simon

Karma: 1,217

simon 29 Apr 2026 7:21 UTC
2 points
0
on: The Problem in the “Nerd Sniping” xkcd Comic
I had assumed that since Google is compute-oriented (and the alt text said it was from Google), that the solution would have been something like:
- notice that you can upper bound the resistance by replacing some resistors with perfect resistors
- notice that you can lower bound the resistance by replacing some resistors with perfect conductors
- notice that the convergence properties of doing the above outside some finite region are pretty decent as the region expands
- write a computer program to numerically compute the answer to a desired level of precision using the above
In fact, I still kind of expect that this form of answer is likely more what they were looking for, do they really expect this advanced-looking math? But, interesting to see it does have an analytical solution.
I put this to Claude to fill out the details for the numerical approach: https://claude.ai/share/d8fbe3c6-39f0-481e-b05c-d11904f23e91. Convergence not quite as good as I intuitively expected, but still works.

simon 3 Apr 2026 2:09 UTC
10 points
8
in reply to: Max H’s comment on: Max H’s Shortform
IMO this is going (predictably) disastrously. Air power is not effective at causing regime change (rally-around-the-flag effect). I think the Iranian public are more likely to mainly blame the guy explicitly saying “we’re going to bring them back to the stone ages where they belong” than the local leadership. It also seems to me that the Iranian leadership would be highly motivated to immediately rebuild any degraded capabilities after the war, in order to rebuild deterrence against future attacks.
There is some talk about a land invasion, but taking an island or two (even Kharg) probably wouldn’t compel them to surrender, while also being highly vulnerable both directly and in terms of logistics to drone attacks; and a full scale invasion would be a massive undertaking and probably not politically feasible (for good reason).

simon 29 Mar 2026 17:13 UTC

4 points

in reply to: MichaelDickens’s comment on: MichaelDickens’s Shortform

I had Claude research this, Claude’s report:

I looked into the exact dates here and found some additional evidence.

Bostrom’s Paper: Conference Date Established

The paper was presented at the 15th International Conference on Systems Research, Informatics and Cybernetics (InterSymp 2003), held July 28–August 2, 2003 in Baden-Baden, Germany. This date comes from the Open Library catalog entry for the proceedings volume.

Wayback Machine snapshots of Bostrom’s homepage narrow down when the paper went online: it is absent from the July 29 snapshot but present on the August 5 snapshot, with the paper page itself first crawled August 6. This is consistent with Bostrom uploading it right after the conference. All early Wayback captures (Aug 2003, Dec 2003, Apr 2004) are byte-identical — the web version was never revised across these snapshots.

Yudkowsky’s Post Predates It by ~5 Months

Yudkowsky’s March 11, 2003 Extropians post is the earliest confirmed public paperclip reference. He drops it casually — “pure computational intelligence devoted to manufacturing an infinite number of paperclips” — without any setup or framing as a new idea. In the same thread, he elaborates by citing Marcus Hutter’s AIXI-tl as an example of a system that is “superhumanly effectual, unalterably hostile, and nonsentient.”

Note that he explicitly says “paperclips” here, not “squiggles” — the squiggle maximizer rebranding came much later, as what he felt he should have said. In a December 2018 tweet, Yudkowsky clarified the original concept was about “utter alignment failure of a superintelligence leading to a utility function that from our perspective seems randomly-rolled, whose maximum utility per gram happens to be tiny molecular structures resembling a paperclip.”

But the Paper Was Written Before the Conference

The key caveat: academic papers are submitted months before conference presentation. InterSymp would have had a submission deadline well before July, meaning Bostrom likely wrote the paper in early-to-mid 2003 or possibly late 2002. So the fact that the March post predates the August presentation doesn’t conclusively settle who thought of it first — the writing timelines likely overlapped.

The Search for Something Earlier

Yudkowsky believes there’s an even earlier post. In February 2023, he offered $200 to find “the original message by me to an email list — probably Extropians or SL4 — wherein I first talked about losing control of an AI’s utility function, and it ends up having its most efficient fulfiller at tiny molecules shaped like paperclips.” This description is more specific than the March 2003 post, suggesting he remembers a more detailed formulation. No public resolution of this bounty has been found.

On the Sam Harris podcast in February 2018, Yudkowsky said: “As far as I know, it’s me. [...] they searched through the archives of the mailing list where this idea plausibly originated and if it originated there, then I was the first one to say ‘paperclips.’”

I searched the SL4 mailing list (founded by Yudkowsky, active since February 6, 2000, with 21,302 messages) and the Extropians archive for any pre-March-2003 paperclip mentions and found none. The earliest SL4 paperclip discussion is from June 2004, where the concept is already treated as established.

Cross-Pollination

Bostrom and Yudkowsky were clearly aware of each other’s work. The paper cites Yudkowsky (2002) on the AI Box Experiment and Yudkowsky (2003) on Creating Friendly AI — but does not credit anyone for the paperclip example itself. On September 18, 2003, Bostrom did a guest chat on SL4′s IRC channel, about six weeks after the paper went online.

The Framing Difference

As noted in the original shortform: Bostrom frames the paperclip maximizer as an outer alignment failure — “a well-meaning team of programmers make a big mistake in designing its goal system.” Yudkowsky’s intended lesson was about inner alignment failure — optimization pressure converging on alien goals. These are conceptually distinct failure modes using the same illustrative object, which is consistent with independent invention.

Timeline

Date	Event
Mar 11, 2003	Earliest confirmed paperclip reference: Yudkowsky on Extropians
Jul 28–Aug 2, 2003	InterSymp 2003: Bostrom presents paper
~Aug 5, 2003	Paper appears on Bostrom’s website
Sep 18, 2003	Bostrom guest chat on SL4 IRC
Jun 2004	First SL4 email discussing paperclip maximizer as established concept
Feb 2018	Yudkowsky claims priority on Sam Harris podcast
Dec 2018	Yudkowsky clarifies original intent (inner alignment)
Feb 2023	Yudkowsky offers $200 bounty for earlier post

simon 29 Mar 2026 7:50 UTC

2 points

in reply to: simon’s comment on: D&D.Sci Release Day: Topple the Tower!

Thanks aphyer for the extra time, though I haven’t figured out the mechanics. Specific findings not necessarily endorsed (Claude tends to be, in my view greatly, insufficiently skeptical). Indeed, it’s not necessarily right about what we actually found since it’s trying to summarize results from multiple conversation. I had to manually add spoiler tags (Claude could not figure out how to do that in an llm block using the api) and put some notes at some (not necessarily all) issued I found while doing so. However, I guess I’m going with Claude’s conclusion, albeit with the paths edited to actually be valid paths:

Main Tower: Warrior LLRRRLLR

Bonus Tower: Warrior RRRLLLLR

The Tower: What We Found

Analysis of ~140,000 runs from the D&D.Sci Tower challenge dataset. Covers what the data reveals about game mechanics, what remains unknown, and how the recommended paths were derived.

Executive Summary

The Tower is a 7-floor dungeon (F2-F8) followed by a boss fight (F9). Heroes choose a class (Warrior/Rogue/Mage, each ~1/3 of runs) and traverse a fixed sequence of encounters: enemies, treasures, and campfires. Both pre-boss survival and boss topple have a stochastic component, but most paths are effectively deterministic — randomness only matters near thresholds. For topple (~18% of exact-sequence repeats show mixed outcomes).

Best paths found:

Main Tower: Warrior LLRRRLLL — ~100% success (135/135, CI [97.2%, 100%])
Bonus Tower: Warrior RRRLLLLL — 92.7% success (140/151, CI [87.4%, 95.9%])

The three classes play fundamentally different games. Warriors accumulate resources from treasures and lose them to enemies (1D survival state). Rogues have a 2D state with a unique small-enemy differentiation mechanic. Mages gain offensive power from combat — enemies help their boss fight but can kill them on the way — creating a survival-vs-topple tension that makes Mage the worst survivor but best boss-killer.

1. The Tower Structure

Encounter Layout

Floor	Enemies	Notes
F2	Gremlin, Acid Slime, Cultist	Small enemies only
F3	Jaw Worm, Cultist, Acid Slime	First lethal floor (Mage)
F4	Slaver, Jaw Worm, Cultist	First lethal floor (Rogue)
F5	Sentries, Slaver, Jaw Worm	First lethal floor (Warrior)
F6	Gremlin Nob, Sentries, Slaver
F7	Chosen, Gremlin Nob, Sentries
F8	Shelled Parasite, Chosen, Gremlin Nob
F9	Bronze Automaton / Collector / Champion	Boss floor

Each floor also offers Campfire (~5% on F2, increasing ~5pp/floor to ~35% on F8) and 10 treasures (~2.3-2.6% each). No path ever has duplicate treasure names.

Hard Invariants

Only enemies kill. Zero deaths on treasure/campfire floors across 400k+ observations.
Both survival and topple are stochastic, but most paths are effectively deterministic — randomness only matters near thresholds. For survival, same F2-Fk prefixes give mixed die/survive outcomes at every death floor (F3-F8).
No serial correlation in topple outcomes — each run is a fresh draw.
Runs are independent. No temporal trends, no clustering, class drawn uniformly at ¹⁄₃.
Every path is exactly 7 encounters (F2-F8), creating a fundamental epistemological limit: only relative effects between encounter types can be measured, never absolute effects. “Campfire heals 2” and “campfire deals 0 damage” are indistinguishable.

