Story: I remember that I used to believe that shuffling cards more makes the pack "more" randomized. It turns out that if I was perfect, I would have given serious advantage to my opponents. Lets see how. :)
Source: William Wu's Puzzle Page
Puzzle: A perfect in-shuffle of a deck of 52 cards is defined as follows. The deck cut in half followed by interleaving of the two piles. So if the cards were labeled 0, 1, 2, …, 51, the new sequence is 0, 26, 1, 27, 2, 28, … With repeated in-shuffles, shall we ever get back the original order? In how many iterations? The shuffling technique described in the puzzle is known as the Faro Shuffle.
Update(12/01/10): On a related note, I was searching for optimal shuffling algorithms and found this an interesting read.
Update (14/01/10): Solution posted by me in comments!!