![]() It is also a very convenient theoretical model because there is a very simple description for the inverse process: To produce the inverse of a random shuffle, go through the deck and random place each card in your left hand or your right, according to an independent coin flip then stack up the decks in your two hands.įor lots more on this model, including the 7 shuffles to randomize result, see Trailing the Dovetail Shuffle to its Lair by Bayer and Diaconis. The top part of the deck is placed in the left hand. The shuffler divides the deck into two part. ADDED JULY 2014 Cope's data still doesn't seem to be public, but you can read an analysis of it here. The meaning of RIFFLE-SHUFFLE is the act or process of shuffling playing cards by first separating the pack into two parts. The Riffle Shuffle is a popular way to shuffle a deck of cards. It's easier to accomplish than it looks, and if you put in some practice, you can make it fancier by performing it in your hands instead of a table. We had an undergrad, Alex Cope, who was paying random people here at Michigan to shuffle cards and checking them against the model he doesn't seem to have published his work yet. Riffle shuffles are commonly used to randomize a deck of cards, or for a flashy effect in a magic trick. Then you loop while n < split, but since theyre both 0 the first time around the condition fails (zero is, after all, not less than zero). There are two possible ways of interleaving the two halves, one (an in-shuffle) where the top and bottom cards wind up inside the deck, and the other (an out-shuffle) where the top and bottom cards wind. You first declare n 0, and then split n // 2 (good on you for using integer division, btw), which is also equal to 0. IIRC, these experiments only used two shufflers, Diaconis and a friend, and Diaconis is a practiced magician, so one might wonder if this is a fair sample. A riffle shuffle is performed by taking a deck of cards, dividing the deck in half ('cutting' the deck), and then interleaving the two halves. This condition is a decent model for real shuffling, according to experiments by Diaconis. The second condition says that, when I have $a$ cards in my left hand and $b$ in my right, the odds that the next card will drop from the left hand is $a/(a b)$, so the thicker pack of cards drops faster. The probability that the deck is cut at position $k$ is $\frac$. There is a standard model of a random riffle shuffle due Gilbert: Let there be $n$ cards in the deck. There is no reason to do any other type of shuffle. A riffle shuffle is defined to take the deck, cut it into an initial segment $A$ and a final segment $B$, and then mix $A$ and $B$ together, preserving the ordering within $A$ and $B$.
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