A game of cards can be something casual and fun, or lead to high-tension situations with a lot of money at stake. Sooner or later, each participant will try to tip the game in their favor, but the fairest thing for everyone is to reach a high level of randomness when shuffling cards. How do you get to that level? Professor Jason Fulman from USC Dornsife and Persi Diaconis from Stanford University not only shared some example videos, but also wrote a book about it….
The French deck has a total of 52 cards divided into four suits. These parameters create an impressive number of combinations... as long as you do a good job when mixing. This may seem contradictory at first: The number of possible configurations is on the order of 8x10^67, larger than the number of particles in the Universe, but there are ways of shuffling that are not quite appropriate, and someone with an excellent memory could gain a certain advantage. What was needed to discover this? The work of two mathematicians who have spent years exploring the topic.
The Best and Worst Ways to Shuffle Cards
The first video shows Professor Jason Fulman from USC Dornsife, and the second belongs to Numberphile, with an interview with Persi Diaconis from Stanford University. Both have written The Mathematics of Shuffling Cards, a book that allows us to learn the mathematical development needed to answer one of the oldest questions: How many times do you have to shuffle the cards for them to be "well mixed"?
In relaxed terms, the method is as important as the number or the time. Both experts mention three styles. The first is known as riffle, that is, cutting the deck in half, using your thumbs, and interleaving the cards in a classic "prrrrrr". Repeating this action seven times is enough to get good results.
The second method is the overhand, much more common, which takes small groups of cards and changes their position. At first glance it seems random, but mathematicians discovered that overhand needs about ten thousand movements, pulverizing the arms and patience of any player. Finally, smooshing involves throwing all the cards on the table and making a chaotic swirl with them. In this case, time is fundamental, and you must shuffle for at least one minute.
If you want to know more about it, I recommend this BBC Future article which reveals how Diaconis and his colleague Susan Holmes "retired" the prototype of a new automatic card shuffler.
