I'd like to see a method to determine how many times a person would need to shuffle a deck of 52 cards until they are back in their original order.

The definition of a perfect shuffle would be to always cut the deck into 2 piles of 26 cards. The top card (top stack) will always end up on top. The remaining are interleaved in perfect succession. Assuming the cards can be represented by unique numbers 1-52:

Before the first shuffle:

1,2,3,4,5 ... 48,49,50,52,51

After the first shuffle we'd have:

1,27,2,28,3,29 ... 25,51,26,52

After two shuffles:

1,14,27,40,2,15 ... 13,26,39,52

After the Nth shuffle:

1,2,3,4,5 ... 48,49,50,51,52

Any takers?