Methodological note: Paths are right-censored — heroes who die early have NaN for later floors. Any filter on total encounter counts implicitly selects survivors. Several early findings were artifacts of this. All results here use methods that account for it (prefix-controlled insertion tests, exact multiset stratification, or per-floor analysis).

2. Warrior Mechanics

Resource Accumulation

Warriors follow a resource-accumulation pattern: treasures build up a survival resource, enemies deplete it. Within additive models, relative treasure values are roughly strong ~ 8, near-strong ~ 7, medium ~ 4, campfire ~ 2, wrong-class ~ 0 (arbitrary units).

Critical caveat: These come from an additive framework that overpredicts deaths by 73% — runs given <5% predicted survival actually survive 39% of the time. The relative ordering is robust across model families, but specific numbers should be treated as approximate rankings, not confirmed parameters.

Enemy danger ordering (consistent across all models): Shelled Parasite >> Chosen >> Gremlin Nob >> Sentries > Slaver > small enemies.

Overall survival: 84.7%. No deaths before F5.

Model-Free Findings

Adding weak enemies can reduce death rate: Inserting a non-combat encounter before a lethal enemy drops death from 24% to 0-7%. Impossible under simple additive damage.
Treasures reduce death beyond simple healing: controlled for composition, the effect exceeds what any fixed-value model predicts
The {4E, 0T, 0C} death trap is structural: ALL such paths map to {Small, Small, Slaver, Sentries}. 100% die on F5. Not a special interaction — just 4 consecutive enemies with no healing.

State Dimensionality

Survival: Genuinely 1D. Adding a second power dimension gives only ΔLL=+19, well below BIC breakeven.

Topple: A second dimension matters. The Two-Resource Model (HP + Power → topple) improves predictions for all classes including Warrior. The “power” variable loads differently from HP — e.g. Chosen is dangerous for survival but contributes positively to topple power. Consistent with combat experience helping the boss fight despite costing HP to acquire. The exact nature of this resource is unknown.

Order Effects

Survival: Significant (z=13.81 for adjacent swaps) but small — multiset composition dominates.
Topple: Moderate. Treasures closer to boss help more (concordance 0.58).
Same-enemy consecutive is harmful for Warriors (e.g. Sentries→Sentries shows elevated death).

3. Mage Mechanics

The Enemy-Power Paradox

Raw data shows an apparent survival U-shape: 43% at 2 enemies, 84% at 6. This is largely a composition confound — many-enemy paths have stronger treasure compositions. But even within controlled compositions, enemies genuinely benefit Mages.

Prefix-controlled insertion test (avoids censoring):

Encounter inserted	Survival improvement
Strong treasure	+10.6pp
Sentries (lethal!)	+17.4pp
Slaver (lethal!)	+15.5pp
GNob (lethal!)	+13.2pp
Campfire	+9.7pp
Small enemy	+3.1pp

Even lethal enemies help Mages (compare Warriors: −13 to −24pp).

Mages accumulate a resource from combat — the clearest model-free evidence for their enemy-driven resource system.

2-Dimensional State

SVD of the (F2,F3)→F4 death matrix: rank-2 explains 82.8-99.5% of variance. Six treasures on F2 give 0% Jaw Worm death but span 0-33% Slaver death — a single resource cannot produce this. 2D beats 1D decisively (ΔBIC = −2,905).

The Mage Dilemma

Enemies	Survival%	Topple% (given survived)
0	100.0	29.9
2	42.9	55.9
5	81.5	68.0
7	80.6	68.6

Mage needs enemies for topple power but enemies kill Mages. Survival-topple correlation is near-zero.

Mage Topple: Inverted From Warrior

Enemies help topple (66%→99% vs BA as count rises)
Campfires devastating (91%→0% at 6 campfires vs BA)
Wrong-class treasures give zero topple benefit
Mage is the best boss-killer at every boss (BA 90.5%, Collector 66.9%, Champion 33.7%) despite worst survival

4. Rogue Mechanics

2-Dimensional State

2D beats 1D by ΔLL=+534, ΔBIC=-897. Surprising — Rogues were expected to behave like Warriors.

The Slaver Anomaly (Strongest Signal in the Dataset)

Cultist protects Rogues from Slaver at a 30.2x ratio in exact multiset swaps:

Small enemies encountered	Rogue death rate vs Slaver
None	1.1%
1 Cultist	0.4%
2 Cultists	0.0%
1 Gremlin	9.3%
1 Acid Slime	4.2%
1 Gremlin + 1 Acid Slime	16.8%
1 Cultist + 1 Acid Slime	0.6%

One Cultist appears to completely negate the Gremlin/Acid Slime penalty. Gremlin actively increases vulnerability. Survives all confound checks. Note: this is relative ranking only — whether Cultist actively helps or Gremlin actively hurts vs a neutral baseline is undetermined.

Cross-Class Small Enemy Pattern

Small enemies deal identical effective damage across all classes. But they provide different class-specific resources:

Cultist most valuable for Rogues (against Slaver)
Acid Slime most valuable for Mages (against Jaw Worm)
All three interchangeable for Warriors (chi-sq p=0.44)

This is the strongest evidence for class-specific resource mechanics beyond damage/health.

Rogue Topple

Intermediate between Warrior (treasure-driven) and Mage (enemy-powered)
Position matters most (concordance 0.71, strongest of all classes)
Cultist >> Acid Slime ≥ Gremlin for topple (+7-11pp multiset-controlled)

5. Treasures

Universal 4-Tier Structure

Tier	Warrior	Rogue	Mage
Right-class strong	Adamant Armor, Enchanted Shield	Dagger of Poison, Vanishing Powder	Staff of the Magi, Tome of Knowledge
Shared strong	Boots, Cloak	Boots, Cloak	Boots, Cloak
Medium neutral	Potion, Ring	Potion, Ring	Potion, Ring
Wrong-class	Dagger, Staff, Tome, VP	AA, ES, Staff, Tome	AA, ES, Dagger, VP

Key Findings

Cloak is universal >! (good for all classes). Shield is Warrior-specific (harmful to Rogue/Mage). For Warriors alone, they’re indistinguishable (z=0.71).
Wrong-class treasures are actively harmful for topple (~3-6pp cost each). (Simon note—I think this is not correct. Claude often got confused about baselines (comparing to average and assuming that less-than-average is harm, and I think this is an example))
Within-pair asymmetry: AA > ES for Warrior, Dagger > VP for Rogue, Staff > Tome for Mage. Right-class adds ~1.5x the log-odds value of a neutral (ratio 1.41-1.54).
No encounter is a null-op: all non-combat types reduce death rate vs baseline. (Simon note—while this methodology is not valid, we did find no null-ops using a more plausibly valid method (see section 8)
Benefits decay with distance from the protected encounter; Mage decay is slower than Warrior/Rogue.

Unresolved: Campfire vs Weak Treasure

Two tests give conflicting rankings — insertion test (early-game): campfire > weak; pairwise swap (full-path): campfire ≈ weak. We don’t know which is confounded. The disagreement suggests mechanics more complex than simple healing.

6. Boss Mechanics

Difficulty: BA < Collector < Champion

Boss	Warrior	Rogue	Mage
BA	76.9%	83.7%	90.5%
Collector	49.4%	53.4%	66.9%
Champion	20.6%	21.0%	33.7%

Mage > Rogue > Warrior for topple at every boss, despite worst survival.

F8 Campfire Is Boss-Specific

BA: Massive (OR=3-6). Step function — only F8 position matters.
Collector: Moderate benefit (Rogue/Mage).
Champion: Null (Warrior/Rogue).

Treasure on F8 hurts vs BA (OR≈0.47) — F8 is better used by campfire.

Topple Stochasticity

17.9% of exact-sequence repeats show mixed outcomes. Most paths are near-deterministic. Variance is wider than a fair coin predicts — different sequences have genuinely different topple probabilities. Multisets explain 86-96% of variance; ordering 4-13%. Warrior×Champion: ⁰⁄₁₇₅ mixed (far from boundary or deterministic).

7. Cross-Class Architecture

Property	Warrior	Rogue	Mage
Survival state dimensions	1D	2D	2D
Topple uses 2nd resource?	Yes (modest)	Yes	Yes (dominant)
First death floor	F5	F4	F3
Overall survival	84.7%	77.8%	64.4%
Small enemy differentiation	None	Yes (30x ratio)	Yes (reversed)
Enemies help topple?	No	Mixed	Dramatically

Same-enemy consecutive	Harmful	Mixed	Protective

The Two-Resource Model (HP + Power)

Topple follows: logit(topple) = boss_intercept + a×HP + c_boss×Power.

HP coefficient consistent across bosses (a ≈ 0.60 for all three).
Power scaling boss-dependent: c_BA=0.57, c_Collector=0.90, c_Champion=1.00. Harder bosses weight Power more.
Power is class-specific (cross-class r=0.01-0.17). Structure is universal; content differs.
Decomposition quality varies: Warrior R²=0.66-0.96 (clean), Mage R��=0.10-0.26 (near-noise).

Resource Alignment

~3 distinct resource dimensions with partial sharing: Warrior and Rogue share one (cos ≈ 0.87), Rogue and Mage share another (cos ≈ 0.76), Mage has a unique combat-power dimension. No pair shares both.

Commutativity

Enemy encounters commute ~94.3% of the time (violations near survival boundary). Treasure order mostly doesn’t affect topple (16% disagreement = stochastic noise), except for Champion specifically (8 deterministic treasure-swap violations, p=0.008).

