The Connection Between Math And Card Shuffling!

 

As we all know, math is used to explain the world around us.  We've found that certain mathematical equations can explain more than one thing.  Mathematicians have been studying the math of card shuffling for the past several decades. This has lead to the development of other concepts such as random walks, group theory, and probability theory.

When the cards are shuffled, the order of the cards s randomized. This means the probability of any particular ordering of the cards is the same as any other possible ordering, assuming the shuffle is truly random.  This means the number of possible orderings of a deck of cards is very large, specifically 52! or about 8 x 10^67 possible orderings.

In order to study the probability of certain card shuffling methods, mathematicians used techniques such as Markov chains and permutation groups.  Markov chains are used to model the probabilities of different outcomes based on previous outcomes, while permutation groups are used to study the possible rearrangements of a deck of cards.

In addition, mathematicians developed a variety of different card shuffling techniques designed to produce different possibilities of different outcomes.  Some of the most commonly used shuffling techniques include riffle shuffling, overhand shuffling, and Hindu shuffling.  By studying these different shuffling techniques mathematically, they have been able to gain a deeper understanding of probability and randomness and even have developed new methods for shuffling that are more effective and fair.

So the study of card shuffling has focused on the basic question of how many shuffles does one need to completely mix a deck of cards. This question is one that is great from both a theoretical view and from a practical because the answer to this question has applications to cryptography and computer science.

One theory - "The Seven Shuffle Theorem" which states it takes no more than seven shuffles to thoroughly mix the deck.  This theorem was first proved in the 1980's but since then it has been refined and extended by other mathematicians. 

The interesting thing about the connection between card shuffling and math is the way shuffling techniques are used in cryptography. See, randomness is essential to any cryptographic system and shuffling is one way to generate random numbers used to encrypt messages. 

The connection between math and card shuffling is a fascinating area of study and has lead to many other insights and applications in both mathematics and in other areas. I've always found this topic interesting and remember hearing about the seven shuffle theorem so when I open a new deck of cards, I always shuffle it seven times.  Let me know what you think, I'd love to hear.  Have a great day?