This was my intuitive reasoning (in much more naive terms) in H.S. But now I think it's not so clear even under the inelastic model's assumptions. One would need to show, I think, that in a random selection of initial conditions from a reasonable probability measure on them, the resulting measure on the position in S^2 of a normal vector to a given face is the uniform measure on S^2. That this is true isn't obvious to me. --Dan On 2012-09-21, at 4:53 PM, Allan Wechsler wrote: . . .
In "the inelastic model", at the moment that the die first contacts the table, all kinetic energy is dissipated: a perfectly inelastic collision. The die stops dead in space, and then topples onto the face under its center of gravity. Under this assumption, it's fairly clear that the probability associated with each face is proportional to the angle subtended at the center of gravity by that face. . . .