This is an entry in the 'Dungeons & Data Science' series, a set of puzzles where players are given a dataset to analyze and an objective to pursue using information from that dataset.
The omens are troubling for we Romans this year! Black doves have been spotted circling above major cities in all three of the Empire's main provinces. Not only that, news from abroad confirms that they have been seen across the world, from the wastes of Britannia in the West to the lush shores of Persia in the East.
There is confident general agreement that the black doves are a Very Bad Omen. No two people quite agree on why, though. Some say that they are emissaries of Pluto, sent out to escort the souls of the dead, and that their coming means Pluto must expect many to die. Others say that the birds have foreseen Jupiter's displeasure, and are taking flight to escape it. Captive philosophers from the Grecian territories say something about how they are the shadows on the walls of a cave cast from the true forms outside - but since the philosophers also say that we are all trapped in a cave at all times, no-one really takes them seriously.
You are a diviner in Rome. Your unconventional data-driven approach to divination has not endeared you to the broader divination community, so business has been quite scarce. However, two weeks ago, the main College of Divination in Rome was struck by lightning and burned down. Few of the staff were actually harmed, but the broad view is that anyone who built their college somewhere it would get struck by lightning clearly isn't a very good diviner. As such, when the recent ill omens arose, the Emperor approached you (as the best-known non-College diviner) to ask for advice on how best to weather this situation. This could be your big break, and your chance to demonstrate the superiority of your school of Data-Driven Divination!
The Emperor has given you the dataset gathered by years of Imperial diviners, which tracks the Omens that were recorded and the Disasters that happened in each year.
The good news is that this dataset is extremely extensive (reaching back to the founding of the Imperial system of Divination, which they mark as Year 0 in their system) and comprehensive (Imperial surveyors gather an annual update on every interesting omen and disaster that happened in the past year, even in foreign countries).
The bad news is that, rather than tracking the things your study of Data-Driven Divination has led you to think might be useful predictors (such as the total population of each region, or the value of goods and services produced therein), it tracks the things the existing diviners think are useful predictors, such as whether children have been born with an unusual number of heads. You're...not actually sure these are good predictors of disaster? Still, they're what you've got, so you might as well work with them.
If you can do well, and impress the Emperor, you think you can convince him to adopt your school of Data-Driven Divination across the Empire, and usher in a new era of data-driven prosperity!
If you do badly...yeah, he'll probably have you executed. So. Uh. No pressure.
DATA & OBJECTIVES
The Emperor has allocated a budget of 60,000 denarii to mitigation efforts for the upcoming year (Year 1081) across the three provinces of the Roman Empire (Hispania, Italia and Grecia). His administrators have devised the following strategies:
- For 5,000 denarii, the priests in any one province can conduct a ritual entreating Vulcan to hold the Titans firmly in their prison beneath the earth. This will reduce the risk of earthquakes in that province by 80% this year.
- For 10,000 denarii, the priests in any one province can entreat the protection of Asclepius to ward off plague. This will prevent all plague in that province this year.
- For 10,000 denarii, the Emperor can invest in a fire protection service in any one province. This will reduce the risk of fires in that province by 70% this year.
- For 10,000 denarii, grain shipments can be made to any one province. This will prevent all famines in that province this year.
- For 10,000 denarii, the soldiers on our border with any one adversary (Britannia, Germania or Persia) can be reinforced. This will halve the chance that we are pillaged by them this year.
- For a further 5,000 denarii (15,000 in total), the soldiers can also be equipped and encouraged to attack that adversary. This will double the chance that we pillage them this year (along with reducing the chance that they pillage us).
He's given you a dataset of historical omens and disasters, and asked your advice on which options to take. You've asked about what exactly your goals should be, and got the following answer:
- Minimize the total number of disasters that take place in the Empire in the upcoming year (year 1081).
- The dataset lists all omens and disasters that have happened in prior years, from Year 0 to Year 1080. The people and the Emperor believe that 'black doves this year' implies 'many disasters incoming', but you're welcome to use the dataset however you wish.
- All disasters are equally bad: three fires and one outbreak of plague, or two famines and two pillagings, both count the same, as '4 total disasters'.
- Successfully pillaging an enemy nation is exactly as good as a disaster is bad - it counts as -1 disasters to your score.
- You can be completely confident that the interventions function as advertised - your goal is simply to figure out which interventions provide optimal protection.
