Let's say you're doing the double slit experiment with a very low flux beam so that one particle is showing up on a scintillation screen at a time. It is well established that the statistics of the system are such that a large number of screen hits will result in an expected pattern: waves or particles depending on the way the experiment is conducted. Sending one through at a time, the particles seem to show up randomly because the pattern (probability amplitude) only becomes apparent in the statistics of large numbers. Given some random pattern of 10 screen hits, it would be a big improvement on the current theory if we had some way to predict where the 11th hit would come. As it is, it appears to us that "God is playing dice" because there is no way to predict where the next particle will show up. The question of whether or not God plays dice, however, asks whether the physics is truly probabilistic in nature, or whether out inability to predict the position of the 11th hit reflects our ignorance of such things as the alignment of the beam on the slits, etc.
Often one responds to the question about God playing dice by with another question, "If we have no way to compute what God is really doing, what does it matter if he plays dice or not?" Personally, I like the Einsteinian predisposition towards determinism. However, I think incomplete knowledge of experimental devices will always result in probabilistic outcomes whether God is playing dice behind the scenes or not. For instance, given a large enough pachinko machine, pic, it will never be possible to ensure the token lands in the same slot in every run. So, even if we had a better theory which does not imply that God plays dice, our experimental results would look exactly as if God was actually playing dice due to systematic uncertainties.
I share Einstein's view that ther's probably a better theory than QM but I don't expect the better theory to stop using the probability amplitude as its dynamical object.
