This is a follow-up to last week's D&D.Sci scenario: if you intend to play that, and haven't done so yet, you should do so now before spoiling yourself.
There is a web interactive here you can use to test your answer, and generation code available here if you're interested, or you can read on for the ruleset and scores.
Note: the web interactive calculates average survival rates/values using Monte Carlo with small sample sizes. The figures in the leaderboard are more accurate.
The underlying ruleset was a resource-management minigame played behind the scenes for each fort.
Players were not expected to reconstruct the entire ruleset - rather, the minigame existed in order to create interesting multivariate effects in the output dataset.
Each fort plays 12 rounds of this minigame to determine survival and value. (After this, a fort either dies, shuts down, or grows sufficiently to take in new migrants/raise children/etc, at which point its starting dwarves no longer matter.)
A site has a biome (chosen at random from the four available) and a Coal Level given by 1d4-1.
There are seven ores (the six mentioned in the dataset, plus Adamantine, which is buried too deep to be prospected for in advance).
Each ore has an independent 40% chance of being present in any site.
Any site where (# of ores found by prospecting + Coal Level) is less than 4, or any Tundra site where it is less than 5, does not get settled. As such, all forts have at least that much coal/ore in them.
The main underlying mechanic is one of resource management - there are a variety of different resources involved, and high-value forts are those that manage to navigate the production chain to create high-value finished goods.
A fort is subject to many threats from the outside, ranging from the occasional goblins and mandrills of the Plains to the dreaded Elephants of the Jungle.
None of these things can destroy a fort on their own. When threats from outside are too serious to deal with, the dwarves seal the gate, set up some traps with whirling serrated blades and huge menacing spikes, and wait for them to go away. The use of Warriors is not directly to keep these threats from destroying your fort - rather, it's to allow your fort to keep access to the outside.
While you have access to the outside:
While you don't have access, your Woodcutters are useless, your Farmers less useful, and you cannot buy emergency Food or Fuel.
Each turn, you determine the Threat Level of your biome:
If you have a # of Warriors >= the Threat Level, you have exterior access that turn. If # Warriors < Threat Level, you are stuck inside that turn.
If you have exterior access, Woodcutters each cut 2 Trees, up to a limit of the # of Trees available in your biome this turn, and you gain 1 Wood per tree cut. If you don't, Woodcutters are useless.
Each ore type has a different Depth - how far below the surface it tends to be found.
The more Miners you have, the deeper you can dig, and the more ores you can find.
Each round, you receive the Yield of each ore present in your fort that you can mine deep enough to reach.
If Adamantine is present in a fort, it has a Thickness of d20+1. Every time Adamantine is mined, that Thickness is reduced by 1. If it ever reaches 0, you have Delved Too Deep, and...well...let's just say that no fort that does this ever survives.
Each Miner also has a chance of (10% * Fort Coal Level) to produce 1 Coal.
These professions create finished goods. Finished goods are the highest-value things you can make, but most require multiple inputs, needing both ore and some kind of fuel.
Each round, each dwarf in your fort eats 1 Food. Your fort begins with 1 round worth of Food (meaning that e.g. your 13-dwarf fort could actually manage with production of 12 Food/round).
Two professions produce Food:
If you do not have enough Food at the end of a round, but do have exterior access, you can buy Food at 3 value of finished goods/Food. This is an extremely high price (reflecting the risks and costs of merchants launching speculative expeditions to your fort), but the alternative is for your fort to collapse of starvation.
Once you know how the rules work:
In your fort, ideal strategy was:
N.B: performance here was Monte-Carlod rather than calculated. There is some ambiguity in ordering re. how you prioritize a small reduction in safety vs a substantial increase in profit - depending on how risk-averse/risk-loving you are, you could choose to rank GuySrinivasan lower or Alexander Ledovsky higher.
*These allocations in theory have a non-zero risk of Delving Too Deep with a string of very lucky/unlucky alcohol-fueled Mining, but in practice the odds are negligible (I believe on the order of 10^-8).
Players all did a good job of identifying how to survive, with no fort risking starvation, and no fort having 7 Miners. There was more variation in how well players produced value, with the top players coming very close but not quite hitting the optimal allocation. The most notable thing that got missed was the depth of available metal ores and how it made bringing fewer Miners reasonable - every submission brought at least 4 Miners, and many went up higher.
Congratulations to all players, particularly to simon (1st) and gammagurke (2nd), who came very close to optimal but most notably brought only 1 Woodcutter each (meaning that quite a bit of money went to buying wood to keep their Smiths and Crafters running), and to abstractapplic (3rd), who brought 2 Woodcutters but went low on Smiths and high on Crafters.
(abstractapplic gained 10 Dwarf Points for their fort's suitably Dwarfy name, but lost 10 Dwarf Points for looking at a fort with four different types of shallow metal deposit and declaring that they were going to make money by crafting things out of wood like some kind of pansy Elf. Our Dwarf Point Leader is therefore Yonge.)