- You can buy an intervention multiple times pointed at different provinces/adversaries: for instance, you could spend 15,000 denarii for earthquake protection in all three provinces.
- You cannot buy the same intervention twice for the same province/adversary: for instance, you cannot spend 20,000 denarii for twice as much fire protection in one province.
- Note that you do not have access to 'what omens happen in 1081' to predict 'what disasters happen in 1081'. By the time the Imperial surveyors have gathered that information, 1081 will be over and the disasters will have already happened. You will need to use omens from previous years (1080 and earlier) to predict what disasters will happen in 1081.
Based on the dataset, you need to advise the Emperor on how to spend his 60,000 denarii of budget.
I'll aim to post the ruleset and results on May 16th (giving one week and both weekends for players). If you find yourself wanting extra time, comment below and I can push this deadline back.
As usual, working together is allowed, but for the sake of anyone who wants to work alone, please spoiler parts of your answers (type a '>' followed by a '!' at the start of a line to open a spoiler block) that contain information or questions about the dataset.
Thank you to abstractapplic, who reviewed a draft of this scenario. (For the avoidance of doubt, abstractapplic does not have inside information on the scenario, and is free to play it).
Thanks for setting up the problem aphyer.
Some observations on plague:
The 9 provinces in the dataset have the following adjacency graph:
8 of the 9 provinces are arranged in a loop:
Britannia <-> Hispania <-> Italia <-> Grecia <-> Anatolia <-> Parthia <-> Scythia <-> Scandinavia <-> Britannia
The last province, Germania, is adjacent to Italia and Scandinavia.
Plague occurs in epidemics of one or more instances of plague. The epidemic usually originates in a single province, but sometimes in multiple. Each year, any provinces adjacent to a province with plague in the previous year have a fairly high chance of getting plague. A province is immune to plague in the 5 years following an instance of plague.
In some cases, a province that is not adjacent (according to my graph described above) to a province that has plague gets plague during an epidemic. This is sufficiently rare that I am assuming that this is due to independent originations rather than due to additional connections on the graph. I can't tell from the dataset if there is any separate rule (beyond the 5 year immunity rule) preventing a province from receiving plague twice from the same origination. There is an apparent case of this in the dataset, but that is sufficiently rare that it could be due to an independent origination that happened to occur adjacent to a plague province.
Plague seems to have some association with Earthquakes and Black Doves (todo: investigate this).
In the previous year, a Plague started in Anatolia. This makes plague protection in the adjacent province of Grecia look prudent this year.
There were also Earthquakes in Britannia, Italia and Parthia, as well as the black doves (everywhere except Germania) as mentioned in the problem description. Todo: investigate if this makes independent plague originations look likely enough to get plague protection for other provinces than Grecia. On average given base rates, plague prevention is not particularly cost effective.
Miscellaneous other observations:
Pillaging follows the same adjacency graph as plague (pillaging a target empire pillages the province of the target that the pillaging empire is adjacent to, which is always unique). All empire pairs except Britain/Persia can pillage each other.
Pillaging an empire (afflicting target province, from "jump-off" province in pillaging empire adjacent to target province) seems to be associated with:
A two headed baby is also associated with fire in the same province the next year (todo - untangle which aspects of this triangle are primary)
Wolves howling at the sun is also associated with fire in the next year in the same province.
Note, Anatolia was pillaged by Romans last year. So, there may be an increased chance of fire in Grecia this year.
Famine is associated with Earthquake or Fire in the previous year. There was no disaster however before the Famine in Italia which occurred last year. There was an earthquake in Italia last year, making famine relief there potentially more attractive.
Geese Flying Backwards is associated with increased chance of Famine in the same province in the next year. (Note: this was observed last year in Hispania).
So, initially at least, Famine relief in Italia and Hispania and Fire protection in Grecia look like possible choices, along with plague prevention in Grecia.
30000 on grain shipments. Red moons, backwards geese and new constellations all aren't good signs for food production and with tons of doves and this being the highest-ev thing to do in a vacuum anyway it seems good enough, even though Italy's just had a famine.
10000 on the protection of Asclepius for Grecia. Stopping the spread >> preventing the outbreak
20000 on fire protection in Grecia and Hispania. Italia's new constellations should help with fires over there.
Defenses against pillaging are nice, but 50% doesn't seem enough to get the ev there higher than any of the others unless there are some major indications.
