Across the world adventurers dive into tombs, mausoleums, and sunken cities in search of treasure. They clear out orcish keeps, goblin camps and dragon lairs to keep the people safe. And they meet with lords who wish to hire them to retrieve a certain item from its lost location.
You are one such lord, the rightful heir of the Kingdom of Calantha. Ever since your family was cruelly cast down from the throne, you have been forced to eke out a miserable existence, with but a few thousand acres of land to call your own, and a couple shabby mansions to live in. But no more! Today your work has born fruit, and you have found out at last where the shards of the Crown of Command were buried when your lineage was deposed.
(It was so unreasonable to object to your family's rulership! Your great-grandfather was the most popular king Calantha has ever had, with 100% approval rating among the populace! Yes, okay, this might have something to do with the Crown's kingdom-wide mind-affecting properties, but it still seems unreasonable for a band of plucky heroes to storm his palace, kill him, break his crown into three pieces, and cast his family into exile).
But now you know where the three pieces were hidden, and you will see your Crown reforged! Then you will reclaim your throne and rule as a wise and just king! (Starting, of course, by wisely hunting down and justly executing every descendent of anyone who was involved with the coup against your great-grandfather).
The three pieces were hidden in dungeons across the land: one in the Lost Temple of Lemarchand, one in the Infernal Den of Cheliax, and one in the Goblin Warrens of Khaz-Gorond. You've been able to find out something about what's defending each of these dungeons, via a mixture of divinations and sending in the last of your dutiful family retainers to scout them out. (Their loyalty and sacrifice will be remembered. Not by you personally, though. You have people for that.) Now all that remains is to hire three teams of foolish adventurers, tell each one you have lost a 'prized family heirloom' in a nearby dungeon, and offer to pay them to retrieve it! Simplicity itself!
Unfortunately, money is...a bit tight. And those greedy adventurers refuse to do anything unless you pay for a 'full party' of 4 of them to enter each dungeon! Not only that, if things start to look bad they'll run away rather than pressing on to the end! (They mutter something silly about the risk of awful death. Isn't that what you're paying them for?)
So it seems you'll have to brush off your mathematics skills, learned when you were a child from your teacher with the help of your whipping boy. (You weren't allowed to whip him unless you got the math problems right, which was extremely unfair to you but did at least encourage you to develop your skills rapidly.)
With some careful analysis of past adventures, you think you can probably select adventuring teams that will be able to successfully conquer those three dungeons. Then, at long last, you will have your vengeance! MUWAHAHAHAHAHAHAHA! (You need to get this maniacal laughter out of your system now, it wouldn't do to show it while you're hiring the adventurers).
An answer key and leaderboard will be posted in about a week, most likely on Monday the 15th.
As usual, working together is allowed and encouraged, but for the sake of those who wish to work alone please spoiler-tag (type '>!' at the start of a line) any comments with information on the dataset.
Edited to add: the original version of this document gave an inconsistent dataset (hiding some information as 'Unknown' in some columns but revealing it in other columns). I've corrected that in the links, thank you simon for the heads-up. The old dataset is here if anyone wants it for comparison purposes, but should be strictly less useful.
Thank you for making this.
The actual backbone of my strategy:
(I reserve the right to change all of these if I come up with a better idea or another commenter shares a new and relevant insight.)
For the Lost Temple of Lemarchand, I’ll send a level 2 Rogue to handle the needletraps*, a level 2 Druid to handle the snakepits, and a level 2 Cleric and a level 2 Mage to handle the various undead.
For the Infernal Den of Cheliax, I’ll send a level 5 Fighter to fight the orcs and the dragon, a level 3 Druid to keep everyone safe from the snakepits and wolves so they’re fresh for the boss fight, and a level 3 Ranger and level 3 Mage to help the Fighter with the dragon (dragons are scary!).
For the Goblin Warrens of Khaz-Gorond, I’ll send a level 4 Fighter to handle the goblin chieftain and the boulders, a level 4 Ranger to handle the rank-and-file goblins, a level 3 Cleric to help the Ranger out, and . . . I guess a level 3 Fighter to support the first one? (I hate to have doubles on a team but there’s no other class that does as well against chiefs and boulders.)
