Who shuffled these? A visual and mathematical introduction to shuffling cards
Note: This blog was created as an entry to the Summer of Math Exposition 3 by 3Blue1Brown which is a part initiative - part competition to increase the number and quality of resources on the internet related to Maths topics. Edit after SoME3 results. You can check out here other interesting entries and math explainers. Motivation You’re with friends playing cards and it’s your turn to shuffle. You think to yourself ‘ I don’t know how to shuffle ’ or ‘ maybe I should ask someone else to do it for me ’. But there is no escape, you shuffle and deal the cards, everyone looks to one another in confusion until someone says: ‘ Who shuffled these? ’ Usually when playing cards, people use the standard method of riffle shuffling (splitting the deck in two and then mixing them) like this: I'm not very good at doing that, so I usually do pile shuffling (creating any number of piles by adding cards from the unshuffled deck) which looks nicer on the board: However a few weeks ago I thoug