in reply to Random shuffling
Or, said in other words, if your random output is not the same as the random output of someone else, then it tends to confirm that this is really random (or, at least, that there is no proof that it is misbehaving). But the fact that your random output is different from someone else random output does not mean that your result is any better or worse than someone else's result.
I think you need to explain more what you are trying to do.
Or did I entirely miss your point? I am not a biologist and my knowledge of genetics essentially dates back from the mid-1970s, so a very long time ago both in terms of what I remember about it and in terms of the progresses made in between.
Then, there is the question of whether the (pseudo-)random order provided by shuffle is good enough to suit your purposes. This is a very difficult question and, besides the fact that I do not know your purposes, I just don't know how good shuffle is. Donald Knuth's The Art of of Computer Programming, Vol. 2, has almost 200 pages on random numbers generation, I think that this shows that this is a rather difficult problem.