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But what do you think physicists do all day? Exactly what you just described. Unfortunately we pretty much have the answer, and it's kind of a resounding NO. Look up "local hidden variable theory".

Lets not put pollute this discussion with that piece of wishful thinking :)

please read Anathem http://www.amazon.com/Anathem-Neal-Stephenson/dp/0061694940/... (if you've not already) I think you will enjoy it :)

[edit: removed wikipedia link... too many spoilers :(]

In that case it turns out that some extremely simple intuitive rules can generate some very unintuitive results. Those results may perhaps best be approximated by extremely complicated mathematics. c.f. chaos theory and turing equivalent 1-d cellular automata.

I can't see any basis on which to assign the probabilities you ask for. A better question might be: on what basis do you believe that the universe should be intuitive? Why should it be so?