Randomization Time for the Overhand Shuffle

1. THE OVERHAND SHUFFLE (~o The two most common methods of shuffling a deck of playing cards are the riffle shuffle and the overhand shuffle. The riffle shuffle is performed by splitting the deck into two halves and interlacing them. Aldous and Diaconis have shown in Ref. I that approximately 2 log N riffle shuffles suffices to randomize a deck (the meaning of this will be made more precise below). In particular, about 7 riffle shuffles are sufficient to randomize a 52-card deck. This paper shows that the overhand shuffle takes order of N 2 or more shuffles to randomize a 52-card deck, explaining why it is only the second most popular shuffle. To perform an overhand shuffle, hold the deck of cards in your right hand and slide a small packet of cards off the top of the deck into your left hand. Repeat this process, putting each successive packet on top of the previous one, until all the cards are in your left hand, so the order of the cards gets reversed in clumps. The overhand shuffle is frequently used by casual card players. It