*This is the one place I feel confident Measure made a mistake: “Rogues help with needletraps” is the most reliable inference I ran into in my encounter-countering research, so I don’t get why they’d include a Mage and a Fighter but not a Rogue in Adventuring Party #1.
The odds don’t seem great. The odds of all three adventures concluding successfully really don’t seem great. And that’s assuming all my inferences are correct, which they aren’t. I know my character is set on this path, but if I was faced with a prospect like this in real life, there’s no way I’d bet anything I’d be afraid to lose.
Everyone's been getting all the names right this time. I'm quite surprised, and feel like I should be awarding roleplaying XP or something.
My analysis found that for poison needle traps, clerics and druids were almost as good as rogues, especially at low levels, and the druid will be better for the snake pits.
I admit that I made my choices without considering that later encounters are harder than earlier ones (I suspect this has something to do with lost hp, though I'm still confused by the sharp cutoff in success rates - not only to all parties beat their first encounter, for dungeons with eight or more encounters, the first two encounters are guaranteed wins, and longer dungeons have an even stronger effect.).
Deciphering the Unknowns (partial solution):
Lost Temple of Lemarchand - All encounters are known.
Infernal Den of Cheliax - The final encounter of an Infernal Den is 1/2 chance Dragon and 1/2 chance Lich. Of 33 explored, 4/4 with Orcs and 7/7 with Wolves contained a Dragon rather than a Lich (No Infernal Den that contained Orcs or Wolves contained a Lich). The final encounter is a Dragon.
Goblin Warrens of Khaz-Gorond - Each Goblin Warrens uses only a single type of trap from among (Boulder Trap, Poison Needle Trap, Snake Pit). This trap is 1/3 of encounters. The remaining 2/3 of encounters are Goblins. The final encounter is 3/4 chance Goblin Chieftain and 1/4 chance regular Goblins (never a trap). Encounters 3-9 are 2/3 Goblins and 1/3 Boulder Trap, and the final encounter is 3/4 Goblin Chieftain and 1/4 Goblins.
Given the potential value of world kingdom domination and the relatively low probability of success, it's probably worth significant risk to borrow/steal additional funds to improve my chances. After all, once I get the Crown, I can repay banish my creditors :)
Excuse me, sir, but there are things one simply does not do.
Yes, your goal is to conquer the world and rule with an iron fist, subjugating all beneath the mailed boot of your immortal tyranny.
But borrowing money? For shame! You have some standards!
The only suggestion more preposterous than that would be the idea that you could raise additional money by cutting back on your living expenses. It is perhaps true that spending 3,600gp per day on candles has cut what you have available for this plan, but if one is to be better than the beasts there are standards one must maintain.
My party selections:
Lost Temple of Lemarchand: (6kgp - 52%)
Infernal Den of Cheliax: (18kgp - 54%)
Goblin Warrens of Khaz-Gorond: (12kgp - 52%)
Total: (36kgp - 15%)
I don't have the skills to play these, but I'm delighted whenever you post one. I just think they're neat.
There is mo obvious correlation between no encounters and probability of success, but it looks like this is caused by better teams of adventurers taking on dungeons with more encounters on average.
There are no teams where more than 2 adventurers are of the same class. There is probably a reason for this.Where there are duplicate types the dungeon is only beaten 55 percent of the time v 64 percent when there are no duplicates, so I will have 4 different types of adventurers in all my teams.
There is no obvious correlation between the rank of the highest adventurer and the probability of beating the dungeon. Suggests having a balanced team is more important than just maxing one out, unless there is specific evidence to the contrary.Looking at the probability of defeating an encounter when a particular type of adventurer is missing suggests the following:Goblins - teams do better than average when a Cleric, Fighter or particularly a Ranger is presentGoblin Chieftain - Teams with a fighter in them do much better than those without, Ranger is second bestWolves - Are very easy to beat regardless of the teamOrcs - Fighters seem to be best followed by clericsOrc Warlord - Teams with fighters do much better than ones without.Orc Shaman - Again fighters are best, though mages and druids seem to be pretty close Skeletons - Easy to beat, though teams with clerics do a bit better than averageZombies - Teams with clerics do best, though mages come closeGhosts - Clerics do bestBasilisk - Druids are best followed by fighters and clericsLich - Clerics are best followed by Mages Dragon - The toughest to beat. Fighters and Rangers seem best followed by mages and clericsBoulder Trap - Fighters do bestLever Puzzle Room - Easy though rangers seem do do slightly better than mostRiddle Door - Mages and Clerics do better than most, though again this is easy for allCursed Altar - CLerics do bestSnake Pit - Easy though Druids do slightly better than mostPoison Needle Trap - Rogues do best Fighters appear to be the best all round adventurer, followed by clerics. Looking at the probability of winning an encounter when particular levels of adventurers are presentsuggests the following.(1) When either a level 6 fighter, ranger or cleric is present an encounter against goblins is almost alwayswon. Rangers seem to be slightly better.
