my roommate and I have been trying to figure this out, and I was attempting to write a program to simulate the problem to shed some light on it.
A deck of 52 cards in "new deck order" (Deck 0) is sorted into two piles by taking the top card and putting it in Pile A and taking the next card and putting it in Pile B and repeating until there are no more cards in the deck. Pile A is then put on top of Pile B, forming Deck 1. After eight different iterations of the sorting algorithm, creating Deck 8, the cards are in new deck order again. Why does it take 8 iterations of this particular sorting algorithm to return the deck of cards to new deck order?
For what it's worth - I modeled it on a spreadsheet - the way I interpreted it Deck 27 is Deck 1 in reverse order and Deck 53 is the first repeat of Deck 1.
So, unless I am misinterpreting how you are shuffling, it will actually take 52 iterations to return to a full deck.