Pushing and fanning
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. This requires skill and practice, as does fanning, which involves spreading the halves into fan shapes and intertwining them.
Pile shuffle
The pile shuffle is not a randomization technique, but a method to dissolve clumps of sticky cards. 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.
Randomization
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 5 good riffle shuffles, and was truly random after 7. (You would need more shuffles if your shuffling technique is poor of course.) Recently, the work of Trefethen et al. has questioned some of Diaconis' results, concluding that 6 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 2 suits in ascending order from ace to king, and the other two suits in reverse (A brand new deck already comes ordered this way.) Shuffle to your satisfaction. Then go through the deck trying to pull out each suit in the order ace, two, and 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.
CUT (CARDS)
The term cutting is also used for a random selection procedure in which a player perform the first part of a cut (removing a group of cards from the top of a deck), then look at the value of the card on the bottom of that portion, then replaces it. Another player then does the same, and the values of the cards thus exposed are used for such things as selecting who deals the game. This is often used as a pure gamble as well, much like flipping coins.
After a deck of cards is shuffled by the dealer, it is often given to a player other than the one who performed the shuffle for a procedure called a cut.
Procedure
The dealer completes their shuffle, and then sets the cards face-down on the table near the designated player. The player cuts the deck by removing a contiguous range of cards from the deck, and places them either on top or bottom of the remaining cards. The simplest form of the cut is done by taking, roughly, the top one-half of the cards, and placing them on the table. Either the
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