Seven Perfect Shuffles Randomize a Deck of Cards. But How Many Sloppy Ones?
Summary
The article discusses the classic result that seven riffle shuffles suffice to mix a deck of cards and presents new work showing a cutoff phenomenon persists even with sloppy, uneven cuts. It introduces a barcode method to track card paths and explains how cold spots in the deck help establish an exponential tail, providing an upper bound on the number of shuffles needed for typical mixing.