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).  

Sunday, April 16, 2017

Applied Wilderness Theory

Due in part to the recent Hexographer 2 beta releases, I've been playing around with building a microsandbox - 10 hexes by 10.  I'm not happy with it yet, but here are some notes that have come out of it:

  • Taking the "wilderness as dungeon" model, 100 hexes is comparable to a hundred-room dungeon.  That's on the upper end of anything I've ever actually built and stocked, so this might be bigger than I really wanted.  On the other hand, I do still have a fair number of "empty" hexes.  Honestly might be a bit too big for the "micro-sandbox" label.
    • It's about the size of a duchy, I think?  A 24-mile hex is ~16 6-mile hexes, so a hundred six mile hexes is about 6 24-mile hexes, which is about right for a duke with 5 vassal counties.
  • Borderlands are the correct civilization level for "wilderness" adventuring.  They're perfect.  Previous hexcrawls were largely wilderness, which per Lairs and Encounters have many (2-8) lairs per hex, which is just impractical to stock (sure, sure, dynamic lairs, maybe some year).  Borderlands tend to average between 0.33 and 1 expected lairs per hex, which is great (gee, sounds familiar).  So in a 100-hex area, I have around 40 lairs - quite a few, but waaay more workable than the Shieldlands campaign, where I probably had 40 lairs within 12 miles of the town the PCs were running.
    • Corollary: About half of borderlands six-mile hexes require zero work to clear.  No lairs, no problem.
    • Assuming civilization more-or-less surrounding the sandbox area, the 25-mile borderlands radius covers almost all of a 10x10 hexmap (close enough for me).  We also know that it's 50 miles from the edge of the sandbox to a class IV or better market (probably about 6 miles from the edge of the sandbox to a class VI market, and maybe 24 miles from the edge to a class V market).  So that lets you track time spent getting to and from markets in civilized areas without actually having to roll random encounters with dirt-farmers or track hex-by-hex movement and rations (presumably you can buy them off of hamlets you're passing through daily).
  • Again thinking of wilderness-as-dungeon, I decided to steal a few pages from the dungeon stocking rules, which note that the random encounter tables generate roughly 33% stupid enemies, 33% beastmen / "factious" enemies, and 33% high-intelligence / high-power "men and monsters".  I tweaked these numbers a bit, towards 50% critters, 33% beastmen, and 17% men-and-monsters.  This yields about 20 animal lairs, 13 beastman lairs, and 7 other lairs.
    • Animal lairs are super low-effort to stock, and present a more natural-feeling wilderness (whether or not predator densities that high are actually sustainable is another question).  I also cut out the really boring animals (goats, normal-size hawks, a lone rattlesnake, ...) in favor of a more...  folklorish, Northern European / Tolkeinesque carnivorous animal selections (boars, bears, wolves, giant spiders, giant bats, giant weasels, ...). 
    • 13 beastman lairs is at the upper edge of the reasonable, I think.  They have a lot of moving parts, and I'll probably need to differentiate them so that players can keep them straight.  I wonder if that was secretly the point of having all of those cookie-cutter beastman races that are mechanically almost-the-same; minimal viable differentiation (which is easier to keep track of: blue orcs vs green orcs, or orcs vs guys with hyena heads?).
    • Seven "men and monsters" were actually pretty easy.
  • One day is almost certainly the analog for a 10-minute turn in dungeon-time here.  This was less true when I ran the Bjornaborg wilderness game on 1.5-mile hexes, but on six-mile hexes at 1-2 hexes per day, that's definitely the correct time to track (and this is an important thing to figure out, because that lets you start honing in on that central play-loop which has historically been poorly-defined and vexing for us [1][2], and also helps figure out the resource model).  Rations start to look sort of like torches in this accounting, in that a torch lasts six turns and non-iron rations spoil in seven days.  Removing water requirements by assuming fresh, drinkable water from abundant streams also greatly eases the logistical burden of rations (down to 1lb/man*day, or 10 man-days per stone, instead of 1 stone per man-day when you have to carry water).  An even simpler abstraction would be 1st per man-week, assuming that you're carrying some backup water or wine or whatever.
