Shuffling (playing cards)
When mixing the generation is called a random sequence of playing cards of a card game . The shuffling is often followed by the removal of the cards.
Mixing methods
There are several methods of shuffling cards. Certain methods result in a better mix, while other methods are easier to learn and use or are better suited to specific situations.
Corrugations
The most common method is called riffle shuffle in English . One half of the cards in each hand is arched inwards with the thumb. Then the thumbs release the cards at the same time, so that they interlock unevenly. Then the halves are pushed into one another.
Arc mixing can be done both in the air and on the table. The latter is a requirement in most casinos to avoid spying on the lower cards. When shuffling casino sheets, the halves are placed on the table with their narrow sides facing each other so that their back corners touch. Then the rear edges are lifted with the thumbs and the halves are interlocked and then pushed together.
One disadvantage of sheet shuffling is the risk that poor quality cards can bend if shuffled carelessly. In the case of games of chance, however, it is customary and advisable to replace your playing cards in the course of the evening.
Overhand
The overhand mixing is another, especially for amateurs popular technique. The cards are usually held on the narrow sides in one hand. With the thumb of the other hand, smaller packets of cards are gradually pulled into it. Compared to sheet mixing, it takes significantly longer and requires more mixing operations to achieve a similar level of mixing. In addition, it offers a lot more opportunities for manipulation and is therefore not used in casinos.
Stripping
Another technique is in English stripping called. Small groups of cards are removed from the top or bottom of the deck and added on the other side or put back together on the table in reverse order. This is a significantly inefficient method and is not recommended unless used in conjunction with bow mixing.
Press into each other and fan
The mesh pressing is a method in which the ends of the two halves are pressed against each of the deck so that they mix together. This requires skill and practice, as does fanning , in which the halves are spread out in the form of a fan and pushed into one another.
Rummage through
The ransacking of the deck (Engl. Washing the deck or scrambling the deck ) is considered by many to be quite unprofessional method of mixing, but gives very good results and is used in casinos when using new card decks and following from time to time. A set of cards is spread out in two sheets or several packets face down in front of the dealer and mixed as well as possible in circular movements with the fingertips and the ball of the hand. New cards are shuffled for one to two minutes, if the rummaging through between games is usually only rummaged through ten to fifteen seconds. The cards are then piled up on a packet and aligned. In professional operations, the rummaging is usually followed by three corrugations, one stripping, another corrugation and then lifting.
stack
Forming stacks is not a randomization method, but is used to loosen cards that are stuck together. The cards are sorted into stacks in turn, so that cards that were previously next to each other are now separated.
Computer-mixed cards
The technology makes it possible to create randomly mixed distributions using different computer programs and to distribute these to the players with the help of a duplicating machine . This variant is particularly used in tournament bridge .
coincidence
Usually the deck of 52 cards isn't shuffled until five good sheet shuffles, and it's not really random until after seven. (With poor mixing methods, of course, more mixing processes are required).
Another opinion is that six shuffles are sufficient. The difference depends on how the randomness of a deck of cards is measured. Diaconis used an extremely sensitive test for chance and therefore came up with a higher result. There are even more sensitive dimensions, and the question of which dimension is best for certain card games is still unresolved.
An example of a very sensitive test:
- You take a Rummy sheet without a joker (i.e. with 52 cards) and divide it up according to colors, with two colors sorted in ascending order (from ace to king) and two colors in descending order (from king to ace); then the deck of cards is shuffled with the required care. You then go through the deck of cards and try to lay out each suit in the correct order (ace, two, three etc.). When you get to the end of the pile, you start all over again.
- The mixing can be assessed on the basis of the number of passes through the stack. In this test you can see how many ascending sequences are left in each color. It takes quite a bit of mixing to get rid of both the ascending and descending sequences in the individual colors.
In practice, the number of arc shuffles required depends both on how good the dealer is at shuffling and how good the other players are at noticing and using the lack of chance. Two to four shuffles are enough for the game for fun. The best blackjack players can literally chase aces through the deck.
There is no manageable method of randomly shuffling a deck of cards. The most reliable but inconvenient method is to rummage through a deck of cards. Even the popular pushing or flipping into one another hardly changes the order of the cards in the deck, even after many rounds in relation to the number of shuffles.
See also
literature
- David Aldous and Persi Diaconis: "Shuffling Cards and Stopping Times". In: American Mathematical Monthly , Vol. 93, No. 5, 1986, ISSN 0002-9890 , pp. 333-348.
- Lloyd N. Trefethen and Lloyd M. Trefethen: “How Many Shuffles to Randomize a Deck of Cards?” In: Proceedings of the Royal Society London. Series A: Mathematical, Physical and Engineering Sciences , Vol. 456, No. 2002, October 8, 2000, pp. 2561-2568.
- Walter Peter Sendfeld: Riffle Shuffle and Cut-Off Effect . Westf. Wilhelms-Universität, Münster 2005 (= diploma thesis). ( PDF ).
- Christian Palmes: Top-to-Random-Shuffles . Westf. Wilhelms-Universität, Münster 2010 (= diploma thesis). ( PDF ).