I’ve been slacking in collating examples of maths i.r.l.
But sometimes it’s easy.
Skyrim, like any Dungeons & Dragons system, has to model certain aspects of reality.
- how likely you are to encounter a random group of bandits on the road
- what are the relevant attributes of a person?
Somewhere the computer stores some tuple that represents everything it knows about your character.
- whether someone likes your character or not
«let me see here … Nice to meet you, Fry.»
- how telepathy works. (What happens if you try to read a horse’s mind?)
- how battles work (will there be hit points? will there be
- how learning, or training works.
The result of the models must be balanced, believable, and fun.
After dragooning your GPU into computing a couple billion triangles per second on the graphics side, the designers of Skyrim decided to go easy on the maths they use to model learning of skills like
- two-handed weapons
. They use a different binomial for each skill.
determines how hard it is to get from “level 5 → level 6” versus from “level 78 → level 79”.
In addition to choosing a paradigm (existence of “levels of alchemy” and “experience points in alchemy”) and calibrating attainment grades, the game designers had to decide how much XP to reward per action.
Here again a binomial per skill, eg smithing:
25 + (3 ∗ item value0.65)base XP for constructing an item.
25 + (8 ∗ item value delta0.6)base XP for improving an item.
Relating this to maths terminology,
25would be the affine
y=mx+b, allowing them to put a floor on each smithing experience;
- "Learning" is modelled by repeating a map.
3 ∗ 0.65, the derivative around
item value=1, would be the first
min a sequence of declining
- Three parameters; that’s almost enough to fit an elephant! And yet the designers made a hit game.
0.65 < 1as an exponent makes learning concave in splendiferousness of the item crafted; repetition is more important than making one spectacular thing.