In reply to John.

The statement "puts (randomly) 1,2,3, or 4 over the other" means that you are using a probabilistic shuffle. See the article, "A statistical model of card shuffling." The algorithm in that article is probably more realistic than assuming that the number of cards from each stack is uniformly distributed in [1,4]. But I don't think the kind of shuffle will change your result: in a deck that has 10 or more cards and is shuffled randomly, it would be very rare to see the deck restored to its original order.