    • At 10x10 hexes with 1-day "turns", your upper-bound on expedition length is about a month (in 30 days you could get to most any point on the map and back, I think).  This does tie back to one complaint that my players had about wilderness adventures - if you have a choice between one adventure a month in the wilderness, or one adventure a week in the dungeon, wilderness needs to have a much higher treasure yield per expedition to make sense in terms of gp/game-time (which matters because of monthly expenses).  I'm not sure that the microsandbox I'm working on has that high-yield property (yet / currently), but that's also less important if the game is explicitly structured/pitched as "a wilderness game" with no / minimal dungeons and all characters starting at like 5th+ level.
      • An orc wilderness lair has an average treasure value of 14kgp, which is like a decent but not outstanding treasure map.  They're also a source of liberated human prisoners, though, which sounds to me like a pretty good way to pick up some mercs or a replacement PC if things went poorly.
      • I'm not sure my players will fall for "legend tells of a great dragon's hoard somewhere in the highlands" again...  maybe I just need to use a bigger dragon, because bigger dragons have bigger treasure.  Right?
  • In terms of calibrating difficulty by analogy with the dungeon, wild animals are low-threat, beastman warbands should be medium-threat, and beastman lairs and special monsters should be higher-threat.  At one encounter per day, a 5th-level party with some merc backup could probably take a warband, in much the same way that a 1st-level party could probably take a gang of 5 orcs in the dungeon (depending some on surprise, tactics, armament, and luck; if the wizard gets sleep/fireball off, you're probably fine, but if he gets interrupted and pincushioned, then it's going to be a rough day).
    • I still think the right way to run such a combat is probably on 30' hexes.  Wilderness movement and ranges are in 30' intervals already, it's about the area of a ground-burst fireball, it translates nicely to DaW on platoon scale, and it's sort of analogous to fitting the whole party into a single 10' square (as happens for small parties in dungeons).
  • Still haven't really worked out local weather patterns for this map yet.  If adventures take weeks-to-a-month, seasonal weather rules might be necessary.  I do have some stuff for temperature (mostly as it related to the choice to have a fire or not when camping, choosing between mercenary morale penalty and no natural healing or an extra random encounter roll - worth noting, of course, that most beastman villages are also going to have fires, so that's a nice way to locate lairs from a distance).
  • Two big differences with dungeons that I'm noticing practically are that you can be in the same hex/room as monsters and not realize it, and that visibility of the structure of the terrain (ie, "that hex is forested") is much easier to see from a distance than the structure of the dungeon.  Most wilderness features are hidden in a hex, while most dungeon-room features are pretty obvious when you're in that room.  I recall being nonplussed with L&E's system for finding hex features, though I forget why; will probably reread those and then work something out.

Tuesday, April 4, 2017

New Autarch Kickstarter

'bit late on the uptake this time, but there's a new ACKS kickstarter, for the Heroic Fantasy Handbook and Barbarian Conqueror King.  The Heroic Fantasy book has been in the works for a long time; I acquired a draft copy a year or two back (thanks Alex!) and we used some of the rules from it (mostly Warrior Code) in the Midnight ACKS campaign.  I'm looking forward to seeing it in its finished form.  I've been reading the Poetic Edda and kicking around a low-magic, Iron-Heroes-esque "mythic Scandinavia at the turn of Christianity" setting, and this should support that well (provisional name: "ACKS-Age, Sword-Age").

I'm a little less excited about Barbarian Conqueror King.  Nothing against Omer, I'm just not huge on pulp.  That said, there was a preview of some Expedition to the Barrier Peaks-style rules for figuring out how to use and repair advanced technology, and it reminded me of D20 Apocalypse...  and that got me thinking further that ACKS and Darwin's World were sort of made for each other.  Then again, maybe Crawford's already done it better with Other Dust.