8. Data Generation

Runs are independent, no temporal trends, class drawn uniformly at ~1/3.
Encounters across floors consistent with independence (max deviation ~0.026).
No duplicate treasure names in any path.
Healing vs not-damaging is fundamentally confounded: fixed path length means “1 heal = 1 fewer enemy.” (Simon note: can somewhat unconfound by looking at partial-run deaths for different length runs that have 1 extra encounter and otherwise the same, assuming that there aren’t length specific and floor-specific effects)

9. Modeling Approaches

Additive HP (Warrior)

Each encounter adds/subtracts from running HP; death when HP ≤ 0. Gets broad strokes right (95.3% multiset classification) but overpredicts deaths by 73%. Useful for ranking encounters; specific parameter values are not mechanically meaningful.

State-Dependent Beta Models (All Classes)

Beta-distributed survival probabilities parameterized by running state. Captures non-linearity better. Warrior 1D, Rogue 2D, Mage 2D with regen. Mage regen model beats pure HP by ~11,500 LL.

Card-Deck Model (StS-Inspired)

Encounters add typed cards to a deck; combat involves random draws. Deck accumulation + random draw beats 1D HP by 5-28pp on held-out test data. But specific combat mechanics don’t matter: abstract power-vs-threshold tied fully mechanistic block/attack/heal/rounds on test NLL. Training advantage of the richer model was pure overfitting. This suggests resource accumulation with stochastic outcomes, but the exact resolution isn’t StS-style combat.

Kitchen-Sink + L1 Regularization

Hundreds of parameters with increasing L1 penalty. Warrior shows clean phase transition where all state-dependent terms die, leaving ~70 additive parameters. Confirms additive structure is the dominant Warrior signal.

Key Methodological Lessons

Right-censored paths: Filtering by encounter counts selects survivors. Multiple early findings were artifacts.
Exact multiset stratification is essential — count-profile controls conflate within-category differences.
Model parameters absorb unmodeled effects>! : Only relative rankings survive across model families.
Circular reasoning: (a) Mage count-logistic (AUC=0.992) — counts proxy survival depth. (b) “All deaths on F8” / “deterministic pre-boss survival” — survivorship bias; dead heroes have NaN for later floors, trivially splitting them into unique groups. (c) Multiset invariant (0 violations) — boss in key separates outcomes tautologically. (d) “175 sequences far from boundary” — inferred distance from outcomes.
Controlled-pair methodology is broken for lingering effects: matching subsequent encounters makes the target floor redundant.
Any claim of “zero X” or “all Y” should be checked for whether grouping makes it tautological.

10. Recommendations

Main Tower: Warrior LLRRRLLL

Route: Enchanted Shield → Campfire → Jaw Worm → Campfire × 4 → The Collector

P(survive) = 100% — Only enemy is Jaw Worm on F4. ⁰⁄_2,687 deaths.
P(topple) = 100%(135/135). Wilson 95% CI [97.2%, 100%].
Broader match (1 enemy, any treasure): ³⁸¹⁄₄₀₃ = 94.5%.
#1 of 70 paths by 5pp. Warrior >> Rogue (0.685) >> Mage (0.621).

Bonus Tower: Warrior RRRLLLLL

Route: Gremlin → Jaw Worm → Adamant Armor → Enchanted Shield → Sentries → Campfire → Vanishing Powder → The Champion

P(survive) = 100% — Three enemy floors, all 0% death with prior encounters.
P(topple) = 92.7% (140/151). Wilson 95% CI [87.4%, 95.9%].
#1 of 70 paths by 31pp (!). Warrior >> Rogue (0.800) >> Mage (0.326).
The ~7% failure is irreducible stochastic risk against Champion.

Why Warrior

Tower layouts are treasure/campfire-rich, perfectly suiting Warrior’s treasure-driven mechanics. Best Mage path (RLLLLLLL, 5E + Tome + campfire F8) reaches ~67% combined — 28pp behind. Mage’s enemy-driven topple can’t compensate when the map doesn’t provide enough enemies.

Confidence

Main Tower: Very high. Pessimistic assumptions still give >91.9%.
Bonus Tower: High. 7.3% failure is genuine stochastic risk, not modeling error. Zero exact path matches in dataset (relies on composition-matched analysis), but gap to #2 is enormous.

11. Major Remaining Unknowns

The actual game mechanics are unknown. We can characterize the state space (1D/2D, resource accumulation, stochastic resolution) but not the rules. Multiple model families fit roughly equally well. (Simon note − 1d, 2d etc are relative to particular wrong models and do not necessarily reflect the actual state space)
Mage mechanics remain poorest understood. 2D power model reaches 95.5% accuracy but the mechanistic basis is unclear.
Stochastic component uncharacterized. Can’t distinguish coin flip from dice roll from continuous distribution.
Bonus Tower prediction is unvalidated (zero exact path matches).
Same-enemy protection/harm — distinct mechanic or missing state variable?
Campfire vs weak treasure disagreement — genuinely different measurements or confound?
Positional decay vs step function — BA is clearly step-function at F8; other bosses unclear.

simon 23 Mar 2026 5:50 UTC
2 points
0
in reply to: aphyer’s comment on: D&D.Sci Release Day: Topple the Tower!
So… still haven’t figured the mechanics out, but actively beating around the bush with Claude finding things of little importance. Second extension?

simon 16 Mar 2026 6:53 UTC
2 points
0
on: D&D.Sci Release Day: Topple the Tower!
Requesting an extension for reason: wanting extra time to see if I can crack the mechanics with Claude. I think Claude suggested some possible answers waaay back but I didn’t pay much attention, telling to focus on the mechanics first. (This might be an abuse of extension requests—it’s not that I haven’t spent time on this.)

simon 9 Dec 2025 6:05 UTC
2 points
0
on: D&D Sci Thanksgiving: the Festival Feast Evaluation & Ruleset
Thanks aphyer for making this scenario and congrats to James Camacho (and Unnamed) for their better solutions.
The underlying mechanics here are not that complicated, but uncovering details of the mechanics seemed deceptively difficult, I guess due to the non-monotonic effects, and randomness entering the model before the non-monotonicity.
It wasn’t that hard though to come up with answers that would do OK, just to decipher the mechanics. I guess this is good in some ways (one doesn’t just insta-solve it), but I do like to be able to come up with legible understanding while solving these, and it felt pretty hard to do so in this case, so maybe I’d prefer if there were more lower hanging fruit mechanics wise. (So maybe I don’t actually prefer simple mechanics as long as some of them are easier to figure out and can be built off of?)
Regarding my own attempt to figure it out:
Thanks to abstractapplic for the comment that tipped me off to the characteristics being quantitative not just a classification, as well as to there possibly being a total food amount characteristic not just spicy/sweet. Multicore’s comment on Roc possibly being in a “meaty” category also helped me in regard to the latter.
Ironically though, the model change actually lowered my performance (from 16.30) presumably due to the improved model not taking as much into account penalties for variance that were implicitly present in the earlier interactions + spicy/sweet dish numbers model. I’m still pleased that the “improved” model had more structural resemblance to the actual reality, even if the answer was worse. (the second change in my answer also lowered my expected performance (from 16.13), but I think this was basically coincidental).
I actually did consider the possibility that the characteristics might have variability, including explicitly considering a uniform distribution between bounds, but Claude did an initial probe and dismissed it. I guess I should have pushed Claude on this! But also I’d been refining imperfect models for a while and and didn’t want to spend the time/effort required to develop a new model at that time if it didn’t instantly seem promising.
I heavily used AI for this scenario. It helps a lot to quickly do stuff that would take a lot more effort without, and in principle should also help with exploring, but I feel like its tendency to focus on what’s right in front of it can also distract me from switching approaches. Also I wish I had done more exploration of the data before asking AI to come up with a solution. As it was Claude (4.5 Opus) found the spicy/sweet categories without me having previously done so, which robbed me of having the pleasure of finding them on my own, as other commenters who mentioned them likely did.
I’m not sure if anyone appreciated my insanely long AI-generated comments, I could avoid doing that in the future if people were annoyed by it.

