Card Shuffling Visualizations

Roger Antonsen

Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture

http://archive.bridgesmathart.org/2018/bridges2018-451.html

@inproceedings{Antonsen18,
  author      = {Roger Antonsen},
  title       = {Card Shuffling Visualizations},
  pages       = {451--454},
  booktitle   = {Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture},
  year        = {2018},
  editor      = {Eve Torrence, Bruce Torrence, Carlo S\'equin, and Krist\'of Fenyvesi},
  isbn        = {978-1-938664-27-4},
  issn        = {1099-6702},
  publisher   = {Tessellations Publishing},
  address     = {Phoenix, Arizona},
  note        = {Available online at \url{http://archive.bridgesmathart.org/2018/bridges2018-451.pdf}}
}

Abstract

This paper discusses a few natural ways to visualize card shuffles, like the perfect in- and out-shuffle and the milk shuffle. These visualizations are designed to highlight interesting properties of the shuffles, like the order of the shuffles and the stay-stack principle. Such properties have attracted magicians and mathematicians alike, and visualizations like these make it possible to see properties that would have been hard to see otherwise.