The title says 'nine black doves', but the dataset says Germania (and only Germania) had no black dove sightings in 1080. Was this intentional?
The dataset you've received is what was reported.
The most common disasters are Fires, Famines, and Pillage. All else being equal, interventions targeting these will have the best ROI.
Earthquakes have a bimodal distribution. They are more common in Italia than in Grecia or Hispania, but rare overall compared to other disasters.
Plague in one province can spread to adjacent provinces next year, but never hits the same province in successive years.
Pillaging your neighbor increases your Fire risk for the next year.
Fire, Earthquake, or being Pillaged increases the next year's risk of Famine.
Plague completely eliminates the next year's risk of Famine.
Earthquakes predict future Earthquakes, especially in the same Province.
Fire rarely occurs following Fire or Earthquake in the same Province.
Persians never Pillage Grecia following a Plague year in Anatolia or Scythia, so Grecia is safe this year.
Plague in Anatolia last year could spread to Grecia this year.
Multiple Black Doves last year also predict Plague in Grecia this year.
Multiple Black Doves last year predict Famine in both Italia and Hispania this year.
Geese Flying Backward in Hispania last year also predicts Famine in Hispania this year.
Fire + Earthquake in Italia last year also predicts Famine in Italia this year.
Roman Pillage in Anatolia last year predicts Fire in Grecia this year.
(10k) Protection of Asclepius for Grecia
(10k) Fire protection service for Grecia
(10k) Grain shipments to Hispania
(10k) Grain shipments to Italia
(10k) Reinforce Hispania against the Britons
(10k) Reinforce Italia against the Germans
Why is it called Nine Black Doves if there were black doves in only eight of the nine
realmsprovinces last year?
Some omens/disasters are clearly correlated with what happens next year, though I couldn't find anything that stood out and made a given disaster nearly certain to happen this year. Some of the signs were also contradictory. I couldn't find any additional clear cut pattern by looking at previous years, though given that several disasters come in clumps I wouldn't be surprised if there was something to learn by looking for correlations > 1 year in the past. I suspect a complicated algorithm could need to be used to pull everything together to produce a highly accurate prediction, however my relatively simple analysis suggests that the following may not be too bad:
Interventions I am very confident are optimal:
- Italia Famine Relief(10000Dn)
- Grecia Plague Prevention(10000Dn)
Interventions that look reasonably likely to be optimal:
- Hispania Famine relief(10000Dn)
- Italia Plague Prevention(10000Dn)
Interventions that look moderately useful, but I suspect aren't optimal:
- Grecia Fire Prevention(10000Dn)
- Hsipania Fire Prevention (10000Dn)
I hope to do more digging and build off other people's comments later in the week, but my preliminary/solo answer would be:
Grainhoard and plagueproof in all three provinces.
On the basis that:
Doves in the previous year strongly predict global plague and weakly predict local famine; also, a crude "ignore every predictor, just look at average output of response variables lol" approach suggests that stockpiling grain is the highest-EV intervention.
However . . .
I haven't been able to figure out how pillaging works at all, and I really doubt it's as random/irrelevant as it seems at first glance. I guess I'll have to rely on my neighbours being too sick to bother attacking.
Insane, unendorsed bonus plan:
Spend most of the money on earthquakeproofing all nine provinces (including the six we don't own), to greatly decrease the probability of black dove sightings (doves and quakes correlate super hard for some reason), so they can't predict plagues, so no plagues happen.
In addition to this being inherently ridiculous, it's rendered extra-implausible by the fact that:
Doves seem to have been getting slightly more common over time, but plagues (and for that matter every other omen and disaster) haven't, suggesting that causality doesn't work that way.
There's something going on with Blood Moons in Britannia. Plotting the cumulative occurrence of "Moon Turns Red" in Britannia yields a weird graph with periods of frequent occurrence alternating with periods of zero occurrence. This seems to correlate with Britannia's pillaging patterns, which show a similar alternation of activity and quiet.
Without looking at the dataset, then:
What if you tell the emperor 'Nine Black Doves means the enemies of the empire and amassing. They will attack in nine years*, and if this war is lost, the empire will fall.' ?
*Or 3 neighboring nations will ally and attack in 3 years.
In nine years the emperor might die...or the horse might die...or I might die. Or the horse might talk!