I also see we've got some new players - congratulations to you as well! I hope you enjoyed the scenario - if you did, the D&D.Sci tag contains a list of past scenarios, and you can subscribe to that tag to get notifications when new ones are posted (abstractapplic and I try to make sure this happens around once a month).
As usual, I'm interested to hear feedback on what people thought of this scenario. If you played it, what did you like and what did you not like? If you might have played it but decided not to, what drove you away? What would you like to see more of/less of in future? Do you think the scenario was too complicated to decipher? Or too simple to feel realistic? Or both at once? Do you have any other feedback?
Thanks for playing, and I hope you had fun!
Reflections on my attempt:
It looks like I was basically right. I could have done slightly better by looking more closely at interactions between features, ore types especially; still, I (comfortably) survived and (barely) proved my point to the King, so I'm happy with the outcome I got.
(I'm also very pleased by the fact that I picked up on the ore-based-vs-wood-based distinction; or, rather, that the ML library I've been building automatically picked up on it. Looks like my homebaked interpretability tools work outside their usual contexts!)
Reflections on the challenge:
Another excellent entry, and a hard act to follow. The jokes landed, the premise was fun but coherent, and the scenario was challenging yet tractable.
Having multiple quantitative success metrics was a fascinating choice. To be honest, I think there was some missed potential here; if the best strategy wasn't simultaneously survival-optimal and money-optimal, there could have been some interesting tension from players deciding their blood-to-treasure exchange rates. I'll have to try and work something like that into a future game.
the ore-based-vs-wood-based distinction
I'm curious as to what exactly you found there. Ore-based vs wood-based production wasn't really an intended distinction - rather, ore and wood were intended to be used together. I added woodcrafting as an afterthought late in development (when Crafters were performing very poorly due to only having two craftable ores), and it still isn't a major source of income. Even in your SHAMEFULLY ELFISH fort, your Crafters spend most of their time on Silver, and only make things out of wood when poor mining yield/alcohol-fueled crafting frenzies make them run out of silver. The intended distinctions were:
There were two goals on my end from this, one of which succeeded and one of which did not:
I'm curious as to what exactly you found there.
Briefly: I told my learner "assume there are two sources of income for Light Forest forts; assume they are log-linked functions of the data provided with no interactions between features; characterize these income sources."
The output graphs, properly interpreted, said back:
(In reviewing my graphs in retrospect I also see a small bump in performance for both sources associated with having exactly one Brewer; I missed that the first time because it looked like noise and I'd assumed Brewers only mattered to the survival half of the challenge.)
This wasn't 100% right, and missed some important detail, but given the bad assumptions I built it on - an additive model with a lot of interactions sprinkled on top would have been a better match - I'm pleasantly surprised by how closely it matches (a valid interpretation of) ground truth.
The larger source of income benefits greatly from Miners, benefits from the presence of every ore (especially Haematite), likes coal, and benefits from having one Smith.The smaller source of income benefits from Woodcutters, benefits from having two (but not more) Warriors, hard-requires at least one Woodcutter and Warrior in order to be viable, actively dislikes Coal, doesn't care about ores (except Copper for some reason), and strongly benefits from Crafters.
Ah, I see! That is a meaningful interpretation of reality, but rather than 'ore-based vs wood-based' I'd phrase it as a distinction between:
Just a quick comment of encouragement. I haven't played and might not play them live or comment, but I still find these scenarios really cool and enjoy reading both the write-ups and how close the players come! It's also great that you're building the backlog because it gives great opportunity to try the older puzzles at my own pace. Great work! Keep it up, you and everyone playing :D
Appreciated, thank you!
Well, I did okayish for a first time player, but I didn't get to the top. Not an unexpected result however.
Question, why do you Monte Carlo win rates rather than calculate them?
Calculating survival and value numbers is straightforward in some cases (e.g. 6 Miners plus a brewer has a readily calculable chance of digging too deep.)
It's much harder in other cases. Your submission, for example, is very hard to calculate expected value for - you need to buy some of your fuel...and you have exterior access half the time but not the other half...and in order to get your first bit of money with which to buy the first fuel your miners need to hit at least one coal...running a simulation for this is much easier than trying to calculate it.
I suppose I could have explicitly calculated some numbers that were easy and Monte Carlod the ones that were hard, but the second reason to Monte Carlo it is that I'm lazy and Monte Carloing everything is much simpler. In order to create the dataset I already needed to write code to simulate a fort, and once I have that code it's very easy to just say 'okay, now run it 100k times with these inputs.'
Well done on your performance - even if not the top performance, you both guaranteed survival and beat the King on value, so you clearly made some good progress!
Yay 100% survival chance with no analysis whatsoever. I just opened up the web interactive and guessed (3x farmers and warriors because food and fighting are essential, 2x woodcutters and miners for good resource supply, and 1x of everything else to cover all the bases). (368.3 value)
I've finally found a way to spoiler my comments or posts: Use the :::spoiler tag and I can spoiler comments.
Question, does anybody use this technique for spoilers?