(2) Where the highest rank of an adventurer is <= 2 the probability of defeating the dungeon is less than 50percent. Between 3 and 7 it gradually increases from 61 percent to 68 percent, but there is a big jump to87 when at least one level 8 adventurer is involved (Though there are only 30 cases of this). Temple of Lemarchland
There are 86 previous dungeons which had encounters which are a subset of those in the first dungeon. It looks very much like a junior dungeon. 4/8 teams which were all of rank 1 managed to beat it, which suggests spending relatively little on this. Infernal Den of Cheliax .
The final encounter of every "Infernal Den" is either a Dragon or a Lich.Every Den which has either wolves or Orcs encounters has a dragon at the end suggesting that we arefacing a dragon here. A high level figher looks like it is the best bet agasint dragons. Goblin Warrens of Khaz-Gorond
All dungeons with Goblin in the name have quite a few Goblin encounters, and most have a Goblin Chieftain. Poison Needle Traps, Snakepits and boulder traps are secondary threats. Teams with at least 1 level 6 of several types look like they have nearly a 100 percent chance of winning against, lower level rangers seem like they are slightly better than other types. Fighters seem to be best against a Goblin Chief, though team with afighter with level > 3 seem to do worse than ones below it, though this is possibly a statistical artefactas the numbers are relatively small. I don't think I can confidentally identify a good choice based on my current understanding.. Peering through the fog my best current guess is: Lost Temple of Lemarchland:level 3 clericlevel 2 roguelevel 2 druidlevel 2 mage Infernal Den of Chelaix:level 7 fighterlevel 2 cleric
level 2 druidlevel 3 rangerGoblin Warrens of Khaz-Gorond level 6 rangerlevel 2 clericlevel 4 fighterlevel 1 rogue
My strategy and analysis:
As abstractapplic notes, parties are less likely to fail on earlier encounters. I can think of multiple possible reasons:
I'm proceeding assuming (1), but on a weak basis: it's the a priori most likely (imo), things don't immediately appear incompatible with this (without me having really checked), and the "Threat Level" stat seems most compatible with this. But I don't really know!
If resource depletion (at least, single-resource) is an accurate model, losses to an encounter type should be fairly informative about the difficulty of an encounter type and what is strong against it, with at least these caveats:
I am keeping these points in mind but have not really done anything to actually deal with them in the analysis.
I'm also assuming things like only the encounters in the dungeon matter and not the name, order of party members doesn't matter, etc.
edited to add: after posting this i did a brief check on the effect of levels and noticed two outliers where a high level party was defeated early:
Abandoned Dungeon of Azmar: Ranger 7 Druid 6 Fighter 6 Rogue 7 Snake Pit lich Lich (...etc, but defeated there)
Forgotten Temple of Stormwind: Ranger 4 Rogue 6 Fighter 5 Cleric 6 Basilisk Basilisk (...etc, but defeated there)
This makes me think a single-resource-depletion model is maybe less likely, and it might be a multiple-resource model (such that repeated encounters deplete the same resource), but I have no time to re-consider things.
The Goblin Warrens of Khaz-Gorond:
Encounters 3-9 are 2/3 Goblins and 1/3 Boulder Trap, and the final encounter is 3/4 Goblin Chieftain and 1/4 Goblins
I confirm, but go a bit further. Dungeons with "Goblin" in the name all seem to have basically the same encounter generation, unless they have the "Night" prefix (in which case they can have Ghosts) or the "Mountain" prefix (in which case they can have Wolves). There are 118 Dungeons with "Goblin" in the name that have 9 or more encounters; all of these end with a Goblin Chieftain. Also, dungeons with "Goblin" in the name never have exactly 8 encounters, suggesting a discontinuity in the generation rules. Thus, the dungeon will end with a Goblin Chieftain (high confidence).
