No, that cannot be guaranteed. Equidistribution in 52 dimensions requires necessarily a minimum state size of 52 log_2(52) bits, which we don't even have. Even

No, that cannot be guaranteed. Equidistribution in 52 dimensions requires necessarily a minimum state size of 52 log_2(52) bits, which we don't even have. Even if we did, it could not be guaranteed anyway. You have already covered the distinction between guaranteed equidistribution and not, so I don't think there is much to add there. I do think the concern is mostly academic, since the difference between a subsequence that doesn't exist and one that will never be reached before the universe collapses is irrelevant to the user. I will note that Richard Brent, someone who is much better qualified than I to discuss this, has argued against the usefulness of equidistribution: http://maths-people.anu.edu.au/~brent/pub/pub240.html http://maths-people.anu.edu.au/~brent/pub/pub240.html