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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
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Bayer, D. & Diaconis, P. (1992). Trailing the dovetail shuffle to its lair. Annals of Applied Probability 2(2): 294313.

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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