D&D.Sci Divination: Nine Black Doves Evaluation & Ruleset
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, or you can read on.
RULESET
Map
Provinces are laid out as follows:
This matters for war, and for the spread of plague (and of black doves). Provinces are at risk of being pillaged by adjacent provinces of different empires (e.g. Italia is at risk of being pillaged only by Germania), and are at risk of plague spreading from any adjacent province, friend or foe (e.g. Italia can contract plague from Germania, Hispania or Grecia).
Congratulations to simon, who I believe was the first to identify the map and the connection to Plague and Pillaging.
Population and Wealth
The main factors driving a province’s exposure to disasters were not the omens directly, but its Population and Wealth. The majority of omens were relevant only insofar as they had relationships to Population and Wealth. Population and Wealth are both represented as integer values that tend to almost always be between 1 and 10.
Both Population and Wealth go up gradually but then decrease with certain disasters. Every year, three things happen in order:
Disasters are determined (details below).
A province suffering a Famine or Plague will lose half (rounded up) its Population.
A province suffering an Earthquake or Fire will lose half (rounded up) its Wealth.
A province being Pillaged will lose half (rounded up) its Wealth, and the pillaging province will gain that Wealth.
Growth is determined.
Each province has an independent 50% chance to gain a point of Population, and an independent 50% chance to gain a point of Wealth.
Omens are determined (details below).
Fire and Famine
These are the two main negative-feedback disasters, keeping Population and Wealth growth in check by occurring when they grow too high:
Any province with Wealth > 4 is at risk of Fire, with a probability of 10% per point of Wealth above 4.
Any province with Population > Wealth is at risk of Famine, with a probability of 10% per point of Population above its Wealth.
Secular Omens
Most things the existing diviners categorize as Omens have nothing supernatural about them. They are still potentially useful to you, however, due to their relationship to Population and Wealth:
Moon Turns Red is caused by high Population. (High Population results in lots of people burning fires, and the smoke will sometimes make the moon look red.) This has a 25% chance of happening in a province in any year when its Population is 5 or more.
Two-Headed Baby is caused by high Wealth. (High Wealth results in people living in cities, and decadently installing indoor plumbing made of lead, which causes babies to be born with two heads.) This has a 25% chance of happening in a province in any year when its Wealth is 5 or more.
Rivers of Blood is caused by low Population. (When people stop maintaining riverways, algal blooms frequently result). This has a 25% chance of happening in a province in any year when its Population is 4 or less.
New Constellations Spotted is caused by low Wealth. (When there are no major cities with lights in them, stars are more readily visible). This has a 25% chance of happening in a province in any year when its Wealth is 4 or less.
Geese Flying Backwards is caused by rapidly growing Population. (When people set up farmland in new places, it confuses the geese). This happens automatically in a province whenever its Population has increased each year for 3 consecutive years (hitting the 50% growth chance) with no Population-reducing disasters.
Wolves Howling at the Sun is caused by rapidly growing Wealth. (When people cut down forests to build cities, it confuses the wolves). This happens automatically in a province whenever its Wealth has increased each year for 3 consecutive years (hitting the 50% growth chance) with no Wealth-reducing disasters.
Rain of Fish is random. Sometimes fish just fall out of the sky. This is a thing that happens. It has a 2% chance of happening any year in any province.
| …Population | ...Wealth | |
| High... | Moon Turns Red | Two-Headed Baby |
| Low... | Rivers of Blood | New Constellations Spotted |
| Growing... | Geese Flying Backwards | Wolves Howling at the Sun |
This means that, for example, a Two-Headed Baby indicates high risk of Fire (since Wealth must be high), but also indicates low risk of Famine for the same reason.
Plague
Plague has a 1% chance of starting in any given province in any given year (though see Black Doves below for another way it can arise).
Once Plague has started, however, it is contagious. If a province has a neighbor that had Plague last year, this year it has a 50% chance to get Plague. If it has two (or more) such neighbors, it has a 100% chance.
