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

Published online by Cambridge University Press:  01 July 2004

Anke van Zuylen  and
Frans Schalekamp
Anke van Zuylen
Affiliation:
Operations Research & Industrial Engineering, Cornell University, Ithaca, NY 14853, E-mail: frans@cs.cornell.edu; anke@orie.cornell.edu
Frans Schalekamp
Affiliation:
Operations Research & Industrial Engineering, Cornell University, Ithaca, NY 14853, E-mail: frans@cs.cornell.edu; anke@orie.cornell.edu
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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 18 , Issue 3 , July 2004 , pp. 315 - 328
Copyright
© 2004 Cambridge University Press

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References

REFERENCES

Bayer, D. & Diaconis, P. (1992). Trailing the dovetail shuffle to its lair. Annals of Applied Probability 2(2): 294–313.Google Scholar
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 Unpublished manuscript.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: 717–722.Google Scholar