, a character or monster will recover 1d3 HP.  If the rest is interrupted, the character or monster will not heal that day."  There is no natural, universal overnight healing from normal rest, that I can find.  This casts the Healing proficiency into ambiguity: "A patient under treatment of Healing naturally heals an extra 1d3 hit points each day."  Presumably (and I think we've been playing it this way), that applies to bed-rest healing, rather than providing overnight healing.  I think there's also an argument to be made that the Cure spells that Healing grants are also intended to be applied to bed-resting patients, rather than as first aid (with the exception of Neutralize Poison, which requires expeditious use, and Comfrey, which is explicitly marked for use "after a battle", and notably tracks usage separately from "patients").  This interpretation is supported by the "Campaign Play" article, published in Axioms on 6 Sept 2016, which lists Healing as a "major" activity, or around six hours of work a day to care for 3/4/5 patients - consistent with "patients" being people under bed rest (but see here for counterpoint...  but that leads to some really weird interpretations with healing fading when you switch patients, which doesn't make any sense at all).  The Cure Light/Serious functions of Healing should be surgery - that's why Healer 3 NPC specialists are "chirurgeons".  So that's very interesting - I expect we'd still see Healing 1 a lot in dungeoneering play, for the mortal wounds bonus and Comfrey use, but Healing 2 and 3 would be much rarer under this interpretation.  What would our mages do with all those general proficiencies freed up from Healing, I wonder?  Some actual wizard-knowledge, perhaps?

Some other interesting things that fall out of the rations rules, under inspection:

Your average character forages successfully 15% of the time (about one day a week), and finds on average enough food for 3.5 characters.  In expectation, you will tend to find about half a man-day's worth of food per day, without Survival, while traveling at full speed.  Obviously, this is somewhat swingy, but with more characters will tend to average itself out.  Depending on how you interpret the starvation rules, this may make starvation quite difficult for large parties.  If starvation's effects only trigger after two consecutive days without food, and a large party tends to find half a man-day of food per forager, each character can (on average) eat every other day and avoid starvation indefinitely.  Granted, this might not be great for morale (UPDATE: see here); I also recommend not ordering pizza during such sessions, to get players in the right mindset.

With Survival, that increases to 1.22 man-days of food per day.  The fact that survivalists can always feed themselves without a roll is also a nice bonus, both because it is reliable and because it reduces the amount you have to carry on expeditions when you are carrying rations.

Hunting yields 2.45 man-days of food per hunter*day in expectation, or 3.85 with Survival, but it also costs a man-day of rations per hunter to execute, since it takes a full day without travel.

If the party is traveling along rivers or camped by a lake, fishing is a safer option than hunting, with equivalent yields but no additional random encounter roll.

For mid-level characters, starvation can take a very long time.  A 5th-level mage averages 12.5 HP, and can go two weeks without food (a bit lower than the "three weeks without food, three days without water, three minutes without air" rule, but that's d4 HD for you).  In those two weeks, you will in expectation find food by foraging twice, which on average buys you roughly a week of not-starving (plus four additional days of "not significantly affected" per success).  But wait, that week of not-starving buys you an extra 5.5 days of not-starving in expectation, which buys you an additional ~3 days of not starving, which buys you an additional...  there's a recurrence here.

This is a somewhat annoying recurrence.  I've poked at it with math for a bit, and I think the easier solution is probably Monte Carlo models. Basically you run a bunch of trials (like, 100,000) and observe the outputs statistically.

Turns out the 5th-level mages survive, on average, about 28 days, with a long tail on the distribution.  The longest-surviving mage lived off the land for one hundred and thirteen days with no healing, with strictly-decreasing HP, before starving to death.  This is just foraging, with no bedrest.  I did roll HP randomly per mage, but none of them had a Con modifier.  12% of mages had perished at the 15-day mark, 25% at the 20-day mark, 50% at the 27-day mark, 75% at the 36-day mark, 90% at the 46-day mark, and 99% at the 66-day mark.



Fighters, as expected, live longer - 49 days on average, 165 days maximum.  Again, that's with no healing.  These guys had at most 40HP, but about 2.5 percent of them survived 4 months or longer.  10% had perished at the 28-day mark, 25% at 37 days, 50% at the 48-day mark, 75% at 62 days, 90% at 75 days, and 99% at 101 days.


...  well that got rather grim, didn't it?  The bottom line, though, is that two weeks without rations is less dangerous than the average dungeon crawl, with 12% wizard casualties and less than 1% fighter casualties.  Henchmen might have a rougher time, though a 3rd-level fighter henchman would have superior HP to a 5th-level MU, on average, and should endure starvation comparably.

And again, that's with no healing, no magic, no survival proficiency, no cleverness, no law of large numbers on multiple party members, nothing - pretty much the worst case, minus monsters.  That's also time that you can spend traveling (hopefully home), because you can forage on the move.

So my conclusions from this analysis:

  • Starvation kills low-level characters very quickly, but is much slower for mid-level characters.  This feels like it could be a very reasonable tension-maintenance mechanic for the wilderness levels, much like torch-counting is at low-levels.
  • If you assume drinkable water is available in the field, a man-month of rations is about 4 stone and 25gp.  A mule can carry 10 man-months of rations at 60' speed.  The requirement to carry water makes deserts, swamps, oceans, frigid wastelands (where there is water but not fuel for fire to melt it), and high mountains much more difficult logistically, since then you're looking at 40 man-days per mule at 60' speed (or 20 at 120').  This also links nicely to Create Water.
    • If you want to keep water relevant in less-hostile environments, having a roll per-week to avoid contracting dysentery (with effects similar to starving or dehydration (no natural healing, HP loss per day), but requires Cure Disease or a series of saves to remove) when you drink local water seems reasonable.
  • We've been playing Healing very wrong, but it's still decent in the wilderness game.  Taking a day of bed rest is not a huge deal - you already need to take a day of rest per week.  If you set up a camp with tents, fires, and a clean water source, "reasonably sanitary" seems plausible to me.  A sixth level cleric can do five Cure Lights and one Cure Serious per day, for a total of 7d6+11 HP of healing (35.5 points in expectation).  A guy with Healing 3 can heal 5d3 HP on resting patients, plus five shots at Cure Serious, each with a 35% success rate (before herbs), or about 1.75 Cure Serious per day.  It's unclear what the caster level for Cure Serious from Healing is, but that's at least another 3d6, for a total expected healing of 22.25 before any caster level bonus.  That's at least 63% of a cleric (on a rest day).