the histogram of snarks by waking-time as a mixture of gaussians

there are 2+ classes with very high variance, polluting everything, or maybe some snarks have a different distribution with a longer right tail than normal.

Looks like we don't hunt Crumbling and are strongly biased against hunting Blunt, so maybe I'll just keep to conventional wisdom there. Of the remaining, very close to exactly 3% aren't hunted, with no discernible correlations? Maybe that's just the baseline "don't hunt this" chance.

First remove all Crumbling and Blunt, then Just pretend you can treat every variable as independent, then pretend you can treat every pair of variables as independent after accounting for first-order effects. Grab log-likelihoods and smush them all together.

Not sure how many to hunt, but in this order:
['V', 'Y', 'G', 'P', 'Q', 'L', 'H', 'W', 'C', 'M', 'B', 'N', 'J', 'R', 'D', 'X', 'K', 'F']

The two suggested criteria would lead to either
['V', 'Y', 'G', 'P', 'Q', 'L'] (maximize my survival), or
['V', 'Y', 'G', 'P', 'Q', 'L', 'H', 'W', 'C', 'M', 'B', 'N', 'J', 'R', 'D'] (maximize snark count EV)

Had I submitted in time, I probably would have chosen to stop at either H, W, or C, because my estimated boojum probabilities have an inflection point there. If I were trying to "beat" everyone else, I'd have stopped at C; if I were ignoring everyone else, I'd have stopped at H, which, interestingly, is only one more snark than the bare minimum.

So, how many species are there?

Hum, about 12 ? Probably at least 8, maybe up to 20, or even more, I don't really know

One interesting point, it looks like there is one species, the Goojam, (or maybe 2 Goojam species), which always attacks, while all other species never attack. I.e. $k$ only contains ones and zeros. This is not something I anticipated, it appeared when running my code, but it makes sense, so this might confirm the approach

BPGYHQ should be the set of 6 letters minimizing the probability of death

The letters, in increasing order of danger, are BPGYHQTSVINRDMKLOJUACWXEF, with BPGYHQTSVINRDMKLOJUACW (without XEF) being the solution maximizing the expected return, at least according to my models

If this is true, the pareto frontier is exactly the set of prefixes of this word, but since one can only submit one word for the bonus task, I will submit BPGYHQTS, a word of length 8 with a very low probability of death

It is remarkable to see that I find similar results to Yonge, despite having wildly different approaches!

baseline  was just the numbers of snarks vs. the number of boojums for cases where all data was the same except waking time, then I fudged based on:

• if there are few or no boojums, see what numbers you get if you relax the non-taste characteristics one by one
• is the waking time typical for a boojum? for a snark? can relax multiple non-taste characteristics for more data
• If Crumbling, I assumed that the early part of the Crumbling distribution is probably snarks and the late is probably boojums, see below. Though, I wasn't actually confident enough to pick any Crumbling ones.

Also, I tried to figure stuff out about the nature of the dataset but didn't end up with particularly actionable information; I did come to a strong suspicion based on comparing the  Crumbling data with the Blunt data that the late Crumbling ones are boojums and the early ones are snarks, but I wasn't confident enough in this to actually pick any Crumbling ones.

The Snarks, so it seems, know just when to wake up;

From one beyond seven, the sun's nigh still up!

But the graph of those times, it hops and it hops:

A possible sign of some smaller sub-pops!

One-forty, two-thirty, two-fifty or so,

These are some peaks one can spot on the go.

But there looks like a broad one whose lateness abounds,

Though it could be a mishmash of all groups not found.

Four-fifty the top of another small mound.

And the Boojums, you see, don't quite seem to respect

The waking-time patterns that one would expect.

But enough of the times - on to matters of Taste!

It looks like the Crumbling ones all go to waste!

But the Crumbling wake times! - one peak is at two,

And it doesn't line up with the Snarks one can view.

Another one peaks around four thirty-five,

Are they from the broad set of Snarks found alive?

But that seems to peak quite a lot before then,

Unless I am missing a time where again

Some Snark group decidedly tends to revive,

So why take the risk if you like to survive?

The Snarks that are Artless are heaped to be broad

With some showing up in the two thirty pod,

Especially when they are Crisp as a pier,

But looking at those that are Neat and are Clear,

The peaks don't line up! Could it be that these here ...

The unsolved issue being - does each sub-population have a consistent wake time distribution regardless of other characteristics individual members may have, or do the other characteristics alter the wake times? I was implicitly assuming the former, but I didn't follow up to really convince myself that this was the case.