A province that suffers from Plague cannot suffer it again for the next 5 years.
Earthquakes
Earthquakes have a 1% chance of happening in any given province in any given year (though see Black Doves below for another way they can occur).
Great Leaders and Pillaging
If a province is more militarily strong than its neighbors, it can Pillage them.
The Strength of a province is given by its Population, plus a bonus if its empire is ruled by a Great Leader.
The birth and death of Great Leaders is heralded by omens sent by the gods: a Flaming Comet in one of an empire’s provinces indicates that a Great Leader was just born there, while Sky Dark at Noon in the capital indicates that the Great Leader died.
While an Empire has a Great Leader whose age is at least 15, all provinces in that empire receive a +4 bonus to Strength (making them usually stronger than their neighbors unless there are very large Population differences). At the time of your scenario, the only empire with a Great Leader is Germania (...maybe don’t tell the Emperor that).
If a province can pillage its neighbors, the odds of doing that are given by the Wealth of the neighbor: 5% * Wealth of neighbor. Nations are less likely to bother pillaging a very poor neighbor, even if they’re strong enough to do so.
Some Omens are taken to herald victory, and while they don’t have any effect on Strength they cause provinces to invade more readily:
Barbarian provinces (British and Germanian) take Wolves Howling at the Sun as an omen of victory.
Civilized provinces (Roman and Persian) take New Constellations Appear as an omen of victory.
The year after one of these omens appears, the province it appeared in will be twice as likely to invade its neighbor(s) if possible.
Black Doves
Long ago, the gods bound the Titans in prisons beneath the earth:
The Titan of Fire was imprisoned beneath Parthia.
The Titan of Famine was imprisoned beneath Britannia.
The Titan of War was imprisoned beneath Italia.
The Titan of Plague was imprisoned beneath Anatolia.
When the Titans rage against the bars of their prisons, two things happen:
There is an Earthquake in the province of their prison.
One or more fragments of them escape (the first into the province where they are imprisoned, additional ones into adjacent provinces). These fragments look to mortals like black doves, but carry fragments of Titanic malice.
Black Doves have various effects on the province they are in:
Fragments of the Titan of Fire triple that province’s chance of experiencing a fire next year.
Fragments of the Titan of Famine triple that province’s chance of experiencing a famine next year.
Fragments of the Titan of War triple that province’s chance of invading a neighbor (note: not its chance of being invaded) next year.
Fragments of the Titan of Plague count as an adjacent province with plague next year (giving it a 50% chance of contracting plague, or 100% if another adjacent province has plague).
The black doves then attempt to travel across the world to spread Titanic evil everywhere they can before they fade away. Each year, they will try to move to an adjacent province that has not had a fragment of that Titan in this breakout—if they succeed, that province will have them next year.
Multiple Titans can break out at the same time. When this happens, each breakout happens independently, and the doves move independently. To you, however, they all look the same: one or more Titan fragments in a region will be recorded as one instance of ‘Black Doves’ in that province.
Over time, breakouts have been becoming more frequent and powerful as the Titans gather their strength:
Titans used to break out every ~40 years, now it is every ~20.
Titans used to break out one at a time, now many can break out at once.
Titans used to create one or two doves in a breakout, now they always create 3.
Doves used to have a ~40% chance of fading away each year, now it is down to ~20%.
In 1079, the Titan of Plague in Anatolia attempted to break out. It caused an Earthquake in Anatolia, and deposited Black Doves in Anatolia, Parthia and Grecia. This year, those black doves may have faded (~20%) or may have spread to Italia and Scythia (~80%).
In 1080, the Titans of War, Famine and Fire all attempted to break out. This caused Earthquakes in Britannia, Italia and Parthia, and deposited Black Doves in many places.
As of the most recent data, while only 8 Black Doves were listed, there are actually at least 9, and possibly as many as 11, because some provinces contain more than one:
Scythia contains a Dove of Fire, and possibly also a Dove of Plague.
