Hi, We normally use a simple symmetry argument to show that the probability of each outcome of a throw of a fair, cube-shaped die is 1/6. However, is it possible to actually model the physics of the throw and show that the probabilities are 1/6? Since this is classical physics, the outcome can in principle be predicted knowing the inital conditions of the throw. So I guess we'd have to show that very similar initial conditions lead to any of the six outcomes. A numerical simulation of the throw might get nasty, but maybe there's a simpler chaos-theoretic argument?