Sure, but what are the odds the universe fundamentally defies intuitive logic versus the odds our small brains currently can't see the full picture but in the meantime have invented insane (but cool) mathematical machinations? I guess it's unknowable.
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".
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?
