Even this wouldn't be random if you could model the exact trajectory that you threw the dice, you know the exact function of the fluid the dice if moving in, the landscape surface on the table, density of dice, it's elasticity, loss of energy due to bouncing/friction, ....
This isn't entirely true. Starting with an over-simplyfied model, you can see that in some cases the die roll will be random, and others it won't be. Starting with a very unrealistic model, I drop the die, from a dead stop, with no rotation on it from about 1 mm in height. Its obvious the die will just fall and roll to which-ever side is closest to straight up. So it looks very deterministic. However, there are some unstable solutions as well. If I dropped with the the center of gravity directly over a vertex or edge we find that we are at a bondary point. In a perfect newtonian system, the die would come to rest on the vertex or edge, but in practice what we have is a boundary condition where a small perturbation in initial state will change the outcome. Around these points a physical system can be affected by apparently insignificant variations and quantum affects.
Now it would be a bit silly in insisting on calling the dropping of a die a short distance with no rotation random, when the initial conditions that produce uncertainty in the results is such a tiny portion of the whole.
But what happens if you know roll the die from higher up, with spin onto a somewhat elastic surface. The interaction of the die with particles, like air molecules on the way down will cause a small uncertainity in the velocity, angular momentum and angle it has when it hits the surface. This uncertainty may be very small, but it will grow each time it bounces. For one, angular momentum it has when it rebounds depends on the angular momentum it had when it touch down, the angle and the velocity it hit at. In the same way, the velocity it has when it rebounds will also depend on the state of the three variables at impact. The affect is that the uncertainity it has on rebound will be much larger than that on impact. Since the die will bounce multiple times, the uncertainty grows.
As your uncertainty grows the set of initial conditions that produce random results grows, and the set of initial conditions which yield predictable results shrinks. Now a die and a single surface is a fairly simple system, so I don't know how high you would have to drop one from to get it so that the majority of initial conditions would lead to random results.
In relation to evolution, many physical system are sets of coupled, non-linear sub-processes which can lead to
Chaotic behaviour. When random elements are adding to chaotic systems, the uncertainty will be amplified, so instead of getting a determistic type result with some small amout of noise, one can get results that are genuinely random at the macroscopic level.
Walt
P.S. Seems this thread has started to grow like the others. Some other things I like to respond to, but don't know if I can get to it before this thread is pages on.