Data Generation

The World

The world has five locations. I loosely imagined the Thunderwood Peaks as a northern mountainous region, the Lordsteppes as a plateau in the west, the Miresmouth Forests as a southern marsh, the Scorchsand Shores as an eastern coastal desert/beach region and the Devil's Maw as a large chasm in the middle of the region at hand. This sort of influenced the flavours of the monsters.

As noted by a few players, weeks 7-19 are spring, weeks 20-32 are summer, weeks 33-45 are autumn and weeks 46-6 are winter.

Monsters

Monsters come in four sizes: small, medium, large and legendary. The first three sizes will be referred to as "standard". They also have a genus: serpent, beast, avian, or drake.

Standard monsters have one of the six elements. They also have a diet which can be carnivore, herbivore, omnivore or scavenger.

Standard monsters have either one or two habitats, carnivores migrate to a secondary location to hibernate in the winter. Herbivores migrate to a secondary location to breed during the summer. Omnivores are found in two places and scavengers in one.

An exception are toxicalas which disappear in summer. In universe this is because when breeding they never leave the treetops so no tracks are left. Out of universe it's because I didn't check my master document or data well enough.

Another exception are thunderclap wyverns which are actually only found in the Lordesteppes, once again technical issues.

There are some restrictions I liked to stick to. All serpents and most drakes are either carnivores or scavengers.

Legendary monsters don't have a "diet" and have two elements or no element. They're species of myth and mystery. Legendary monsters also have weird patterns of movement.

Crows That Break The Sky are migratory. They rotate through four regions by season, spending spring in the Thunderwood peaks, summer in the Lordesteppes, autumn in the Miresmouth Forests and winter in the Scorchsand Shores. Their elements are ice and fire.

Sliding Queen Shashes show up for weeks 3 in autumn in the Devil's Maw, followed by 6 weeks in the Miresmouth Forests, then back to the Devil's Maw for 3 weeks. They're not found outside of then as they hide deep in the caves. They have the earth and poison elements.

Bull-Kings of Heaven are actually on an 11-week cycle as their herd tramples around the earth. Then they're found in the Thunderwood Peaks, Lordesteppes, and Scorchsand Shores sequentially. Their elements are thunder and wind. The herd are passing through on weeks 12-14 of this year which makes them an excellent target.

Biologists

The biologists send out three trackers per week. They abide by "ancient rules" which suspiciously correspond to never sending a tracker out to a location where a legendary monster is present. This means they never find tracks of those. They also never find evidence of the raging windriders which never land.

What they do find is a totally random sample of all available tracks present in the region, which is good.

Their "total knowledge" isn't great. They don't know how big any serpents are as they just leave long trails for tracks. They barely know anything about earthmovers as they just leave piles of mud, etc. They don't know a few of the monsters elements. Their knowledge of the legendary monsters is quite poor.

Hunters

I'm not sure how smart our hunter is really. Every week she picks a location, weapon, and armor completely randomly.

Encounters are decided based on an "aggression" variable. For herbivores its 1 all year except being 3 in spring (they're establishing territory before mating). For carnivores its 1 all year except being 3 in autumn (they're stocking up on food before hibernation. For omnivores it's 3 in one location and 1 in the other. For scavengers it's always 1.

Most Legendary monsters have 10 when they show up. They're pretty angry. Crows that break the sky only have 2 since they're around all the time and I didn't want them to become crows that break the encounter rate.

Fights

Each fight is determined by choosing a random number uniformly distributed between 0 and 1 a number of times for each party, and whichever side gets the highest total wins. Hunters start with n = 3, and monsters start with n = 1, 2, 3, or 5 depending on size.

Elements can also give you +/- 1. The attacker gets +1 if their attacking element beats the defending element and -1 vice versa. Monsters use their element(s) for both attacking and defending. Hunters use their weapon for attacks and their armor for defence. For legendaries the two modifiers are just added together (so a +1 and a -1 cancel out, and two +1s make a +2). Certain elements are therefore incredibly effective against some of the legendary monsters.

The element chart is as follows, an arrow means that element X beats Y (and correspondingly Y loses to X):

Poison, stone, and cold weapons/armor are the best for unknown targets, but for Crows (which a couple of people decided to target) they're all neutral or bad. Taking a mixed set sometimes has marginal advantages because it makes you less likely to lose to small/medium monsters compared to taking a matched set (losing two elemental matchups is less likely than losing just one).

