What Is The Best Way To Shuffle Cards?
Shuffling a deck of cards may seem like a simple skill, and something anyone can do, but in fact there is proper shuffling technique, and it pays to know how to shuffle properly.
Shuffling is a procedure used to randomize a deck of playing cards to provide an element of chance in card games. Shuffling is often followed by a cut, to ensure that the shuffler has not manipulated the outcome.
A typical sequence between hands of poker, for example, is a wash, two riffles, a strip, a third riffle, and a cut, which an experienced dealer can accomplish in as little as five seconds.
Several techniques are used to shuffle a deck of cards. While some techniques achieve a better randomization, other techniques are easier to learn and handle or better suited for special situations.
The most common shuffling technique is called a riffle, in which half of the deck is held in each hand with the thumbs inward, then cards are released by the thumbs so that they fall to the table intertwined. Many also lift the cards up after a riffle forming what is called a bridge which puts the cards back into place.
This can also be done by placing the halves flat on the table with their rear corners touching, then lifting the back edges with the thumbs while pushing the halves together. While this method is a bit more difficult, it is often used in casinos because it minimizes the risk of exposing cards during the shuffle.
Stripping or Overhand
Another procedure is called stripping or overhand or slide shuffle, where small groups of cards are removed from the top or bottom of a deck and replaced on the opposite side (or just assembled on the table in reverse order). As this is an effective randomizing procedure, it remains a very common shuffle, especially amongst occasional players.
Pushing or Weave shuffle
Pushing is the procedure of pushing the ends of two halves of a deck against each other in such a way that they naturally intertwine. Sometimes the deck is split into equal halves of 26 cards which are then pushed together in a certain way so as to make them perfectly interweave. This is known as a Faro Shuffle and is quite difficult to master. Eight perfect Faro shuffles in succession will bring the deck back to its original order.
The deck is held face down, with the middle finger on one long edge and the thumb on the other on the bottom half of the deck. The other hand draws off a packet from the top of the deck. This packet is allowed to drop into the palm, and the maneuver is repeated over and over until the deck is all in the second hand.
Cards are arranged in piles by putting the top card from the deck in turn on one of several piles. Then the piles are stacked on top of each other. This ensures that cards that were next to each other are now separated. This is the only method of "human" shuffling approved in bridge when four piles are used (each pile is then assigned to the four players in this game). "Machine Shuffling" is also allowed when required (see below).
Beginner shuffle or Wash
This involves simply spreading the cards out face down, and sliding them around and over each other with one's hands. Then the cards are moved into one pile so that they begin to intertwine and are then arranged back into a stack. This method is useful for beginners and small children or if one is inept at shuffling cards. However, the beginner shuffle requires a large surface for spreading out the cards and takes longer than the other methods.
The Mongean shuffle, or Monge's shuffle, is performed as follows (by a right-handed person): Start with the unshuffled deck in the left hand and transfer the top card to the right. Then repeatedly take the top card from the left hand and transfer it to the right, putting the second card at the top of the new deck, the third at the bottom, the fourth at the top, the fifth at the bottom, etc.
The Faro Shuffle is performed by cutting the deck into two, preferably equal, packs in both hands as follows (right-handed): The cards are held from above in the right and from below in the left hand. Separation of the deck is done simply lifting up half the cards with the right hand thumb slightly and pushing the left hand's packet forward away from the right hand. The two packets are often crossed and slammed into each other as to align them. They are then pushed together by the short sides and bent (either up or down). The cards will then alternately fall into each other, much like a zipper. A flourish can by added by springing the packets together by applying pressure and bending them from above.
A perfect Faro Shuffle, where the cards are perfectly alternated, is considered one of the most difficult sleights by card magicians, simply because it requires the shuffler to be able to cut the deck into two equal packets and apply just about the right pressure when pushing the cards into each other. If one does perform 8 perfect Faro Shuffles in a row, the order of the deck will return to the original order, if there are 52 cards in the deck.
Because standard shuffling techniques are seen as weak, and in order to avoid "inside jobs" where employees collaborate with gamblers by performing inadequate shuffles, many casinos employ automatic shuffling machines which perform continuous shuffles on a pack of cards, and can produce any number of cards on demand. These machines are also used to lessen repetitive motion stress injuries to a dealer. Note that the shuffling machines have to be carefully designed, as they can generate biased shuffles otherwise: the most recent shuffling machines are computer-controlled.
There are approximately 52 factorial (about 8 x 1067) possible ways to order the cards in a 52-card deck. The magnitude of this number means that it is exceedingly improbable that two randomly selected, truly randomized decks, will ever, in the history of cards, be the same. However, while the exact sequence of all cards in a randomized deck is unpredictable, it may be possible to make some probabilistic predictions about a deck that is not sufficiently randomized.
The mathematician and magician Persi Diaconis is an expert on the theory and practice of card shuffling, and an author of a famous paper on the number of shuffles needed to randomize a deck, concluding that it did not start to become random until five good riffle shuffles, and was truly random after seven, in the precise sense of variation distance described in Markov chain mixing time; of course, you would need more shuffles if your shuffling technique is poor. Recently, the work of Trefethen et al. has questioned some of Diaconis' results, concluding that six shuffles is enough. The difference hinges on how each measured the randomness of the deck. Diaconis used a very sensitive test of randomness, and therefore needed to shuffle more. Even more sensitive measures exist and the question of what measure is best for specific card games is still open.
Here is an extremely sensitive test to experiment with. Take a standard deck without the jokers. Divide it into suits with two suits in ascending order from ace to king, and the other two suits in reverse. (Many decks already come ordered this way when new.) Shuffle to your satisfaction. Then go through the deck trying to pull out each suit in the order ace, two, three ... When you reach the top of the deck, start over. How many passes did it take to pull out each suit?
What you are seeing is how many rising sequences are left in each suit. It probably takes more shuffles than you think to both get rid of rising sequences in the suits which were assembled that way, and add them to the ones that were not!
In practice the number of shuffles that you need depends both on how good you are at shuffling, and how good the people playing are at noticing and using non-randomness. 2?4 shuffles is good enough for casual play. But in club play, good bridge players take advantage of non-randomness after 4 shuffles, and top blackjack players literally track aces through the deck; this is known as "ace tracking", or more generally, as "shuffle tracking".