simon 8 Dec 2025 16:54 UTC
2 points
0
in reply to: simon’s comment on: D&D.Sci Thanksgiving: the Festival Feast
# Feast Quality Model: Full Parameter Specification (simon note: AI generated)
## Executive Summary
This document presents two piecewise linear models for predicting feast quality based on the balance of spicy, sweet, and bulk characteristics. Both models use learned per-dish weights for each dimension, with penalties applied when totals fall outside optimal zones.
**Key Finding:** The “spicy peak” model shows marginal RMSE improvement and is **marginally significant** (p=0.034) by F-test, but **BIC favors the simpler flat model**. Given the mixed evidence, we recommend targeting the **center of the flat model’s optimal zones** for maximum robustness.
---
## Model Comparison
| Metric | All-Flat Model | Spicy Peak Model |
|--------|----------------|------------------|
| RMSE | 1.9635 | 1.9583 |
| Parameters | 64 | 67 |
| AIC | 2440.9 | 2437.9 |
| BIC | 2789.5 | 2802.8 |
**Statistical Test (F-test):**
- F-statistic: 2.892
- Degrees of freedom: (3, 1647)
- **p-value: 0.034**
**Interpretation:** The peak model’s improvement is marginally significant (p=0.034), but BIC favors the simpler flat model (delta = −13.3). This mixed evidence suggests caution in adopting the more complex model.
---
## Model 1: All-Flat (3-Piece Piecewise Linear)
### Structure
For each dimension (spicy, sweet, bulk):
- **Below optimal zone:** Linear penalty with slope
- **In optimal zone:** No penalty (flat)
- **Above optimal zone:** Linear penalty with slope
```
Quality = Intercept + SpicyEffect + SweetEffect + BulkEffect
SpicyEffect = -slope_low * max(0, t1 - total_spicy) - slope_high * max(0, total_spicy—t2)
SweetEffect = -slope_low * max(0, t1 - total_sweet) - slope_high * max(0, total_sweet—t2)
BulkEffect = -slope_low * max(0, t1 - total_bulk) - slope_high * max(0, total_bulk—t2)
```
### Optimal Zones and Penalties
| Dimension | Lower Threshold (t1) | Upper Threshold (t2) | Slope Below | Slope Above |
|-----------|---------------------|---------------------|-------------|-------------|
| Spicy | 3.213 | 3.558 | 1.573 | 0.899 |
| Sweet | 3.068 | 4.461 | 1.593 | 1.273 |
| Bulk | 7.136 | 8.677 | 0.877 | 1.028 |
**Intercept:** 16.742
### Per-Dish Weights
| Dish | Spicy Weight | Sweet Weight | Bulk Weight |
|------|-------------|--------------|-------------|
| Ambrosial Applesauce | 0.000 | 1.456 | 0.000 |
| BBQ Basilisk Brisket | 0.821 | 0.831 | 1.404 |
| Chili Con Chimera | 1.304 | 0.078 | 1.502 |
| Displacer Dumplings | 0.052 | 0.075 | 0.086 |
| Ettin Eye Eclairs | 0.124 | 2.815 | 0.371 |
| Fiery Formian Fritters | 1.337 | 0.000 | 0.918 |
| Geometric Gelatinous Gateau | 0.176 | 2.078 | 0.583 |
| Honeyed Hydra Hearts | 0.000 | 1.537 | 0.851 |
| Killer Kraken Kebabs | 2.146 | 0.054 | 2.434 |
| Mighty Minotaur Meatballs | 0.069 | 0.181 | 2.233 |
| Opulent Owlbear Omelette | 0.008 | 0.016 | 1.788 |
| Pegasus Pinion Pudding | 0.124 | 0.621 | 0.786 |
| Roc Roasted Rare | 0.004 | 0.290 | 3.493 |
| Scorching Salamander Stew | 2.138 | 0.035 | 1.520 |
| Troll Tenderloin Tartare | 0.062 | 0.000 | 0.960 |
| Vicious Vampire Vindaloo | 3.015 | 0.148 | 1.570 |
| Wyvern Wing Wraps | 0.657 | 0.181 | 0.749 |
---
## Model 2: Spicy Peak (4-Piece for Spicy, 3-Piece for Sweet/Bulk)
### Structure
For spicy: 4-piece continuous function with potential peak
- Piece 1: spicy < t1 → slope s1
- Piece 2: t1 ⇐ spicy < t2 → slope s2 (if positive, quality increases)
- Piece 3: t2 ⇐ spicy < t3 → slope s3 (if negative, quality decreases = peak at t2)
- Piece 4: spicy >= t3 → slope s4
For sweet/bulk: Same 3-piece flat structure as Model 1.
### Spicy Parameters (4-Piece)
| Parameter | Value | Interpretation |
|-----------|-------|----------------|
| t1 (breakpoint 1) | 1.016 | Below this: slope s1 |
| t2 (breakpoint 2) | 2.697 | **Peak location** (if s2>0, s3<0) |
| t3 (breakpoint 3) | 5.872 | Above this: slope s4 |
| s1 (slope 1) | 2.043 | Slope for spicy < t1 |
| s2 (slope 2) | 1.856 | Slope for t1 ⇐ spicy < t2 |
| s3 (slope 3) | −1.253 | Slope for t2 ⇐ spicy < t3 |
| s4 (slope 4) | −0.268 | Slope for spicy >= t3 |
**Peak Location:** ~2.70 (where slope changes from positive to negative)
### Sweet/Bulk Parameters (3-Piece)
| Dimension | Lower Threshold | Upper Threshold | Slope Below | Slope Above |
|-----------|-----------------|-----------------|-------------|-------------|
| Sweet | 3.028 | 4.591 | 1.600 | 1.299 |
| Bulk | 6.692 | 8.486 | 0.980 | 1.126 |
**Intercept:** 13.752
### Per-Dish Weights (Peak Model)
| Dish | Spicy Weight | Sweet Weight | Bulk Weight |
|------|-------------|--------------|-------------|
| Ambrosial Applesauce | 0.000 | 1.452 | 0.000 |
| BBQ Basilisk Brisket | 0.642 | 0.871 | 1.395 |
| Chili Con Chimera | 1.020 | 0.071 | 1.427 |
| Displacer Dumplings | 0.036 | 0.062 | 0.089 |
| Ettin Eye Eclairs | 0.070 | 2.904 | 0.410 |
| Fiery Formian Fritters | 1.079 | 0.000 | 0.973 |
| Geometric Gelatinous Gateau | 0.139 | 2.104 | 0.522 |
| Honeyed Hydra Hearts | 0.000 | 1.515 | 0.745 |
| Killer Kraken Kebabs | 1.693 | 0.042 | 2.322 |
| Mighty Minotaur Meatballs | 0.000 | 0.182 | 2.228 |
| Opulent Owlbear Omelette | 0.052 | 0.010 | 1.673 |
| Pegasus Pinion Pudding | 0.125 | 0.592 | 0.653 |
| Roc Roasted Rare | 0.000 | 0.279 | 3.229 |
| Scorching Salamander Stew | 1.691 | 0.041 | 1.614 |
| Troll Tenderloin Tartare | 0.071 | 0.000 | 0.914 |
| Vicious Vampire Vindaloo | 2.361 | 0.163 | 1.545 |
| Wyvern Wing Wraps | 0.518 | 0.157 | 0.711 |
---
## Optimal Feast Recommendations
### Degeneracy Analysis
Both models have **degenerate optimal solutions** - multiple feasts achieve the same (or nearly the same) predicted quality:
| Model | Best Score | # Degenerate Solutions |
|-------|------------|------------------------|
| Flat Model | 16.74 | 135 |
| Peak Model | 16.87 | 6 |
| In All Flat Zones | 16.74 | 119 |
To break this degeneracy, we select the feast **closest to the center** of each optimal zone, providing maximum robustness against model uncertainty.
### Target Centers (Flat Model)
| Dimension | Optimal Zone | Center | Width |
|-----------|--------------|--------|-------|
| Spicy | [3.21, 3.56] | 3.386 | 0.344 |
| Sweet | [3.07, 4.46] | 3.764 | 1.393 |
| Bulk | [7.14, 8.68] | 7.907 | 1.540 |
---
## RECOMMENDED FEAST (Center-Targeted)
This feast is in all optimal zones AND closest to the center of each zone.
| Dimension | Value | Target Center | Deviation |
|-----------|-------|---------------|-----------|
| Spicy | 3.388 | 3.386 | 0.003 |
| Sweet | 3.675 | 3.764 | 0.089 |
| Bulk | 8.041 | 7.907 | 0.135 |
**Predicted Quality:** 16.74 (flat model), 16.80 (peak model)
**Normalized Distance from Center:** 0.160
**Dishes (7):**
- BBQ Basilisk Brisket
- Displacer Dumplings
- Geometric Gelatinous Gateau
- Killer Kraken Kebabs
- Opulent Owlbear Omelette
- Pegasus Pinion Pudding
- Troll Tenderloin Tartare
---
## Alternative Recommendations
### Best by Flat Model
*(135 feasts tied at this score)*
**Example:** Predicted Quality: 16.74
- Spicy: 3.388, Sweet: 3.675, Bulk: 8.041
- Dishes (7): BBQ Basilisk Brisket, Displacer Dumplings, Geometric Gelatinous Gateau, Killer Kraken Kebabs, Opulent Owlbear Omelette, Pegasus Pinion Pudding, Troll Tenderloin Tartare
### Best by Peak Model
*(6 feasts tied at this score)*
**Example:** Predicted Quality: 16.87
- Spicy: 2.695, Sweet: 3.138, Bulk: 6.864
- Dishes (5): Geometric Gelatinous Gateau, Pegasus Pinion Pudding, Roc Roasted Rare, Troll Tenderloin Tartare, Vicious Vampire Vindaloo
---
## Caveats and Limitations
1. **Peak model has mixed evidence:** The F-test p-value of 0.034 is below 0.05, but BIC favors the flat model. The evidence is not conclusive.
2. **High degeneracy:** 119 different feasts fall within all optimal zones of the flat model. The center-targeting approach provides a principled way to select among them.
3. **Weights are continuous:** The per-dish weights are fitted continuous values. Integer or simple-fraction approximations may exist but are not explored here.
4. **Variance heterogeneity:** Residual variance increases when above optimal thresholds (especially for bulk). This is not captured in the point predictions above.
5. **Model uncertainty:** All predictions have associated uncertainty (~2.0 quality points RMSE). The differences between top feasts are often smaller than this uncertainty.
---
## Summary
**Use the center-targeted recommendation** for maximum robustness:
**BBQ Basilisk Brisket, Displacer Dumplings, Geometric Gelatinous Gateau, Killer Kraken Kebabs, Opulent Owlbear Omelette, Pegasus Pinion Pudding, Troll Tenderloin Tartare**
This feast:
- Falls within all optimal zones of the flat model
- Is closest to the center of each zone (normalized distance: 0.160)
- Scores well on both flat (16.74) and peak (16.80) models

simon 8 Dec 2025 16:26 UTC
2 points
0
in reply to: simon’s comment on: D&D.Sci Thanksgiving: the Festival Feast
further followup:
So I have (had AI generate) a new better model, in which the sweet/spicy/bulk dimensions have continuous values, each independently having a piecewise linear effect on feast quality. In one version, the piecewise linear functions have a flat middle, with drop offs at higher and lower values. This results in a range in which all feasts are equivalent. In another version, there’s a peak at low spiciness and we try to pick near that spiciness peak. A combined hedge version has us pick as low a spiciness value as possible within the flat range. The resulting feast pick is:

~~**[‘Geometric Gelatinous Gateau’, ‘Pegasus Pinion Pudding’, ‘Roc Roasted Rare’, ‘Troll Tenderloin Tartare’, ‘Vicious Vampire Vindaloo’]**~~

~~Which I guess is now my pick.~~
I’m still not that satisfied with it: it’s pretty ad hoc, with non-integer values, and I haven’t properly understood the error sources (there’s some theory that there might be a base error distribution with possibly stochastic penalties for going too high in each dimension and possibly deterministic penalties for going too low). Anyway, full model specification of these questionable models in a reply post again for ease of separately hiding it.

edit: changed my mind. I’m not going to hedge towards the alternate model with the peak, I’ll instead hedge toward the center of the (claimed in the simpler model) flat zone, which seems safer. It also seems dumb because probably I don’t need to go all the way to the center to be reasonably safe, so probably I could hedge to lower spiciness without penalty. Still, I’m at this point considering myself “done” (in the sense of not feeling it worth it to keep going, not in the sense that I couldn’t keep going or am satisfied). I will see what I failed to account for soon enough! The centered feast, which is now my pick, is:

**BBQ Basilisk Brisket, Displacer Dumplings, Geometric Gelatinous Gateau, Killer Kraken Kebabs, Opulent Owlbear Omelette, Pegasus Pinion Pudding, Troll Tenderloin Tartare**
The reply post will contain the full description of the models discussed here.

simon 8 Dec 2025 11:43 UTC
2 points
0
in reply to: simon’s comment on: D&D.Sci Thanksgiving: the Festival Feast
followup after reading other answers:
abstractapplic says that it’s total quantity of sweetness/spiciness that matters, and I feel like that’s almost certainly true. Probably the hearty/ethereal thing is quantitative too if it exists (may or may not relate to total food quality, I note Claude thought Roc had x2 food contribution, after I suggested it as a possible explanation for only Roc feasts going down to 2 ingredients and some tests seemed to corroborate.). I had some AI generated quantitative stuff (including sweet, spicy and hearty/ethereal axes), but not sure it was even used in the actual model before the AI pushed me to an interactions model that couldn’t possibly be the simplest model but at least beat an initial sweet count and spicy count model. Anyway, also Multicore pointed out that total ingredients matter in a non-linear way, which the interactions model probably doesn’t take into account in an optimal way (also even the spicy/sweet counts, maybe). So I’m even more sure that I’m missing the optimal model which likely does include optimal levels of spiciness and sweetness and total food quantity that all aren’t based on a simple count.
Edit: I’m following up on this...