Using a sword against a beast or avian gives you a +1, using a bow against a serpent or avian gives you a  +1. Hammers are big and unwieldy and really if you hit your opponent once you win, but if you miss your first swing you lose the fight. This means using a hammer gives you and your opponent a +100, which eliminates a lot of advantages. This will come into play later.

Here's a rough estimate of win probability for a few different cases (n = 100,000 Monte Carlo simulations)

Weapon advantage means having the advantageous weapon element/type. Double weapon advantage means having both.

Also, it's possible to have a +3 weapon and +2 armor advantage against the Bull-Kings of Heaven and Sliding Queen Shashes. This gives a win chance of 96%. This isn't possible against Crows That Break The Sky.

The Ivory Drakewyrm

This was perhaps a touch unfair. Whoops! Simon, Yonge, and Measure all noticed the pattern in the biologists movements and were so close to finding this.

There's a legendary drake which shows up once a season on weeks which are a multiple of 13, "opposite" to the Crows (Miresmouth Forests week 13, Scorchsand Shores week 26, Thunderwood Peaks week 39, and the Lordesteppes week 52). It has no element which makes it much harder to deal with. It's not been successfully hunted or tracked. The best shot for killing it would be any hammer.

I was also in a troll-ish mood when I came up with the idea to have five of every other genus but six drakes.

Scoring Method

Monsters are worth points based on size and rarity. Size points are 1, 2, 3, and 6 for small, medium, large, and legendary monsters respectively. Rarity points are based on ranking all of the monsters the biologists have seen (or not seen) and giving points based on that. 6 points for a legendary, 5 points for something they've never seen, then 4 for the rarest four, 3 for the next four, 2 for the next four and 1 for the most common four. The exception is that an Ivory Drakewyrm is worth 8 rarity points as they don't even know it exists. Here's a chart of monster points:

Plus repeat monsters count for less.

Key monsters to go for are the Ivory Drakewyrm, other legendaries, the Raging Windrider, Macrophants and Thunderclap Wyverns.

Evaluation

These evaluations are based on Monte Carlo simulations, n = 100,000. The benchmark for "optimal" play is my own attempt at findingthe best strategy based on knowing 100% of the generation and scoring, with a few test runs to check. I also include the expected score of a random strategy.

Here's the number of monsters of each type each player could expect to hunt:

"Optimal" play was to spend the first three weeks hunting for crows taking a fire sword and lightning armor first to the scorchsand shores, the moving to the thunderwood peaks for two weeks. Taking a balance of weapons/armor improves the variety of monsters hunted. Then spend four weeks in the lordesteppe with the poison bow and poison armor, which is effective at most things there. The first three weeks we're hunting for thunderclap wyverns and macrophants, the fourth we're hoping for bull-kings. Then take any hammer and armor (I went with poison as it's generally just a powerful element) to the miresmouth forests to hunt for ivory drakewyrms. Then scorchsand shores with poison bow and armor to go for another shot at the bull-king. Same the next day as we also have a chance to bag raging windriders there. This is far more complex than any reasonable person could have worked out so anything approaching 40 I consider to be an excellent score.

I think the biggest pitfall anyone fell into was repetition. Returns on almost any area fall off hard after a few visits. This also makes random play unusually effective as a strategy compared to a lot of puzzles. An empirical-ish strategy of just taking good-looking gear to good-looking areas outperforms most attempts to optimize for anything unless you know a lot about the generating system.

Reflections

I have zero previous experience with puzzle design so I'm pretty pleased with how this has turned out overall. All of the contestants did better than random and there were only two technical glitches, neither of which turned out to be serious.

As usual for novice puzzle designers it was probably more complicated than optimal. I think the hammer mechanics were arguably the most difficult to guess, and the weapon/element mechanics in general were probably too much given the relatively small amount of data available. I was hoping that working these out would be possible based on the aggregate of data but in retrospect it wasn't obvious enough what to even look for.

I plan to do some more of these in future. In that case I'll definitely consider the amount of data given relative to the number of possible hypotheses. I should have at least run a few statistical tests on the data to see what information can be pulled from it.

I' also wish I'd considered what a good answer should look like. I wish I'd come up with a way to express the scoring system more clearly, as I didn't want to say "by the way just so you know if you find a monster that nobody's seen ever you'll get more points (hint hint)". This made it harder for players to optimize.

Thanks for playing everyone and congratulations to Measure for winning! (and Simon for coming second by just 0.2 points!)