Under quantum mechanics this can't explain non-even distributions. With no effects making high probability events more prevalent than others you can not (reliably) observe differentiated probabilities.

And once again, cardinalites appears. A thing whose possible variations correspond to infinite integers can't match that with have variations matching the real numbers. An infinite line won't correspond to an infinite hypercube in infinite dimensions. Gotta consider combinatorics from statistics too, as well as entropy. The number of permutations mapping to normal states simply has to far exceed the strange states for us to observe a normal universe.