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THE ACHILLES' HEEL OF THE GSR SHUFFLE: A NOTE ON NEW AGE SOLITAIRE

  • Anke van Zuylen (a1) and Frans Schalekamp (a1)
Abstract

We show that winning the game New Age Solitaire only depends on the number of rising sequences in the deck used. The probability of winning for the special case of a new deck that is shuffled using the GSR shuffle (and two variants) are studied. We show that this game pinpoints the Achilles' heel of the GSR shuffle as is demonstrated using the variation distance.

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REFERENCES

Bayer, D. & Diaconis, P. (1992). Trailing the dovetail shuffle to its lair. Annals of Applied Probability 2(2): 294313.
Gilbert, E. (1955). Theory of shuffling. Technical Memorandum, Bell Laboratories, Murray Hill, NJ.
Mann, B. How many times should you shuffle a deck of cards? www.dartmouth.edu/∼chance/teaching_aids/books_articles/Mann.pdf.
Reeds, J. (1981). Unpublished manuscript.
Tanny, S. (1973). A probabilistic interpretation of Eulerian numbers. Duke Mathematical Journal 40: 717722.
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Probability in the Engineering and Informational Sciences
  • ISSN: 0269-9648
  • EISSN: 1469-8951
  • URL: /core/journals/probability-in-the-engineering-and-informational-sciences
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