Threat Level: 3.95 (but beware potential bias regarding perceived difficulty of Goblins, reported by abstractapplic)
Goblins: Rangers are strongest.
Goblin Chieftain: Looks like a relatively hard encounter (but be aware of late dungeon bias). Fighter is strongest.
Boulder Trap: looks like a relatively easy encounter. Fighter is strongest.
Ranger and Fighter are obvious choices.
There are a decent number of very similar dungeons to this in the data. Restricting to dungeons with 7 or more total encounters including Goblins, Boulder Trap, Goblin Chieftain and no other encounters, there are 12 wins and 22 losses, maybe not enough to do accurate statistical analysis, but certainly enough for me to engage in my favourite pastime of overfitting to spurious patterns.
Looking at these particular dungeons, Rangers look incredibly strong, Mages look very bad, and Clerics look uncharacteristically meh (they are usually quite good). Going by strongest-looking to weakest-looking and selecting the top four different types, it looks like Ranger, Fighter, Druid, Rogue would be the strongest party.
However, going further down the overfitting-to-spurious-patterns rabbit hole, Druids and Rogues together have a terrible record (1-9) on these dungeons. Note, Druids and Rogues don't seem to have particular antisynergy in general, so this is most likely completely spurious. However, double Ranger (2-1) looks better assuming the likely spurious patterns are real. Who to drop of Druid and Rogue?
Ranger+Rogue looks good, Fighter+Rogue not so much, Ranger+Druid and Fighter+Druid both OK, so Druid looks the safer choice.
All of this, to be clear, is far too low N to be of any reliable use. But I'm doing it anyway because, whatever, maybe there's something there.
Another possibility would be Ranger+Fighter+ double Cleric, since both double Cleric parties won. But I'm sticking with double Ranger, Fighter, Druid.
Levels: see below.
The Lost Temple of Lemarchand:
Threat Level: 4
None of these look like particularly tough fights.
Skeletons, Zombies, : Cleric looks best, followed by mage.
Ghosts: Cleric still looks best, but mages look about comparable to fighters in distant second place.
Note: Ghosts commonly occur in both physical and undead-oriented dungeons, while Skeletons and Zombies are more restricted to undead-themed dungeons. So, potential for different biases to creep in from parties being weakened by other fights in different dungeon types.
Poison Needle Trap: Rogues do best, as reported by abstractapplic and yonge.
Snake Pit: Druids do best, as reported by abstractapplic and yonge. Possibly notable: Fighters don't look especially good here, despite Snake Pits commonly occuring in physical-oriented dungeons.
Obvious choice from just this info is Cleric+Mage+Rogue+Druid.
There isn't a big pool of dungeons with this exact encounter combo to look at for my overfitting. Although undead-themed dungeons with Skeletons, Zombies and Ghosts are common, and they often have Poison Needle Traps, they don't often have Snake Pits. In fact, dungeons with "Undead" in the name never have Snake Pits. However, Undead-themed dungeons without "Undead" in the name apparently have looser rules.
However, we can look at dungeons that have subsets of these encounters (with the understanding that the sample is low in Snake Pits).
Looking at this, Clerics, Mages and Rogues look good as expected, but next place is Fighter. Druids look quite bad.
If we look at synergies between these in this tiny data pool, all of Clerics, Mages and Rogues work well with each other, and while Druids still don't look as good as Fighters, they do OK when paired with these. So, I speculate that druids are only bad for missing something we needed more and we probably have what we need with this party, and that therefore taking Druid to deal with Snake Traps is probably worth missing out on whatever Fighter is bringing us on other fights.
So: Cleric+Mage+Rogue+Druid (same as abstractapplic and Yonge)
Level: see below
The Infernal Den of Cheliax:
The final encounter is a Dragon.
Threat Level: 4.5
Orcs: Fighters do best, then Clerics (as reported by Yonge).
Snake Pit: encounter is also in The Lost Temple of Lemarchand. Druids do best, as reported by abstractapplic and Yonge.
Wolves: Looks like an easy fight, but I expect this is largely because both Fighters and Druids do well against them, and since parties typically have 4 of the 6 classes the large majority of parties will have at least one Fighter or Druid. Fortunately, we are likely to want a Fighter for Orcs or a Druid for Snake Pits anyway.
