how random is shuffling cards ?

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how random is shuffling cards ?

Here are some links that might be useful to you:

https://fredhohman.com/card-shuffling

https://fredhohman.com/card-shuffling
The Math of Card Shuffling – Fred Hohman
Place the top card of the deck randomly inside the deck. This means taking the A♠ and placing it randomly somewhere in the deck. The top card then becomes 2♠. If this procedure is repeated, eventually the top card will be placed at the very bottom of the deck, shifting the K♦ to the penultimate position.

https://math.stackexchange.com/questions/1637656/measure-of-card-shuffling-randomness

https://math.stackexchange.com/questions/1637656/measure-of-card-shuffling-randomness
combinatorics – Measure of card shuffling randomness – Mathematics …
Shuffling cards is mathematically more interesting than one would expect. There are numerous publications on the matter and depending on how exactly you plan to shuffle your deck, various phenomena can occur. … No individual deck configuration is more random than another in any sense that is meaningful for probability and statistics. Rather …

https://math.stackexchange.com / questions / 671 / when-you-randomly-shuffle-a-deck-of-cards-what-is-the-probability-that-it-is-a

https://math.stackexchange.com / questions / 671 / when-you-randomly-shuffle-a-deck-of-cards-what-is-the-probability-that-it-is-a
When you randomly shuffle a deck of cards, what is the probability that …
Every shuffle ever is completely (theoretically) random and unaffected by biases caused by human shuffling and the games the cards are used for; By deck of cards, I refer to a stack of unordered $52$ unique cards, with a composition that is identical from deck to deck.

https://stats.libretexts.org/Bookshelves/Probability_Theory/Book:_Introductory_Probability_(Grinstead_and_Snell)/03:_Combinatorics/3.03:_Card_Shuffling

https://stats.libretexts.org/Bookshelves/Probability_Theory/Book:_Introductory_Probability_(Grinstead_and_Snell)/03:_Combinatorics/3.03:_Card_Shuffling
3.3: Card Shuffling – Statistics LibreTexts
30 juil. 2023However, there is an easy formula which gives the number of such pairs that lead to a given ordering. Theorem 3.3.3. If an ordering of length n has r rising sequences, then the number of cut-interleaving pairs under an a -shuffle of the identity ordering which lead to the ordering is. (n + a − r n).

https://lifehacker.com/the-best-way-to-shuffle-and-randomize-a-deck-of-playing-1700072587

https://lifehacker.com/the-best-way-to-shuffle-and-randomize-a-deck-of-playing-1700072587
The Best Way to Shuffle and Randomize a Deck of Playing Cards
April 25, 2015. The whole point of shuffling a deck of cards is to randomize the order of them as best you can. For the best results, you need to give the deck at least seven basic rifle shuffles …

https://www.npr.org/2017/12/29/574598877/no-easy-answer-to-growing-number-of-stray-dogs-in-the-u-s-advocate-says

thescienceexplorer.com/universe/how-many-times-should-you-shuffle-deck-cards
How Many Times Should You Shuffle a Deck of Cards?
A dealer would need to do this for 30 seconds to a minute. Diaconis goes on to explain the method behind finding out how likely a perfect shuffle is. Pretend that you have a deck of cards and look at the bottom card. In his case, it is a King of Hearts (KoH). Now, take the top card and place it anywhere in the deck.

https://phys.org/news/2017-02-shuffle-cards-maths.html

https://phys.org/news/2017-02-shuffle-cards-maths.html
Here’s the best way to shuffle a pack of cards – with a little help …
The usual shuffling produces a card order that is far from random, Diaconis has said. Most people shuffle cards three or four times. Five times is considered excessive.

https://en.wikipedia.org/wiki/Shuffling

https://en.wikipedia.org/wiki/Shuffling
Shuffling – Wikipedia
Shuffling. Riffle shuffle. Shuffling is a procedure used to randomize a deck of playing cards to provide an element of chance in card games. Shuffling is often followed by a cut, to help ensure that the shuffler has not manipulated the outcome. [citation needed]

https://www.sciencenews.org/article/shuffling-cards-math-does-trick

https://www.sciencenews.org/article/shuffling-cards-math-does-trick
Shuffling the cards: Math does the trick – Science News
Shuffling the cards: Math does the trick. When to stop shuffling depends on the game. … Choosing a new random solution in a Markov Chain Monte Carlo simulation is a bit like a shuffle of the …

https://math.uchicago.edu/~may/REU2013/REUPapers/Guo.pdf

https://math.uchicago.edu/~may/REU2013/REUPapers/Guo.pdf
PDF CARD SHUFFLING – University of Chicago
De nitions 2.2. An a-shu e is achieved by cutting a deck of n cards into a packets such that the number of cards in each packet is distributed according to a multinomial distribution. That is, the probability of having j 1 cards in the rst packet, j 2 cards in the second packet and so on is given by P(j 1;j 2;:::;j a) = n! anj 1!j 2!:::j a!:
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