simon 8 Dec 2025 11:14 UTC
0 points
0
in reply to: simon’s comment on: D&D.Sci Thanksgiving: the Festival Feast
# Feast Analysis Summary (simon note—AI generated, also obsolete. I’ve un-upvoted it which might hide it)
This document summarizes findings from analyzing feast quality variance, optimal feast selection, and ingredient distribution patterns.
---
## 1. Noise Model Analysis
### Approach
We analyzed duplicate feast configurations (same dishes, multiple observations) to understand the underlying noise distribution. With 67 n=2 pairs and 10 n=3 triplets (excluding WWW), we computed spread distributions and compared them to various hypothesized noise models using full likelihood calculations.
### Findings
**Spread distribution (observed, no WWW):**
| Spread | Count | Percentage |
|--------|-------|------------|
| 0 | 10 | 14.9% |
| 1 | 23 | 34.3% |
| 2 | 20 | 29.9% |
| 3 | 3 | 4.5% |
| 4+ | 11 | 16.4% |
**Model comparison:**
- A **U[-1,0,1] + penalty** model (one-sided negative shock) fits reasonably well
- Best-fit parameters: penalty size ~3-4, probability ~15-20%
- Chi-square test (p=0.23) does not reject this model
- However, with only n=67 duplicates, sampling noise is substantial and other models may also be consistent with the data
**Heteroscedasticity by dish:**
- Earlier analysis suggested WWW and SSS may increase variance
- Evidence is suggestive but not conclusive due to limited duplicate data when split by dish presence
### Caveats
- Comparing duplicate spreads to model residuals is complicated: residuals include model error, which inflates variance
- Bootstrap resampling from duplicates showed the mismatch between observed and predicted spread distributions could plausibly be sampling noise
- The “true” noise model remains uncertain
---
## 2. Joint Mean-Variance Model
### Approach
We fit a joint maximum likelihood model:
- **Mean model**: Linear + pairwise interactions (154 parameters)
- **Variance model**: log(σ) as linear function of dishes (18 parameters)
This avoids the problems of two-stage estimation where mean and variance are fit separately.
### Findings
**Heteroscedasticity is statistically significant:**
- Likelihood ratio test: LR = 63.2, df = 17, p < 0.0001
- AIC favors heteroscedastic model (-29), BIC is mixed (+63)
**Dishes that increase variance (σ multiplier, from heteroscedastic-only model):**
| Dish | σ multiplier |
|------|--------------|
| Honeyed Hydra Hearts | 1.22x |
| Roc Roasted Rare | 1.17x |
| Killer Kraken Kebabs | 1.14x |
| Scorching Salamander Stew | 1.14x |
| Chili Con Chimera | 1.14x |
**Dishes that decrease variance:**
| Dish | σ multiplier |
|------|--------------|
| Displacer Dumplings | 0.90x |
Predicted σ ranges from 1.50 to 3.85 depending on dish combination.
**Note:** When count features are added to the model, some of these effects are absorbed by the count terms (e.g., Roc’s effect drops from 1.17x to 1.03x). See Section 5 for the combined model’s variance estimates.
### Caveats
- The optimizer did not fully converge for some regularization values
- Effect sizes are modest (most dishes change σ by <20%)
- With 172 total parameters and 1714 observations, overfitting is a concern despite regularization
---
## 3. Pairwise Interaction Structure
### Approach
We categorized dishes into flavor groups and examined whether interaction coefficients align with these categories.
**Well-supported categories:**
- SPICY: Chili Con Chimera, Fiery Formian Fritters, Killer Kraken Kebabs, Scorching Salamander Stew, Vicious Vampire Vindaloo
- SWEET: Ambrosial Applesauce, Ettin Eye Eclairs, Geometric Gelatinous Gateau, Honeyed Hydra Hearts, Pegasus Pinion Pudding
**Remaining dishes** (no clear category): BBQ Basilisk Brisket, Displacer Dumplings, Mighty Minotaur Meatballs, Opulent Owlbear Omelette, Roc Roasted Rare, Troll Tenderloin Tartare, Wyvern Wing Wraps
### Findings
**Mean interaction coefficient by category:**
| Interaction Type | N | Mean Coef |
|------------------|---|-----------|
| SPICY-SPICY | 10 | **-2.29** |
| SWEET-SWEET | 10 | **-1.62** |
| SPICY-SWEET | 25 | −0.09 |
**Statistical test:** Same-category (SPICY or SWEET) vs other interactions: t = −6.80, p < 0.0001
**Most negative interactions:**
1. Ettin Eye Eclairs × Geometric Gelatinous Gateau: −4.33 (SWEET-SWEET)
2. Killer Kraken Kebabs × Vicious Vampire Vindaloo: −4.17 (SPICY-SPICY)
3. Scorching Salamander × Vicious Vampire Vindaloo: −3.57 (SPICY-SPICY)
### Validation of SPICY/SWEET Categories
We verified the category assignments by checking each dish’s mean interaction with SPICY vs SWEET groups:
- All SPICY dishes have much more negative interactions with other SPICY dishes than with SWEET dishes
- All SWEET dishes have much more negative interactions with other SWEET dishes than with SPICY dishes
- All 10 SPICY-SPICY interactions are negative (-0.84 to −4.17)
- All 10 SWEET-SWEET interactions are negative (-0.04 to −4.33)
**Pegasus Pinion Pudding** is the weakest SWEET member (mean interaction with SWEET group only −0.58), but still fits the pattern.
### Remaining Dishes
The 7 dishes not in SPICY or SWEET do not form clear additional categories:
- **Roc Roasted Rare** has negative interactions with almost everything (mean −1.13 with other remaining dishes)
- **Displacer Dumplings** is the only dish with mostly neutral/positive interactions (+0.06 mean)
- The others (BBQ, Mighty Minotaur, Opulent Owlbear, Troll, Wyvern) have mixed negative interactions but don’t cluster into coherent groups
**Roc Roasted Rare** has negative interactions with *both* SPICY (-1.66) and SWEET (-0.65) groups, suggesting it may be a “universal intensifier” that doesn’t combine well with strongly-flavored dishes.
### Interpretation
- Combining multiple SPICY or multiple SWEET dishes incurs a quality penalty
- Cross-category combinations (SPICY + SWEET) are roughly neutral
- No strong evidence for additional flavor categories beyond SPICY and SWEET
---
## 4. Model with Count Features
### Approach
We extended the pairwise model to include count features:
- Total number of dishes
- Number of SPICY dishes (and squared term)
- Number of SWEET dishes (and squared term)
This allows the model to capture effects like “too many spicy dishes” beyond pairwise interactions.
### Findings
**Model improvement is statistically significant:**
- Likelihood ratio test: χ² = 232.6, df = 9, p < 0.0001
- AIC improved by 214.6
**Marginal effect of adding SPICY dishes:**
| Change | Effect on Mean |
|--------|----------------|
| 0→1 SPICY | **+1.84** |
| 1→2 SPICY | +0.12 |
| 2→3 SPICY | **-1.60** |
| 3→4 SPICY | −3.32 |
**Marginal effect of adding SWEET dishes:**
| Change | Effect on Mean |
|--------|----------------|
| 0→1 SWEET | +0.02 |
| 1→2 SWEET | **-1.05** |
| 2→3 SWEET | −2.12 |
**Marginal effect of total dish count:**
| Change | Effect on Mean |
|--------|----------------|
| 5→6 total | +0.74 |
| 6→7 total | +0.03 |
| 7→8 total | −0.68 |
### Interpretation
- First SPICY dish adds significant value; second is roughly neutral; third and beyond hurt quality
- SWEET dishes show diminishing returns starting from the second dish
- Optimal total dish count appears to be around 6-7
### Residual Pattern
Adding count features modestly improves the model:
- RMSE: 2.025 → 2.005 (1% improvement)
- Skew: −0.111 → −0.080 (slightly more symmetric)
- Systematic biases by SPICY/SWEET count are reduced but not eliminated
---
## 5. Optimal Feast Selection
### Approach
Using the combined heteroscedastic + count-features model (which models both dish-dependent variance and SPICY/SWEET count effects), we searched all 5-7 dish combinations to optimize:
- (a) Expected quality (mean)
- (b) 90th percentile (high upside)
- (c) 10th percentile (reliable floor)
### Results
| Objective | Mean | σ | Q10 | Q90 |
|-----------|------|---|-----|-----|
| Best Mean | **17.51** | 2.09 | 14.83 | 20.19 |
| Best Q90 (upside) | 17.40 | 2.48 | 14.22 | **20.58** |
| Best Q10 (reliable) | 17.48 | 1.89 | **15.05** | 19.91 |
**(a) Best Mean:**
- Ambrosial Applesauce
- BBQ Basilisk Brisket
- Geometric Gelatinous Gateau
- Opulent Owlbear Omelette
- Roc Roasted Rare
- Vicious Vampire Vindaloo
(6 dishes: 1 SPICY, 2 SWEET)
**(b) Best Q90 (high upside):**
- Ambrosial Applesauce
- BBQ Basilisk Brisket
- Fiery Formian Fritters
- Honeyed Hydra Hearts
- Killer Kraken Kebabs
- Opulent Owlbear Omelette
- Pegasus Pinion Pudding
(7 dishes: 2 SPICY, 3 SWEET — includes high-variance Honeyed Hydra Hearts)
**(c) Best Q10 (reliable):**
- Ambrosial Applesauce
- BBQ Basilisk Brisket
- Geometric Gelatinous Gateau
- Roc Roasted Rare
- Troll Tenderloin Tartare
- Vicious Vampire Vindaloo
(6 dishes: 1 SPICY, 2 SWEET — includes low-variance Troll Tenderloin)
**Core dishes (in all three):**
- Ambrosial Applesauce
- BBQ Basilisk Brisket
- Vicious Vampire Vindaloo
**Dishes in Best Mean and Best Q10 (but not Q90):**
- Geometric Gelatinous Gateau
- Roc Roasted Rare
**High-variance dishes (for Q90 upside):** Honeyed Hydra Hearts, Killer Kraken Kebabs, Fiery Formian Fritters
**Low-variance dish (for Q10 reliability):** Troll Tenderloin Tartare (σ x0.96), Displacer Dumplings (σ x0.88, but not in optimal)
### Variance Effects by Dish
The model estimates these variance multipliers per dish:
| Dish | σ multiplier | Notes |
|------|--------------|-------|
| Honeyed Hydra Hearts | 1.07x | Highest variance |
| Chili Con Chimera | 1.06x | |
| Opulent Owlbear Omelette | 1.06x | |
| Roc Roasted Rare | **1.03x** | Slight increase, not decrease |
| Troll Tenderloin Tartare | 0.96x | Lower variance |
| Displacer Dumplings | 0.88x | Lowest variance |
**Note on Roc:** Earlier analysis suggested Roc might decrease variance, but the combined model shows Roc has a **slight variance increase** (σ x1.03). The confusion arose because:
- The heteroscedastic-only model found Roc σ x1.17
- With count features, some of Roc’s apparent variance effect is absorbed by the count terms
- Roc appears in Best Mean and Best Q10 due to its high base quality value, not low variance
### Model Sensitivity
Different model specifications produce somewhat different optimal feasts, suggesting substantial model uncertainty. However, core dishes (Ambrosial, BBQ, Vicious Vampire) appear consistently.
### Caveats
- None of these optimal feasts appear exactly in the data
- Model predictions are extrapolations; actual performance may differ
- The optimizer showed convergence warnings, though restarting improved the solution
---
## 6. Validation Against Observed Data
### Highest quality feasts in data (Quality = 20)
- Ambrosial, Chili, Honeyed Hydra, Killer Kraken, Mighty Minotaur, Roc (6 dishes)
- Ambrosial, Honeyed Hydra, Killer Kraken, Roc, Scorching Salamander (5 dishes)
- Ambrosial, Chili, Honeyed Hydra, Roc, Scorching Salamander (5 dishes)
**Notable:** These include multiple SPICY dishes, which the model predicts should have negative interactions. This could indicate:
1. These are lucky high-variance outcomes (model predicts lower mean but high upside)
2. The model is missing something
3. Small sample of quality=20 feasts (only 4 observations)
### Highest-mean duplicate configurations
| Mean | Qualities | Dishes |
|------|-----------|--------|
| 18.0 | [17, 19] | Ambrosial, Geometric, Opulent, Roc, Vicious Vampire |
| 18.0 | [18, 18] | Ambrosial, Honeyed Hydra, Killer Kraken, Roc, Vicious Vampire |
| 17.5 | [16, 19] | Chili, Ettin, Opulent, Roc, Scorching |
**Roc Roasted Rare** appears in nearly all high-quality duplicate configurations, and the combined model’s Best Mean and Best Q10 feasts now include it. This suggests Roc’s high base value compensates for its negative interactions.
---
## 7. Ingredient Distribution Patterns
### Global Variance Constraint
The total number of ingredients per feast has **compressed variance** compared to what independent selection would produce.
| Metric | Observed | Expected (if independent) |
|--------|----------|---------------------------|
| Mean ingredients | 5.37 | 5.37 |
| Std dev | 1.27 | 1.89 |
| Variance ratio | 0.43 | 1.00 |
Ingredient selection appears to target a relatively fixed total count (~5-6 ingredients), creating **negative correlations between all ingredients**. When one ingredient is present, others are slightly less likely.
### Roc Roasted Rare “Counts as 2”
When treating Roc as contributing 2 to the effective count:
- Minimum effective count = 3 (never violated)
- Mean effective count = 5.88
- The variance compression is consistent with targeting this effective count
### No Hard Constraints on Ingredient Co-occurrence
After properly adjusting for the variance constraint and multiple testing, **no statistically significant hard constraints** were found on which ingredients can appear together.
**The “4-tuple constraint” is likely noise:**
We initially found that {Ambrosial Applesauce, Ettin Eye Eclairs, Honeyed Hydra Hearts, Wyvern Wing Wraps} never all appear together (max 3 of 4).
| Test | p-value |
|------|---------|
| Raw (vs independence) | 0.0006 |
| Bonferroni-corrected (2380 4-tuples) | 1.0 |
| Vs variance-constrained simulation | 0.016 |
With 2380 possible 4-tuples, finding one with this property is expected ~43% of the time by chance. This is **probably not a real constraint**.
### Duplicate Feasts
110 of 1714 feasts are duplicates (6.4%), with 1604 unique combinations.
| Size | Observed Dups | Expected (uniform) | Expected (prob-adjusted) |
|------|---------------|-------------------|-------------------------|
| 2 | 4 | 0.3 | 0.4 |
| 3 | 18 | 5.7 | 7.5 |
| 4 | 50 | 22.8 | 31.3 |
| 5 | 29 | 20.6 | 29.6 |
| 6 | 7 | 8.3 | 12.3 |
Small feasts (size 2-4) have **more duplicates than expected** even after accounting for non-uniform ingredient probabilities. The variance constraint likely causes this: small feasts are in the tail of the distribution, so only the most probable combinations occur.
### Positive Correlations (Unusual)
Under a pure variance constraint, all ingredient correlations should be negative. However, several **positive correlations** were found:
| Pair | Correlation |
|------|-------------|
| Displacer Dumplings + Mighty Minotaur Meatballs | +0.050 |
| Ambrosial Applesauce + Roc Roasted Rare | +0.028 |
| Ambrosial Applesauce + Scorching Salamander Stew | +0.024 |
| Displacer Dumplings + Fiery Formian Fritters | +0.021 |
| Displacer Dumplings + Killer Kraken Kebabs | +0.018 |
| Fiery Formian Fritters + Killer Kraken Kebabs | +0.018 |
| Ettin Eye Eclairs + Roc Roasted Rare | +0.017 |
These pairs appear together more often than the variance constraint would predict. This could indicate thematic groupings, ingredient affinities, or statistical noise (correlations are small, ~0.02-0.05).
### SPICY and SWEET Groups: Selection vs Quality
**SPICY**: Killer Kraken Kebabs, Scorching Salamander Stew, Vicious Vampire Vindaloo, Fiery Formian Fritters, Chili Con Chimera
**SWEET**: Ambrosial Applesauce, Ettin Eye Eclairs, Geometric Gelatinous Gateau, Honeyed Hydra Hearts
Do these have co-occurrence constraints?
- **SPICY**: All 5 appear together in 5 feasts (no hard constraint)
- **SWEET**: All 4 appear together in 6 feasts (no hard constraint)
**Conclusion**: These groups affect **quality** (pairwise conflicts reduce quality) but do NOT create hard constraints on ingredient selection. The slight under-representation is explained by the variance constraint.
### Time-Based Changes
Roc Roasted Rare and Honeyed Hydra Hearts show apparent frequency changes over time:
| Ingredient | Raw p-value | Permutation p-value |
|------------|-------------|---------------------|
| Roc | 0.0006 | 0.032 |
| Hydra | 0.004 | 0.137 |
With 17 ingredients, some apparent changes are expected by chance. The permutation p-values (accounting for multiple testing over split points) are weak. There may be a real change in Roc frequency, but the evidence is weak after accounting for multiple testing.
---
## 8. Summary of Key Findings
### Quality Model
1. **Noise structure**: Evidence is consistent with a discrete noise model (U[-1,0,1] + occasional penalty), but sample size limits certainty
2. **Heteroscedasticity**: Statistically significant; some dishes (Honeyed Hydra Hearts, Roc) increase variance by ~15-20%
3. **Interaction structure**: SPICY-SPICY and SWEET-SWEET combinations have strong negative interactions (~-2 to −4 quality points); cross-category mixing is neutral. The SPICY/SWEET category assignments are well-supported by the interaction data.
4. **Count effects**: Adding count features significantly improves the model. First SPICY dish adds ~1.8 points; 2+ SPICY or 2+ SWEET dishes show diminishing/negative returns. Optimal total count is ~6-7 dishes.
5. **Optimal feasts**: Core dishes include Ambrosial Applesauce, BBQ Basilisk Brisket, and Vicious Vampire Vindaloo. Best Mean and Best Q10 feasts include Roc Roasted Rare; Best Q90 swaps in high-variance dishes instead. Different model specifications produce somewhat different recommendations.
6. **Roc Roasted Rare**: Appears frequently in high-quality observations and is included in Best Mean and Best Q10 optimal feasts. Despite negative interactions with both SPICY and SWEET groups, its high base value compensates.
### Ingredient Selection
1. **Target effective count**: Selection targets ~5.9 effective ingredients (where Roc counts as 2)
2. **Variance compression**: The selection process constrains variance to ~43% of what independence would produce
3. **No hard constraints**: Any ingredient combination is possible; apparent constraints are explained by variance compression
4. **Possible weak affinities**: A few ingredient pairs (Displacer+Mighty, Ambrosial+Roc) may have slight positive associations, but evidence is weak
5. **Possible time change**: Roc frequency may have increased around index 1134, but evidence is marginal
---
## Limitations
### Quality Model
- Model has many parameters relative to data (160-181 vs 1714)
- Optimal feasts are model extrapolations, not observed configurations
- Different model specifications produce different optimal feasts
- Noise model analysis limited by small duplicate sample (n=67)
- Some optimizer convergence issues in joint model fitting
### Ingredient Distribution
- Sample size (1714) limits power to detect subtle effects
- Simulation-based null models may not perfectly match true data-generating process
- Small positive correlations (~0.02-0.05) are at the edge of detectability
Whelp that was even longer than I feared, and has some formatting issues. For completeness I’ll mention that there was some speculation of a hearty/ethereal aspect as well the sweet and spicy categories, where e.g. (IIRC) Roc is hearty and Vampire is ethereal.