Dragon: a very hard fight. No class looks to have a big advantage; Fighters, Rangers, Mages and Clerics all do comparably well/badly with Druids worse (by a bit) and Rogues worst.
There are few dungeons that are really close to this one, so only really looked at the individual fights.
If you look at parties with Fighters in them Rangers seem to do better against Dragons than Mages, so I am thinking: Fighter+Ranger+Druid+Cleric.
I have not analyzed the effect of levels. I will just slightly buff up the characters that seem the most important and on the dungeons I expect to be harder, and vice versa. I don't know the effect of giving different characters much different levels and will avoid that to avoid possible danger.
Solution (unless I change it later):
The Lost Temple of Lemarchand (9,000gp):
The Infernal Den of Cheliax (14,000gp):
The Goblin Warrens of Khaz-Gorond (13,000gp):
Are we supposed to understand that each dungeon name is unique (despite the rather weird cartesian-product naming scheme)?
The lists of dungeon-crawls in the dataset includes four for the "Lost Temple of Lemarchand" but the encounters listed for them don't seem compatible with the ones described in the text. It includes none for the "Infernal Den of Cheliax", which is a little odd. (Maybe everyone who tried got killed by the orcs, but that seems a bit unlikely.)
The text says "Goblin Tunnels" at one point and "Goblin Warrens" at another. It seems like the difference is probably significant. Are they supposed to be consistent with one another?
[EDITED to add:]
Are we supposed to understand that each dungeon has a fixed sequence of encounters, and that any given crawl meets with some subset of them, in a consistent order? Obviously any possible dataset is consistent with that hypothesis, if we allow the sequence of encounters to be large enough; just eyeballing a few cases it's not a hypothesis I'd be much inclined to make if the text didn't kinda imply that, at least as far as the three dungeons we really care about are concerned.
[EDITED to add:] I've spoiler-tagged all the above, although I don't really see how any of it would give nontrivial information to someone else attacking the challenge.
Dungeon names are not necessarily unique - this dataset spans a long time, and so if the Lost Temple of Lemarchand is looted, and fifty years later a new Lost Temple is found in Lemarchand, that different dungeon may be given the same name, even though it is a different dungeon with potentially very different encounters.
"Warrens" is intended, I'll update that.
You are at your local village's Evil Overlords Club meeting. (Yes, Evil Overlording, or to be more precise, wanna-be Evil Overlording, is very popular in this civilization).
Several other club members have coincidentally also taken an interest in arranging for adventures, and some fruitful discussions have taken place (see other people's comments for details).
One of the club members, however, reveals some further information:
"When I sent to get adventuring data from the guild" said your fellow club member, who you only know as simon, "the Evil Overlords liaison there showed my representative something he wasn't supposed to see. It was only a moment, but that was enough - he got it with his Secret Encoder Ring. It was a list of adventure data, but with an additional column, for something called "Threat Level".
"What," you say, "the liaison didn't show my representative that. I thought the liaison was supposed to show data to all Evil Overlords International member representatives equally."
"Indeed. Which caused me some concern that it might strain relations if I used it. But, I wasn't specifically told to throw it away. Now, the liaison said that this data, supposedly, "didn't end up being used", but even if it wasn't "used", it's potentially of interest since it might be in some way related to dungeon difficulty or perception of difficulty - or someone's perception of what someone else might perceive as the difficulty - or something. Anyway, this "Threat Level" column had numbers in it and I figured out a formula for the numbers. If you're interested, keep listening."
"So, what's the formula?"
"Simple. It's a sum of contributions from the individual encounters in the dungeon, minus 0.25.
Goblins = 0.325
Orcs=Skeletons=Zombies=Boulder Trap=Lever Puzzle Room=Riddle Door=Cursed Altar=Snake Pit=Poison Needle Trap=0.5
Goblin Chieftain=Wolves=Orc Shaman=Ghosts=0.75
"Yes, that does seem simple," you say, "I assume that was pretty easy to figure out."
