Posted: Dec 20, 2012 12:48 pm
CarlPierce wrote:i've been trying to derive the equations for the probability of a cuboid dice landing on its six faces if the X,Y,Z lengths are not equal.
I don't think it is so simple as being proportional to the area of the face.
Interesting question. The probabilities will depend on the position of the center of mass. The dice is more likely to land on the side for which the center of mass is closest to the ground. I don't know how to calculate the odds, though.
EDIT: I found a discussion about this: http://physics.stackexchange.com/questions/41297/how-to-determine-the-probabilities-for-a-cuboid-die