I've recently become fascinated by the idea of a role-playing game system that involves advanced math.
By advanced math (admittedly, a very vague description), I generally mean that it should involve mathematical concepts such as vectors, matrices, and integration. I don't necessarily mean it should be unreadable to anyone who isn't a mathematician.
Here are a few specific concepts that might feature in such a system:
- A system that defines damage as the integral of attack over time.
- A system in which chances of success are represented using concepts from probability theory (e.g. probability distributions)
- A system that defines mathematical, quasi-physical laws that determine how the world behaves.
- One where some outcomes and effects are resolved by the application of matrix multiplication.
- A magic system that is described using complex numbers, vectors, or similar.
To clarify, I'm looking for a system defined using these concepts, not one that can be analyzed and partially represented using these concepts. D&D for example can be analyzed, and this analysis may include terms such as 'probability distribution'. However, the game itself still involves rolling dice and adding modifiers.
I don't mean that the system should have a large amount of convoluted calculations, or very long numeric tables.
The game doesn't have to be playable in practice, though it would be nice if it is. I would also be interested in the system if it was designed to be implemented by computer.
I'm almost certain such systems exist, basically because I've seen similar treatments of fictional subjects and games on the internet (e.g. explicit details of the physics in a fantasy world, a proof that Magic: The Gathering is Turing complete).
Is anyone familiar with such a system?