"Uh...of course," Evil Overlord simon responded, with a slightly pained look. "Not that it had to be easy... a lesser mind than myself might have proceeded from the assumption that there's no 0.25 subtraction, and then, since the first entries when sorted by Threat Level each include exactly one physical trap (by which I mean Boulder Trap, Lever Puzzle Room, Snake Pit, or Poison Needle Trap), counted the physical traps as having 0.25. And then later, that lesser mind would have noticed that they needed to count extra physical traps beyond the first as having 0.5. And, if they had extended that as well to magic traps (by which I mean Riddle Door and Cursed Altar) everything would have worked out, since all dungeons have at least one trap of one sort or another. But, that lesser mind might have been tripped up by the fact that the first magical traps, when the dungeons are sorted by threat level, occur along with a physical trap - so the 0.25 subtraction is accounted for already - and before dungeons with two physical traps are encountered, so before they knew that traps after the first contributed 0.5 to the threat level. So it looks like magic traps are a straight 0.5 and different from physical traps. And since many later dungeons have some magical and no physical traps, the lesser mind would then get the wrong answer for those dungeons and add epicycles. And then become tied in knots trying to make the epicycles work, knowing something is wrong but expecting some simplification to become apparent when they just add enough epicycles, but not looking back to the very earliest assumptions. Of course, super-smart Evil Overlord that I am, avoided that easily."
"That's, um, a very specific pitfall. How did you avoid it."
"Intuition," Evil Overlord simon grimaced. "By the way," he added, changing the subject. "there were some very tiny discrepancies that look like rounding errors. Like, on the order of 10 to the minus 16th or thereabouts. Anyway, I won't be looking into those. I consider my duty to equalize the information properly discharged."
Intellectual Integrity Score: 10/10
Evil Overlording Score: 0/10
If we filter the data based on the encounter which ended an unsuccessful Adventuring party, I notice that the groups foiled by Poison Needle Traps disproportionately had no Rogues.Filtering by adventurer type, I notice that groups with no Rogues did not do well against dungeons with PNTs.Thus, I think including at least one Rogue on the team heading for the Lost Temple of Lemarchand is wise.
Regarding the overall levels of successful teams: I was surprised to see that the total average level of adventurers on victorious teams was 3.69474, and on defeated teams it was 3.477. That's not as big a difference as might be guessed, and it suggests that the precise composition of the team (mix of types of adventurers) matters a lot more than the overall level. This is very helpful, because levels are the primary constraint on our resources.To get possible insight into the various roles, I calculated the victory rates of teams that lacked a specific type of adventurer. Here they are:No Fighters: 740/1247No Rangers: 845/1308No Mages: 766/1235No Clerics: 654/1230No Druids: 821/1215No Rogues: 832/1247Overall, missing a Cleric seems to hurt the most, and missing a Druid seems the easiest to overcome. But again, the success/failure rates still seem to be tied more to tailoring the party to the specific threats it will face, rather than finding a strong-across-the-board team.
A potential issue with the dataset:
The listings for total number of encounters of the different types appear to include the actual encounters that are shown as "Unknown" in the main list of encounters. Is that intended?
Yikes, good catch. That was not intended, but under the circumstances I'm going to provide more information rather than less. Feel free to use that information, and I'll update the file to replace the 'Unknown' entries with the actual encounters (let's assume the adventurers successfully scout the whole dungeon even if they only manage to clear part of it).
Thanks. Actually though, could you keep both versions available? Having some entries listed as "Unknown" makes it easier to check what a party actually fought - something I had been intending to extract from the "# of <x> Encounters" columns when I noticed the issue.
edit: thanks. comment was made before seeing aphyer's comment on the corrected version being available and the edits to the post.
Should be already done, if you look at the edit at the end I've left the old version available.
Should be corrected now, mind taking a look at the new links and letting me know if everything looks good on your end?
OK, but you've added a new column for "Threat Level", is that intended?
...no, thank you again. That's a column that didn't end up being used, removed it.
Anyone who wants to know about "Threat level" can now find information in a separate comment.
This might be a reading comprehension problem on my part, but I couldn't find the objective explicitly stated. Is the objective to maximize the probability of successfully retrieving all 3 fragments? or to maximize the expected number of fragments retrieved?
You're right, I didn't make that explicit, this is a good question to ask. The objective is the first - the fragments are useless on their own, your win rate is the probability of getting all three.
So a 50% chance of each fragment is better than guaranteed success on two and guaranteed failure on the third.