Sacred Geometry is a feat that lets you add metamagic to your spells without increasing their level (instead you raise the casting time a la spontaneous caster metamagic) if you roll a certain way on Knowledge: Engineering.
The mechanic for doing this is the following: You roll a number of d6 equal to your ranks in Knowledge (Engineering). You then see if you can create an arithmetic expression that yields certain prime numbers. The specific target primes are different depending on the modified level of the spell you are trying to cast.
I can't actually imagine using this mechanic in actual gameplay, since it either requires you to pause the game for three minutes while you add up dice, or write a program to do it for you.
So here's the program to do it for you.
If you want to build the arithmetic equations in addition to just doing sacred geometry calculations, download from source. This code is written in Rust (partially as an exercise in learning Rust, so please pardon my syntax).
./sacred_geometry ranks spell_level
or
To use the solver, run ./sacred_geometry ranks spell_level. For example, for
a caster with 8 ranks in Knowledge (Engineering) casting an effective 9th-level
spell, run ./sacred_geometry 8 9
The output will look something like this:
$ ./sacred_geometry 8 9
Die rolls: [6, 2, 4, 6, 4, 6, 1, 6]
101 = ((((6) * ((4) * (((6) * (6)) / (2)))) / (4)) - (6)) - (1)
I ran 100 trials for each effective spell level from 1-9 and each number of ranks between 1 and 10. (You start really feeling the exponential increase in runtime after 10 ranks.) Here are the reuslts:
-
A brute-force solver for sacred geometry. The brute force solution has exponential runtime in the number of ranks you have; it takes a prohibitively long time when you start using higher numbers of skill ranks.
I used this algorithm to solve this problem. -
An analysis of how many ranks you need to make Sacred Geometry good. You really don't need more than 7 ranks (8 to be safe) to make this feat succeed nearly every time. If you take Sacred Geometry, get eight ranks in Knowledge (Engineering) and call it a day.
-
Eventually, this will contain an analysis of the arithmetic problem itself. This problem feels like it might be NP-complete, but I haven't managed a reduction yet. But it feels like it should reduce from subset sum or 3SAT.
As always, comments and criticism are always welcome. I especially welcome any comments on my Rust, which is a new language for me.