simon 8 Dec 2025 11:02 UTC
2 points
0
on: D&D.Sci Thanksgiving: the Festival Feast
Thanks for the extension aphyer.
And after the extension, I wound up just doing more LLM analysis (having already done some beforehand) and while it’s probably better than nothing, I would not be surprised at all if there were a simple ruleset which wasn’t found due to being outside the considered hypothesis space. Anyway, with some trepidation I’ll go with Claude’s Q10 feast from the summary by Claude 4.5 Opus, which I’ll put in a reply comment so it can be separately collapsed. That feast is:
~~Ambrosial Applesauce, BBQ Basilisk Brisket, Geometric Gelatinous Gateau, Roc Roasted Rare, Troll Tenderloin Tartare, Vicious Vampire Vindaloo.~~
Edit: now
~~**[‘Geometric Gelatinous Gateau’, ‘Pegasus Pinion Pudding’, ‘Roc Roasted Rare’, ‘Troll Tenderloin Tartare’, ‘Vicious Vampire Vindaloo’]**~~
actually
**BBQ Basilisk Brisket, Displacer Dumplings, Geometric Gelatinous Gateau, Killer Kraken Kebabs, Opulent Owlbear Omelette, Pegasus Pinion Pudding, Troll Tenderloin Tartare**
following revised model in followup comment.
AI summary in reply comment:

simon 20 Nov 2025 0:28 UTC
2 points
0
in reply to: habryka’s comment on: Don’t let people buy credit with borrowed funds
In my view:
- facilitation of stag-hunt-like cooperation is really useful. Because cooperating to do stuff beyond the capabilities of individuals is useful but hard.
- the dynamic you discuss in the post applies to stag hunt facilitation because their success depends on willingness of others to provide more resources (up to some point where they can generate more)
- the difference between, e.g., Theranos and standard entrepreneurship does not lie in the dynamic you discuss in the post. It lies in how egregiously Elizabeth Holmes was lying relative to the standard level of misleadingness. (and of course, more honesty would be better...)
- It would of course be very valuable to determine if a stag hunt will pay off or will fail! But the difference between the two does not lie in the dynamic you discuss in the post (which applies to both ultimately successful and unsuccessful stag hunts).

simon 19 Nov 2025 18:09 UTC
11 points
2
in reply to: habryka’s comment on: Don’t let people buy credit with borrowed funds
aimed in a relatively broad sense at people who care about how well societies and groups of people function.
I don’t think allowing financial fraud is a thing current institutions mostly want? The difficulty is more in figuring out how to stop it without stopping legitimate activity as well (A lot of successful entrepreneurship will look kind of a lot like this, I think). If you are calling for normal speculative investment to be banned, it’s very likely not worth the loss of innovation. (It may make sense perhaps to be more strict about what level of falsehood leads to fraud prosecution, but I would keep it to banning false claims).

simon 22 Sep 2025 15:17 UTC
2 points
0
on: D&D.Sci: Serial Healers
My accusations, at least so far:
Danny Nova for curing:
- Babblepox (always present in same sector)
- Bumblepox, Scramblepox (always present in same sector OR Azeru in adjacent sector
- Gurglepox (always present in same sector OR Dankon Ground in opposite sector)
- Chucklepox (Danny Nova in same sector for about half of cures. All other cases Lomerius Xardus was present somewhere (todo: investigate if more patterns than mere presence))
- Rumblepox (suspiciously high ratio of presence/absence in Calderia when cured, but plenty more cases unexplained—TODO: explain more)
- ~~Disquietingly Serene Bowel Syndrome (on weak evidence, see below)~~
Azeru for curing Bumblepox, Scramblepox (see Danny Nova)
Lomerius Xardus for curing Chucklepox (see Danny Nova)
Boltholopew and Moon Finder, collectively, for curing Disease Syndrome, Parachordia, Problems Disorder (each one positioned in different adjacent sectors to the curing event)
Tehami Darke on weak evidence (see below) for curing Disquetingly Serene Bowel Syndrome
Dankon Ground for curing;
- Gurglepox (present in opposite sector OR Danny Nova in same sector)
- Mildly But Persistently Itchy Throat (always present in opposite sector)
Zancro for curing Scraped Elbow, Scraped Knee (always present in same sector)
Nettie Silver for curing Smokesickness (always present in same sector. It seems she is always present in Calderia, but her location and the Smokesickness curing location, when it occurs, do vary)
I have not figured out The Shivers.
Disquietingly Serene Bowel Syndrome seems tricky. Cures only started on Day 390. Tehami Darke came to Calderia on Day 162, Lomerius Xardus first arrived on day 494, Zeledin Zura first arrived on day 427, Gouberi first arrived on day 397, Ricewined first arrived on day 994. None of which is particularly suggestive of a causal connection though the p-values would be very low assuming (falsely) that each day was independent. Cures seem more likely to occur in the sector where Tehami Darke is present, which is pretty weak without further investigation (e.g. is he hanging out in some sector where it’s more likely to occur anyway? I haven’t checked). Conditioned on day 390+, the average number of cures is slightly higher on days when Danny Nova is present, also weak, but the prior for Danny being involved is high, so ~~might as well accuse him as well~~. (edit: no, seems there is no upside to this accusation given the scoring rule and the high confidence Danny Nova has been curing other stuff)

