I didn't understand you from the first post - either in this thread or any other one. I don't understand the gist of it and I certainly don't understand the particulars.
I'm not aware that anyone uses a program in an attempt to prove or disprove god. I would a priori doubt the conclusions of any such program.
In computers, I think the closest we could come to truely random distribution would be hooking it up to a device that measured some supposedly random event - like decay of a particle.
Most computers opt instead to use what is called a Pseudo-random number generator, or PRNG. A PRNG gives numbers that meet certain criteria that we expect to see in random numbers, but are actually derived from a mathematical algorithm.
For most purposes - whether gaming, or scientific research - this is sufficient, and even desirable. It is sufficient because it gives the sort of results that we expect in the outcome and it is desirable because it gives us something that we really like in science - repeatability. In a sense, a PRNG is a simulator. It simulates an RNG (or true Random Number Generator).
The PRNG is a powerful tool for the simulationist.
Some PRNGs are better than others - better in the sense that they better match those criteria: including the actual sample distribution, the means, and variance (over time and in segments), and in the length of the sequence before it starts repeating.
I've never quite made the jump to "individual realities" as opposed to individual perceptions of reality in the general sense. I understand that in some cases relativity comes into place and that actual reality can be different - but this is a VERY long from saying that "anything goes" or that "every perception is 'just as real' as any other perception." I understand that there are people who assert otherwise. I don't know that you are one of them, but there are some people who do make this sort of assertion. I do not believe them - and I suspect that if they understood what they were saying, that they wouldn't believe it either.
At the end of the movie "Brazil," the main character goes deep inside his head and is free in his own mind no matter that his tormenters are torturing him horribly and relentlessly. In the movie we are happy for this character. *I* was happy for the character. But no matter what he perceived, had his torturers put a few amps through his gray stuff - or dropped him from a helicopter - his reality would have ceased to exist. There was - there is! - a higher reality.
I only vaguely get the connection you're trying to make here. I think it's entirely possible that we don't understand everything about randomness - that there's more to it than meets the eye. I think it's possible that we (collectively in the majority) make a lot of assumptions about what randomness means and what it implies that may not be strictly true. I certainly think that this opinion holds true for many lay people, and I think it's even probable among many scientists. It's even possible that experts in statistical sciences are mistaken in this way, though less likely in my view.
This is still a long way from saying that all perceptions are equally real. I'm really not following your point.
