I'm working on a project involving non-standard dice where each face can have a different size, but the overall shape and weight distribution of the die are uniform. I'm interested in finding out how to calculate the probability of the die landing on a particular face based on the size of its faces.
Assumptions:
- The die maintains a uniform shape and weight distribution.
- The die has 'n' number of faces, each potentially with a different area.
- We ignore the complexities of rolling dynamics and assume the die lands flat on its faces.
I am looking for an equation or a model that can accurately calculate the probability of landing on a face, given the area/dimensions of each face.