Shuffling a deck of cards may seem like a mundane action, but competitive games or gambling can be largely affected by the way cards were shuffled beforehand. Many questions arise from this: how do you know if a deck is "well-shuffled" ? Is a given shuffling method "more efficient" than another ? How should a casino dealer shuffle the deck to prevent players from cheating ? Those questions have been studied in a mathematical framework in the last decades, which lead to a precise definition of shuffle efficiency and many practical applications. The goal of this talk is to present the basics of the theory (which originates from the study of Markov chains' mixing times), as well as results on some classical shuffling methods.
