The challenge

A fresh, unopened deck of playing cards is brought to the floor of the Taj Mahal casino in Vegas. They arrive at the table of Doyle Shufflington, a veteran dealer of the Taj, who is dealing no-limit Texas Hold-em to eight high rolling businessmen from New York.

Upon the deck's arrival to his table, Doyle opens the brand new box of cards, tosses the jokers into the trash, and splits the remaining 52 cards into a perfect 26 and 26, taking the top half with his left hand and the bottom half with his right hand. He then begins to shuffle the two halves together using the classic riffle method (fanning the two packs into each other). His shuffle begins with the bottom card of the left-hand pack, followed by the bottom card of the right-hand pack, then the second-to-bottom card in the left-hand pack, followed by the second-to-bottom card from the right-hand pack. He continues this to perfection until all 52 cards are shuffled one on top of the other. 

After his first shuffle, Doyle pauses, carefully sets the deck down in front of him, and takes a sip of water. He then poses this question to the players in front of him:

"Gentlemen, as you all probably know, a newly opened deck of standard poker playing cards comes arranged ace to king in ascending rank, divided into the four suits, which are hearts, diamonds, spades, and clubs. I have just shuffled the deck one time so that the two packs of 26 cards have been equally and perfectly mixed. If I continue to shuffle the pack as I have just done, following the exact method of the first shuffle, would I ever shuffle the pack back into its original order? And if you think it can be done, how many shuffles do you reckon it would take, in total, gentlemen?"

The most cavalier businessman stood up first and stated that even if it could be done, he didn't care to ponder such a trivial question. He was in the business of making money, not humoring a stiff old card sharp like Doyle. 

The next expressed a similar opinion, but then added his personal conviction that it couldn't be done.

A third withdrew his chips from the action in order to think, and after some time he gave his answer...


And now, readers, I pose the same question to you. Can it be done? If so, how many shuffles would it take?