[rprospero]

That's a good question and you're actually pretty close to the right track. The catch is the difference between the wave function and the actual measurement. Quantum mechanics and Schrodinger's equation gives us the wave function. If you know the current wave function, there's a well established way to calculate the wave function at a future point in time.

The catch is that the wave function doesn't tell us values - only probabilities. So knowing the probability distribution at any given point in time doesn't make anything less random because it's all still probability and not actual measurements.

As an analogy, imagine a casino where the roulette wheel has an LCD label for each number. Each round, they change the layout of the wheel. Sometime, they make all the labels black. Other times, it's 2/3rds red and all the numbers are primes. They also have a big book in the corner that tells you what the layout of the roulette wheel will be each round. As a result, if I put down a bet, you can tell me the odds of my bet coming up each round. However, you still can't actually tell me what will WIN the round.

The layout of the labels is like the wave function, the pages of the book are the time evolution operator, and the roulette ball is the fundamental randomness of quantum mechanics. The results are still random, just as Bell said that they must be, but we are at least allowed to know the odds.