# D&D.Sci May 2021 Evaluation and Ruleset

This is a followup to [the D&D.Sci post](https://www.lesswrong.com/posts/afcBzhBmmiL6ba5vm/d-and-d-sci-may-2021-monster-carcass-auction) I made last week; if you haven’t already read it, you should do so now before spoiling yourself.

[Here](https://h-b-p.github.io/d-and-d-sci-may/) is the web interactive I built to let you evaluate your solution; below is an explanation of the rules used to generate the dataset. You’ll probably want to test your answer before reading any further.

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Ruleset
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(Note: to make writing this easier, I’m using standard D&D dice notation, in which “4d8+3” means “roll four eight-sided dice, sum the results, then add three”.)

Species
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The carcasses brought back by adventurers are 2/13 Yetis, 5/13 Snow Serpents, and 6/13 Winter Wolves.

Days Since Death
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The days since each creature’s death is modelled by rolling two d12s, taking the lowest result, and subtracting 1.

(For the rest of this post, let “\[DSD\]” stand in for “Days Since Death”.)

Butchery
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Carver takes a “collect anything the local alchemists might pay for, then carve out all the technically-edible meat you can still access” approach to her vocation.

The amount Carver gains from a Yeti carcass is given by 72+1d6-\[DSD\]d6, the amount from a Snow Serpent is 20+2d6 (she can’t prepare snakemeat, so all the profit comes from non-degrading components like scales and fangs; ergo, no time effects), and the amount from a Winter Wolf is 25-2*\[DSD\]+4d6.

Bidders
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There are three bidders at a given auction: Alistair, Betty, and - except for today's auction, where you take her place - your employer Carver.

### Carver the Butcher

Carver bids 32-2*\[DSD\]+2d20 on Yeti carcasses, 7+2d10 on Snow Serpent carcasses, and 31-3*\[DSD\]+2d8 on Winter Wolf carcasses.

### Alistair the Butcher

Alistair has a different business model to Carver, focusing on extracting the highest quality cuts and selling them to rich clients; as such, his utility sharply decreases with time since death.

He is very predictable, bidding 55-6*\[DSD\] for Yetis, 60-20*\[DSD\] for Snow Serpents, and 50-12*\[DSD\] for Winter Wolves.

### Betty the Necromancer

Betty doesn’t care how long something’s been dead, so long as no-one’s interfered with the body.

She bids 29+1d6 on Yetis, 9+1d8 on Snow Serpents, and 19+1d4 on Winter Wolves.

Strategy
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The relevant factors are summarized in these graphs.

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/5f2b2bcd13bac6f280416e28f1a64141ce7915fbc575efd3.png)

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/62e043df74fa0fe6fbe1825015cc7242f6bd8f8df0e64cbe.png)

![](https://39669.cdn.cke-cs.com/rQvD3VnunXZu34m86e5f/images/b638d8b570151fd90ca1394476455cc57f720c5e68a334e9.png)

In almost all cases where rivals aren’t making bids greater than the Expected Value of the lot to Carver, the EV-maximizing choice is to bid the lowest amount that would guarantee winning the lot. The one exception is with lot #11, where it’s possible to eke out a tiny amount of extra EV by bidding 21 or 22 silver pieces.

Reflections
===========

I aimed to make this entry as straightforward and approachable as I could. From the, uh, *comprehensiveness* with which it was solved, I think it’s fair to say I succeeded. Congratulations to simon and GuySrinivasan for reaching perfect answers; and then, between them, managing to deduce my entire generation process.

The main problem with this scenario from my point of view is that I once again ended up making a puzzle when I was aiming for a challenge. It’s premised on some Weird Crap (distorting effects of selection bias, auctions against rival agents) but the fact it needs a ‘proper’ solution obligates the Weird Crap to impose itself with a reliability it would never possess in real life (Carver acts implausibly randomly to limit the effect of selection bias, opposing bidders are wind-up toys who don’t know anything you don’t), and so players develop abilities optimized for synthetic problems.

I’m mad about this, but only a little. While my game failed to live up to my standards of quote-unquote-'realism', it succeeded at its primary objectives: being playable, giving players an excuse to practice technical skills, and setting things up for the Bonus Round (which I’m pleased to report is *absolutely* not a puzzle).

Scheduling
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Oh yeah, there’s a Bonus Round. It’s all written up and ready, but I’m delaying it slightly so I can have it both be a week long and end on a weekend; I plan to run it starting next Monday and conclude it the Monday after, unless I get hit by a truck or someone in the comments gives me a reason to use a different time window. Watch this space.