Shuffling

Another common technique is the riffle shuffle, where the deck is split into two halves and interleaved.

The Mongean shuffle involves a specific sequence of transferring cards between hands, resulting in a predictable order.

Johan Jonasson wrote, "The overhand shuffle... is the shuffling technique where you gradually transfer the deck from, say, your right hand to your left hand by sliding off small packets from the top of the deck with your thumb.

The overhand shuffle offers sufficient opportunity for sleight of hand techniques to be used to affect the ordering of cards, creating a stacked deck.

A common shuffling technique is called the riffle, or dovetail shuffle or leafing the cards, 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 interleaved.

Many also lift the cards up after a riffle, forming what is called a bridge which puts the cards back into place; it 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 more difficult, it is often used in casinos because it minimizes the risk of exposing cards during the shuffle.

The Gilbert–Shannon–Reeds model provides a mathematical model of the random outcomes of riffling that has been shown experimentally to be a good fit to human shuffling[2] and that forms the basis for a recommendation that card decks be riffled seven times in order to randomize them thoroughly.

[3] Later, mathematicians Lloyd M. Trefethen and Lloyd N. Trefethen authored a paper using a tweaked version of the Gilbert–Shannon–Reeds model showing that the minimum number of riffles for total randomization could also be six, if the method of defining randomness is changed.

The maneuver is repeated over and over, with newly drawn packets dropping onto previous ones, until the deck is all in the second hand.

This method is useful for beginners, but the shuffle requires a large clean surface for spreading out the cards, and it may take more time than is desired.

Then the cards are moved into one pile so that they begin to intertwine and are then arranged back into a stack.

Weaving 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.

A flourish can be added by springing the packets together by applying pressure and bending them from above, as called the bridge finish.

Performing eight perfect faro shuffles in a row restores the order of the deck to the original order only if there are 52 cards in the deck and if the original top and bottom cards remain in their positions (1st and 52nd) during the eight shuffles.

It takes quite a long time, compared with riffle or overhand shuffles, but allows other players to fully control cards which are on the table.

The Mexican spiral shuffle was popular at the end of the 19th century in some areas of Mexico as a protection from gamblers and con men arriving from the United States.

Magicians, sleight-of-hand artists, and card cheats employ various methods of shuffling whereby the deck appears to have been shuffled fairly, when in reality one or more cards (up to and including the entire deck) stays in the same position.

A leading figure in the mathematics of shuffling is mathematician and magician Persi Diaconis, who began studying the question around 1970,[9] and has authored many papers in the 1980s, 1990s, and 2000s on the subject with numerous co-authors.

[9] Recently, the work of Trefethen et al. has questioned some of Diaconis' results, concluding that six shuffles are enough.

After shuffling, the measure of randomness is the number of rising sequences that are left in each suit.

The Fisher–Yates shuffle, popularized by Donald Knuth, is simple (a few lines of code) and efficient (O(n) on an n-card deck, assuming constant time for fundamental steps) algorithm for doing this.

A new alternative to Fisher-Yates, which does not use any array memory operations, is the use a Pseudo Random Index Generator (PRIG) function algorithm.

For this reason, many online gambling sites provide descriptions of their shuffling algorithms and the sources of randomness used to drive these algorithms, with some gambling sites also providing auditors' reports of the performance of their systems.