simon 2 May 2025 2:59 UTC
2 points
0
in reply to: abstractapplic’s comment on: D&D.Sci Tax Day: Adventurers and Assessments Evaluation & Ruleset
Interesting link on symbolic regression. I actually tried to get an AI to write me something similar a while back^[1] (not knowing that the concept was out there and foolishly not asking, though in retrospect it obviously would be).
From your response to kave:
calculate a quantity then use that as a new variable going forward
In terms of the tree structure used in symbolic regression (including my own attempt), I would characterize this as wanting to preserve a subtree and letting the rest of the tree vary.
Possible issues:
1. If the coding modifies the trees leaf-first, trees with different roots but common subtrees aren’t treated as close to each other. This is an issue that my own version would likely have had even if actually implemented^[2]. However, I think PySR might at least partially address this issue (It uses genetic programming and the pictures in the associated paper seem to indicate that it is generating trees which at least sometimes preserve subtrees.) (Though the genetic programming approach is likely to make it hard to find the very simplest solutions in practice imo.^[3])
2. Even if you are treating trees with common subtrees as close to each other, if your evaluation of trees is only comparing final calculated values on the entire dataset, then it’s hard to make the call “I know this subtree is important even if I don’t know the rest of the tree” because the results are not likely to be all that close unless you already have a reasonable guess for the rest of the tree. One partial (heh) answer might be to award part marks to solutions that work well for some of the data even if wildly off for other parts. Careful thinking might be required to do this in a way that doesn’t backfire horribly, though. Hmm—or maybe you CAN do that in the existing paradigm by including if/then nodes in the tree? Say, a node that has three child nodes/subtrees, and chooses between two of them based on the value of the third? And then (in some genetic-programming-like approach perhaps) explore what happens if you copy those subtrees elsewhere, or existing subtrees into new if-then nodes?) (I can imagine the horrific unreadable mess already though...)
edited to add: it might be more appropriate to say that I had been planning on asking an AI to code something, but the initial prototype was sufficiently lame and gave me enough insight into the difficulties ahead I didn’t continue. Claude chat link if anyone’s interested.
edited to further add: hmm, what you are wanting (“new variable”) is probably not just preserving a subtree, but for the mutation system to be able to copy that subtree to other parts of the tree (and the complexity calculator to not give to much penalty to that, I guess). Interestingly, it seems that PySR’s backend at least (SymbolicRegression.jl) does have the capability to do this already, using a “form_random_connection!” mutation function that apparently allows the same subtree to appear as child of multiple parents, making a DAG instead of a tree. In general, I’ve been pretty impressed looking at SymbolicRegression.jl. Maybe other symbolic regression software is as feature-rich, but haven’t checked.
1. ^
  Apparently November 2024. Feels longer ago somehow.
2. ^
  I hadn’t actually gone beyond breadth-first search though.
3. ^
  This is informed by (a tiny amount of) practical experience. After SarahNibs’ comment suggested genetic programming would have worked on the “Arena of Data”, I attempted genetic programming on it and on my initial attempt got … a horrific unreadable mess. Maybe it wasn’t “halfway decently regularized” but I updated my intuition to say: complicated ways to do things so greatly outnumber the simple ways that anything too reliant on randomness is not likely to find the simple way.

simon 29 Apr 2025 17:42 UTC
2 points
0
in reply to: aphyer’s comment on: D&D.Sci Tax Day: Adventurers and Assessments Evaluation & Ruleset
And just now I thought, wait, wouldn’t this sometimes round to 10, but no, an AI explained to apparently-stupid me again that since it’s a 0.25 tax rate on integer goods, fractional gold pieces before rounding (where not a multiple of 0.1) can only be 0.25, which rounds down to 2 silver, or 0.75, which rounds up to 8 silver. Which makes it all the more surprising that I didn’t notice this pattern.

simon 29 Apr 2025 5:42 UTC
6 points
0
on: D&D.Sci Tax Day: Adventurers and Assessments Evaluation & Ruleset
Thanks aphyer, it was an interesting puzzle. I feel like it was particularly amenable to being worked out by hand relative to machine learning because of the determinism, rules easy to express in a spreadsheet, and simple subsets of the data (like the special cleric bracket) that could be built on.
This is resolved using python’s round() function...my apologies to simon, who seems to have spent a while trying to figure out when it rounded up or down.
I don’t recall that taking all that long really, I added one monster part type at a time (much like the main calculation but much easier since it’s just binary and only for the special 5U+ tax bracket, so less interactions to worry about).
Funny thing is, after seeing the calculation I still didn’t understand why it rounded the way it does, until I asked an AI which explained that Python rounds to even numbers on ties (apparently called “banker’s rounding” or “banker’s rule”). The only source of non-integer values is U which provides a single factor of 2 in the number of silver pieces, resulting in all rounding being of numbers with 0.5 in the remainder of silver pieces and so applying this rule. The other monster parts provide 2 factors of 2 of each, not directly causing rounding but each one incrementing the tax by 1 silver (modulo 2 silver) and thus changing whether this rule rounds up or down (except 2nd and up dragon heads which provide 3 factors of 2) .
Amusingly, I could have much more simply expressed this rounding rule as “if rounding is required, round to the nearest even number of silver pieces” but I wasn’t thinking about it in terms of output, so missed this and expressed it much more complicatedly in terms of the input. Oops!
if taxed_goods[‘U’] >= 5: tax_rate = min(tax_rate, 0.25)
Ah, makes sense that this would be its own special tax rate rather than the 50% bracket with a X2 discount (which amounts to the same thing in the end). That min though with the tax rate from other sources is another thing that was never triggered (and literally couldn’t be triggered since 5U alone is enough to get to the 30% bracket and also prevents eligibilty for the cleric bracket).

simon 17 Apr 2025 16:58 UTC
9 points
0
on: D&D.Sci Tax Day: Adventurers and Assessments
Thanks aphyer. Solution:
Number of unique optimal assignments (up to reordering) (according to AI-written optimizer implementing my manually found tax calculation): 1
Minimum total tax: 212 (err thats 21gp 2 sp)
Solution 1:
Member 1: C=1, D=1, L=0, U=0, Z=4, Tax=0
Member 2: C=1, D=1, L=0, U=1, Z=1, Tax=0
Member 3: C=1, D=1, L=0, U=1, Z=1, Tax=0
Member 4: C=1, D=1, L=5, U=5, Z=2, Tax=212
Tax calculation:
1. Add up the base values: 6 for C, 14 for D, 10 for L, 7 for U, 2 for Z
2. If only L and Z, just take the total base and exit.
3. Otherwise, set a tier as follows: tier 0 if 0 < base < 30, tier 1 if 30 ⇐ base < 60, tier 2 if 60 ⇐ base < 100, tier 3 if base >= 100.
4. If U >= 5, then use the max tier regardless (but a 2x discount is also triggered later).
5. If D >=2, then increase the base as if the extra dragons beyond 1 are doubled. This doesn’t change the tier.
6. multiply the base value by tier + 2
7. If U >= 5, divide by 2
8. Discount by 60*Ceiling(C/2) (can’t go below 0)
Rounding is needed if U is an odd number >=5. To determine if you round up or down, add up the numbers for C,L and Z, add to (U-1)/2, plus 1 if there is at least one D. Then round down if that number is odd and up if it is even. (Presumably this arises in some more natural way in the actual calculation used, but this calculation gives 0 residuals, so...). Todo: find a more natural way for this to happen.
Post-hoc rationalization of optimal solution found: giving everyone a C helps get everyone an up to 60 tax credit. Spreading the D’s out also prevents D doubling. The C and D add up to a base value of 20. We can fit up to 9 more base value without going to the next tax bracket; this is done using 4Z (8 base value) or 1U 1Z (9 base value). The last member has to pay tax at the highest bracket but U=5 also gives the factor of 2 discount so it’s not so bad. They get everything they have to take in order to not push the others above 29 base, but no more.
This seemed relatively straightforward conceptually to solve (more a matter of tweaking implementation details like D doubling and so on - I expect many things are conceptualized differently in the actual calculation though). I went from the easiest parts (L and Z), then added U, then looked at D since it initially looked less intimidating than C, then switched to C, solved that, and finally D). It would have been much harder if it were not deterministic, or if there wasn’t data within simpler subsets (like L and Z only) for a starting point.
The ultimate solution found is 12 sp better than the best solutions available using only rows that actually occur in the data (also found using AI-written script).
Tools used: AI for writing scripts to manipulate CSV files and finding optimal solutions, etc. LibreOfficeCalc for actually looking at the data and figuring out the tax calculation.
Additional todo: look at the distributions of part numbers to try to find out how the dataset was generated.
edited to add: my optimizer used brute(ish) force, unlike DrJones’. It uses double meet-in-the-middle (split two ways, then split again) with memoization and symmetry reduction using lexicographical ordering (symmetry reduction and memoization was optimization added by AI after I complained to it about the time an initial version, also written by AI, was taking).
P. S. I used GPT-4.1 in Windsurf for the AI aspects. They’re running a promotion where it costs 0 credits until, IIRC, April 21.

simon 3 Apr 2025 18:53 UTC
21 points
2
in reply to: Mateusz Bagiński’s comment on: Why Have Sentence Lengths Decreased?
FWIW there is a theory that there is a cycle of language change, though it seems maybe there is not a lot of evidence for the isolating → agglutinating step. IIRC the idea is something like that if you have a “simple” (isolating) language that uses helper words instead of morphology eventually those words can lose their independent meaning and get smushed together with the word they are modifying.