Italia contains a Dove of War, and possibly also a Dove of Plague.
Hispania contains a Dove of War and a Dove of Famine.
STRATEGY
Current province statuses are:
| Province | Population | Wealth | Has Great Leader? | Black Doves |
| Britannia | 7 | 4 | No | Famine |
| Germania | 5 | 6 | Yes | None |
| Scandinavia | 4 | 6 | Yes | Famine |
| Anatolia | 1 | 1 | No | Fire |
| Parthia | 4 | 2 | No | Fire |
| Scythia | 3 | 1 | No | Fire, 80% Plague |
| Grecia | 5 | 7 | No | War |
| Hispania | 5 | 4 | No | War, Famine |
| Italia | 4 | 0 | No | War, 80% Plague |
Some of these Population and Wealth values could be worked out exactly (for example, Grecia had the Low-Population omen ‘Rivers of Blood’ in 1079 but the High-Population omen ‘Moon turns Red’ in 1080, uniquely identifying its Population as 5.
Others could only be estimated: for example, Italia’s Wealth can be identified as necessarily very low, but it’s plausible it could be 1, and theoretically possible it could even be 2.
Fortunately, which interventions were valuable was robust to small variations in Population and Wealth. The probabilities of various disasters were:
| Hispania | Italia | Grecia | |
| Chance of Fire | 0% | 0% | 30% |
| Chance of Famine | 30% | 40% | 0% |
| Chance of Plague | 1% | 40% | 50% |
| Chance of Earthquake | 1% | 1% | 1% |
| Chance to be Pillaged | 20% | 0% | 0% |
| Chance to Pillage | 0% | 0% | 5% |
Given these strategies, the optimal strategy was to buy:
Famine protection in Hispania and Italia.
Plague protection in Italia and Grecia (Grecia is at risk of contagion from its neighbor, Italia from a likely Black Dove of Plague).
Fire protection in Grecia.
Protection against invasion by the British (for Hispania).
LEADERBOARD
| Player | Hispania | Italia | Grecia | Expected # disasters |
| Optimal Play | Famine, Pillage | Famine, Plague | Fire, Plague | 0.18 |
| Yonge | Famine, Fire | Famine, Plague | Fire, Plague | 0.28 |
| abstractapplic | Famine, Plague | Famine, Plague | Famine, Plague | 0.48 |
| Measure | Famine, Pillage | Famine, Pillage | Fire, Plague | 0.58 |
| gammagurke | Famine, Fire | Famine | Famine, Fire, Plague | 0.68 |
| simon* | Famine | Famine | Fire, Plague | 0.68 |
| Random Interventions | ? | ? | ? | 1.39 |
| No Interventions | None | None | None | 2.09 |
*simon’s comments on the scenario listed only 40,000 denarii of interventions. His score here reflects only those. Sorry, simon. At least you saved the Emperor money while still hitting most of the valuable interventions!
Congratulations to all players, particularly Yonge, who managed to correctly protect Italia from Plague without also protecting Hispania.
FEEDBACK REQUEST
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 underlying data model was too complicated to decipher? Or too simple to feel realistic? Or both at once? Was the need to use joins to analyze the data too large a barrier to entry?
Thanks for playing!
Thank you for posting this.
The need to join to other records was trivial for me.
I think the data model was too complex too fully decipher with a reasonable amount of effort, but this wasn’t a problem as it wasn’t necessary to get a decent answer (I might actually have got the optimal one if I hadn’t blundered and missed that Italia suffered a famine in the previous year—though I was uncertain on a number of points and wasn’t expecting to do as well as I did). In particular the wealth/population dependency completely passed me by.
Overall in terms of difficulty it felt OK.
I set up the same kind of thing that abstractapplic did:
then bounced off because while I had decent ideas of what I wanted to look for, I never got excited enough to get past the activation energy of trying to look for it.
