Abstract
The analysis of random processes is a familiar duty in life (“How long does it take to get to the airport during rush-hour?”) as well as in mathematics. Of course, getting meaningful answers to such problems heavily depends on formulating meaningful questions. For the card shuffling problem, this means that we have
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to specify the size of the deck (n = 52 cards, say),
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to say how we shuffle (we’ll analyze top-in-at-random shuffles first, and then the more realistic and effective riffle shuffles), and finally
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to explain what we mean by “is random” or “is close to random.”
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References
D. Aldous & P. Diaconis: Shuffling cards and stopping times, Amer. Math. Monthly 93 (1986), 333–348.
D. Bayer & P. Diaconis: Trailing the dovetail shuffle to its lair, Annals Applied Probability 2 (1992), 294–313.
E. Behrends: Introduction to Markov Chains, Vieweg, Braunschweig/ Wiesbaden 2000.
P. Diaconis: Mathematical developments from the analysis of riffle shuffling, in: “Groups, Combinatorics and Geometry. Durham 2001” (A. A. Ivanov, M. W. Liebeck and J. Saxl, eds.), World Scientific, Singapore 2003, pp. 73–97.
M. Gardner: Mathematical Magic Show, Knopf, New York/Allen & Unwin, London 1977.
E. N. Gilbert: Theory of Shuffl ing, Technical Memorandum, Bell Laboratories, Murray Hill NJ, 1955.
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© 2004 Springer-Verlag Berlin Heidelberg
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Aigner, M., Ziegler, G.M. (2004). Shuffling cards. In: Proofs from THE BOOK. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05412-3_24
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DOI: https://doi.org/10.1007/978-3-662-05412-3_24
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