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Joy, I think 'little box' is an apt metaphor. Probability is without a doubt the least understood branch of mathematics -- and even less understood when applied to physical phenomena.
One has to be reminded that to calculate probability, what one puts into the box determines what one gets out of it. When actual physical results turn up more than the box can hold, one is compelled to assume that one created something (entanglement) that wasn't in the box before one made a measurement (nonlocality).
Take the calculation of the constant Pi by the Monte Carlo method:
It is only because we know that the value of Pi exists before we describe the statistics by which Pi is a solution to the condition we have set (pi = 4M/N) for a circle we have prescribed, that the method generates to any arbitrary accuracy the value we know to exist as the exact solution to the equation.
When we do the same thing with Bell-Aspect results, we are only getting confirmation of our assumption of entanglement and nonlocality. We specified the conditions and we got the solution we asked for.
Problem is that the universe doesn't live in a little box. There's no 'pi in the sky' as John Barrow put it. We can't impose our mind's conditions on nature's structure and say we have 'found' something that wasn't there.
(By the way, Peter, the foregoing illustrates exactly why your program doesn't work.)