Back in H.S. I wondered about this for any polyhedron, and guessed a face's probability of landing down is proportional to the solid angle it subtends from the center of gravity. That might be almost true if it landed on a soft surface, but for a hard surface there might be other things to consider. --Dan On 2012-09-20, at 5:48 PM, Veit Elser wrote:
On Sep 20, 2012, at 11:20 AM, Warren Smith <warren.wds@gmail.com> wrote:
--Here's a different problem: Devise a convex polyhedron with 5 faces, such that the probability it lands on each face, is 1/5. I have a solution in mind which in fact works for any number N>=4 of faces (here N=5), although I'm not sure whether we should accept my solution. The question inside the question is: "what is the right probabilistic model?" And the answer inside the answer is not so obvious to me.
--Warren D. Smith
I made a 2-sided dice (a right circular cylinder) that is fair according to a simple physical model and proved to be fair in actual experiments.