Is it really impossible to calculate in advance the result of throwing dice? After all, the physics of dice throwing is in the world of classical mechanics, rather than quantum mechanics.
This question was studied fairly recently by a team at Edinburgh University. Their paper is available here, though I'm not sure if you can get it without having to hand over some cash.
The bottom line is that in principle the trajectory of a die can be calculated, but it is a chaotic system and that means tiny inaccuracies in the measured initial conditions lead to large changes in the final state. In practice it would be impossible to measure the initial translational and rotational velocities accurately enough to make useful predictions.