My guesses about why include:
creating pretty plots was harder and (I expected) less useful
creating useful features for some kind of model, given the obvious time lag needs, felt like it’d be messy and I couldn’t just sit down and start making progress that felt good, so I never did
messy includes finnicky to get non-buggy, different for different columns, and especially figuring out what to do about the almost-certainly-important province-adjacency
less slack during those 10 days than ideal
Not certain any of this is necessarily bad, but it’s where my friction was.
I found this challenge difficult and awkward due to the high number of possible response-predictor pairs (disaster A in province B is predicted by disaster/omen X in province Y with a Z-year delay), low number of rows (if you look at each province seperately there are only 1080 records to play with), and probablistic linkages (if events had predicted each other more reliably, the shortage of data would have been less of an issue).
This isn’t necessarily a criticism—sometimes reality is difficult and awkward, and it’s good to prepare for that—and I get that it’s incongruous to hear “it’s too hard!” from the person who took second place out of a cohort that all did much better than random. Still, I think this problem would have been more approachable if we’d had fewer predictors and/or more data.
Misc other thoughts:
Example of the problems caused by too few rows per column: I managed to convince myself there was a weak but solid connection between Rain of Fish and Plague in some provinces. (In my defense, it made intuitive sense that having rapidly-decaying fish all over your territories might make people sick.)
. . . so my joke answer of “earthquakeproof every province, including the ones that don’t belong to you” would actually have been a good idea longterm? That’s delightful.
I did my analysis without using joins. I created a sub-df for each province, reset their indices, then recombined; and for “does this predict that with a lag of N years?” investigations, I shifted one of the sub-dfs back by N before recombining. Joins would have made more sense in retrospect, but not knowing about them wouldn’t have stopped me cold.
My hope was that people would figure out the existence of the Population and Wealth sub-variables, at which point I think figuring out what effects omens had would have been much much easier. Sadly it seems I illusion-of-transparencied myself on how hard that would be to work out. People figured out a lot of the intermediate correlations I expected to be useful there (enough to get some very good answers), but no-one seems to have actually drawn the link that would have connected them.
My hope was that you would start with sub-results like:
Famine in Year X means that Famine is unlikely in Year X+1
Plague in Year X also means that Famine is unlikely in Year X+1
Either Famine or Plague in Year X means that you are unlikely to Pillage a neighbor in Year X + 1
Omens in Year X that predict a high/low likelihood of Famine in Year X+1 (e.g. Moon Turns Red/Rivers of Blood) also predict a high/low likelihood of you Pillaging a neighbor in Year X+1
and eventually arrive at the conclusion of ‘maybe there is an underlying Population variable that many different things interact with’.
(I even tried to drop a hint about the Population and Wealth variables in the problem statement. I guess it’s just much harder than I expected to make deductions like that.)
That...is in fact a join?
This is something I noticed from some earlier .scis! I forget which, now. My hypothesis was that finding underlying unmentioned causes was really hard without explicitly using causal machinery in your exploration process, and I don’t know how to, uh, casually set up causal inference, and it’s something I would love to try learning at some point. Like, my intuition is something akin to “try a bunch of autogenerated causal graphs, see if something about correlations says [these] could work and [those] probably don’t, inspect them visually, notice that all of [these] have a commonality”. No idea if that would actually pan out or if there’s a much better way. There’s a lot of friction in “guess maybe there’s an underlying cause, do a lot of work to check that one specific guess, anticipate you’d go through many false guesses and maybe even there isn’t such a thing on this problem”.
What I was (haphazardly, inarticulately) getting at is that I never used any built-in functions with ‘join’ in the name, or for that matter thought anything along the lines of “I will Do a Join now”. In other words, I don’t think needing to know about joins was a barrier to entry, because I never explicitly used that information when working on this problem.
So people were only able to use any type of protection for a given province once. (Like, no extra grain shipments?)