shuffle

Shuffling is a technique used to randomize a deck of playing cards, introducing an element of chance into card games. Various shuffling methods exist, each with its own characteristics and potential for manipulation.
One of the simplest shuffling techniques is the overhand shuffle, where small packets of cards are transferred from one hand to the other. This method is easy to perform but can be manipulated to control the order of cards. Another common technique is the riffle shuffle, where the deck is split into two halves and interleaved. This method is more complex but minimizes the risk of exposing cards. The Gilbert–Shannon–Reeds model suggests that seven riffle shuffles are sufficient to thoroughly randomize a deck, although some studies indicate that six shuffles may be enough.
Other shuffling methods include the Hindu shuffle, commonly used in Asia, and the pile shuffle, where cards are dealt into piles and then stacked. The Mongean shuffle involves a specific sequence of transferring cards between hands, resulting in a predictable order. The faro shuffle, a controlled shuffle used by magicians, involves interweaving two halves of the deck and can restore the original order after several shuffles.
Shuffling can be simulated using algorithms like the Fisher–Yates shuffle, which generates a random permutation of cards. In online gambling, the randomness of shuffling is crucial, and many sites provide descriptions of their shuffling algorithms. Shuffling machines are also used in casinos to increase complexity and prevent predictions. Despite these advances, the mathematics of shuffling continue to be a subject of research, with ongoing debates about the number of shuffles required for true randomization.

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