# D&D.Sci: The Mad Tyrant's Pet Turtles

*This is a D&D.Sci scenario: a puzzle where players are given a dataset to analyze and an objective to pursue using information from that dataset.*

You steel your nerves as the Mad Tyrant[^gaqkcxaqkic] peers at you from his throne. In theory, you have nothing to worry about: since the Ninety Degree Revolution last year, His Malevolence[^5hq84btw9ju] has had his power sharply curtailed, and his bizarre and capricious behavior has shifted from homicidally vicious to merely annoying. So while everyone agrees he’s still getting the hang of this whole “Constitutional Despotism”[^9t60rb2php] thing, and while he *did* drag you before him in irons when he heard a Data Scientist was traveling through his territory, you’re still *reasonably* confident you’ll be leaving with all your limbs attached (*probably* even to the same parts of your torso).

Your voice wavering only slightly, you politely inquire as to why you were summoned.

He tells you that he needs help with a scientific problem: he’s recently acquired several pet turtles (by picking at random from a nearby magic swamp), and wants to know how heavy each of them is, *without* putting his Precious Beasts[^8ohgeggjdsk] to the trouble of weighing them. To encourage you to bring your best, he will be penalizing you 10gp for each pound you overestimate by-

(An advisor with robes like noontime in summer rushes to the Tyrant’s side and whispers something urgent in his ear before scuttling away.)

-which will be deducted from the 2000gp stipend he will *of course* be awarding you for undertaking this task, because compelling unpaid labor from foreign nationals is no longer the done thing.

(The bright-robed advisor visibly sighs in relief.)

*However*, he snarls with a sudden ferocity, if you *dare* to insult his turtles by *under*estimating their weight, he will have you executed-

(An advisor with robes like the space between stars rushes to the Tyrant’s other side and whispers something urgent in his other ear before scuttling away.)

-that is, he’ll have you maimed-

(The Tyrant looks briefly to the dark-robed advisor, who shakes their head sadly.)

-lightly tortured-

(Another sad head-shake.)

-he’ll deduct 80gp-

(An encouraging gesture.)

-for *each* pound you underestimate by-

(An approving nod.)

-and he’ll *also* commission an unflattering portrait of you to hang in his throne room.

(The dark-robed advisor gives the Tyrant a big smile and two thumbs up.)

The meeting apparently having been concluded to his satisfaction, the guards see you out. Some time, some help, some adverse reactions to ambient magic[^t5ses6i1jd], and several waterlogged sets of clothes later, you have [a dataset](https://raw.githubusercontent.com/H-B-P/d-and-d-sci-Turtles/main/data.csv) representing a random sample[^rup6mbnbitp] of the other turtles in that swamp. You also convince some palace officials to give [reliable testimony](https://raw.githubusercontent.com/H-B-P/d-and-d-sci-Turtles/main/pets.csv) on some characteristics of the Tyrant’s pets, though no-one is willing to provide any actual measurements[^ziqgakjjdml].

What numbers will you give the Tyrant?

* * *

I’ll post an interactive you can use to test your choices, along with an explanation of how I generated the dataset, sometime on ~~Monday 8th April~~ Tuesday 9th April or Wednesday 10th April. I’m giving you nine days, but the task shouldn’t take more than an evening or two; use Excel, R, Python, Tiger Instincts, or whatever other tools you think are appropriate. Let me know in the comments if you have any questions about the scenario.

If you want to investigate collaboratively and/or call your choices in advance, feel free to do so in the comments; however, please use [spoiler blocks](https://www.lesswrong.com/tag/guide-to-the-lesswrong-editor#Spoiler_blocks) or [rot13](https://rot13.com/) when sharing inferences/strategies/decisions, so people intending to fly solo can look for clarifications without being spoiled.

* * *

### Notes:

*   You may assume that you are wealthy and courageous enough to prioritize maximizing Expected Value, though the value you assign to providing honest estimates and to the possibility of being unflatteringly depicted is entirely up to you.)
*   To provide an example of the scoring function: if you predict 10.1lb for a turtle which is actually 11.3lb, you'll be penalized 96gp; if you predict 13.7lb for that same turtle, you'll be penalized 24gp.

[^gaqkcxaqkic]: You checked, that’s his actual job title. 

[^5hq84btw9ju]: You checked, that’s his actual preferred term of address. 

[^9t60rb2php]: You checked, that’s the actual name of their new system of government: between this and the fact they’re voluntarily keeping him on the throne, you’re beginning to suspect this population deserves their ruler. 

[^8ohgeggjdsk]: You can hear him enunciate the capital letters. 

[^t5ses6i1jd]: There’s so much thaumatic interference in the swamp, you wouldn’t be surprised if these creatures’ biology was completely uncorrelated with that of ordinary turtles. 

[^rup6mbnbitp]: Of course, you made sure to mark each turtle, to avoid counting it twice. 

[^ziqgakjjdml]: While gathering this information, you ask some courtiers how the Tyrant could determine the accuracy of your estimates. They reply that the Tyrant will simply weigh his turtles: while His Malevolence is too honorable to subject his turtles to measurement merely for the sake of satisfying his curiosity, he will absolutely do it in order to determine whether a suspicious outsider is impugning his pets. They don’t seem to see anything amiss with this logic; your suspicion that they deserve their ruler swiftly matures into a conviction.