The Kruskal Count

Jeffrey C. Lagarias (), Eric Rains () and Robert J. Vanderbei ()
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Jeffrey C. Lagarias: University of Michigan
Eric Rains: California Institute of Technology
Robert J. Vanderbei: Princeton University

A chapter in The Mathematics of Preference, Choice and Order, 2009, pp 371-391 from Springer

Abstract: The Kruskal Count is a card trick invented by Martin D. Kruskal (who is well known for his work on solitons) which is described in Fulves and Gardner (1975) and Gardner (1978, 1988). In this card trick a magician “guesses” one card in a deck of cards which is determined by a subject using a special counting procedure that we call Kruskal's counting procedure. The magician has a strategy which with high probability will identify the correct card, explained below. Kruskal's counting procedure goes as follows. The subject shuffles a deck of cards as many times as he likes. He mentally chooses a (secret) number between one and ten. The subject turns the cards of the deck face up one at a time, slowly, and places them in a pile. As he turns up each card he decreases his secret number by one and he continues to count this way till he reaches zero. The card just turned up at the point when the count reaches zero is called the first key card and its value is called the first key number. Here the value of an Ace is one, face cards are assigned the value five, and all other cards take their numerical value. The subject now starts the count over, using the first key number to determine where to stop the count at the second key card. He continues in this fashion, obtaining successive key cards until the deck is exhausted. The last key card encountered, which we call the tapped card, is the card to be “guessed” by the magician.

Keywords: Markov Chain; Failure Probability; Success Probability; Coupling Method; Geometric Distribution (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/978-3-540-79128-7_23

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