This is a followup to the D&D.Sci post I made ten days ago; if you haven’t already read it, you should do so now before spoiling yourself.

Here 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.

Ruleset

Below is a summary of how the dataset works; full generation code is available here.

(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”.)

Mana types

Solar

Solar is the strongest and most complicated mana type. It can be decomposed into an average (40), a small amount of random noise (+ 1d2 - 1d2), two seasonality components, and the effects of distant supernovae.

The power of Solar on Day 384 is 45 + 1d2 - 1d2

Lunar

The moon reflects and inverts the effects of the sun, with a delay. It provides a power of 75 minus the amount of Solar power 14 days ago.

The power of Lunar on Day 384 is 16, because the power of Solar on Day 370 was 59.

Earth and Ocean

Earth and Ocean combine to create the World. World Mana can be decomposed into an average (68), some random noise (1d4 - 1d4), and a seasonality effect.

On a given day, Earth takes (15+1d80)% of World Mana, rounded down; Ocean gets the rest.

The combined power of Earth and Ocean on Day 384 is 77 + 1d4 - 1d4.

Breeze

The breeze varies, as does its variance. It is composed of an average (13), and some random noise which varies seasonally (1dN - 1dN, where N is given in the graph below).

The power of Breeze on Day 384 is 13 + 1d4 - 1d4

Flame

Flame catches, sputters and starts, building and waning randomly. Today’s Flame mana is yesterday’s, minus 25% (rounded down), plus the lowest of two d20 rolls.

The spread of possibilities at Day 384 looks like this:

Ash

Ash is what remains when Flame is extinguished. Today’s Ash is the 25% removed from yesterday’s Flame.

The spread of possibilities at Day 384 looks like this:

Void

Void is timeless; all motion within it is random, and all apparent trends or correspondences are merely noise. The power of Void on Day 384 – and all other days – is 24+1d8-1d8.

Doom

Doom builds gradually, then diminishes sharply as it is fulfilled. On a typical day, it can be decomposed into a starting point (24), some random noise (1d6), and a jagged seasonality effe...