No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.

Sorry but, few or many, no hidden variables can account for the randomness in QM. It looks like it really is random in the proper sense of the word.

(This may be a bit off topic, but since I thought it up, I should write it down somewhere.) For those that can't imagine how randomness can lead to apparent determinism, thry this. Imagine a truly random coin. (Not a physical one, which would be more accurately described as chaotic.) Imagine a particle that would move left on heads or right on tails. From one moment to the next, you wouldn't be able to predict where that particle would be next. Now imagine a ball composed of 100,000 of these particles. Connections between them mean that they pull each other around when one moves. Now after 100,000 coin flips, very nearly 50,000 went left, and the rest went right. That means that the ball, as a whole, barely moved, if at all. So even if you can't predict how each particle in the ball will move, you can say that, overall, the ball won't move. Of course, it's still possible for all 100,000 coins to come up heads causing the ball to suddenly jump to the left, but it's not likely.