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 Supreme Successive Shuffle (Posted on 2009-12-15)
A deck of M cards is numbered 1 to M and shuffled, and dealt from top to bottom.

Denoting the probability of dealing at least one pair of successive cards in their proper order (that is, a 1 followed by a 2 or, a 2 followed by a 3, and so on) at any position in the deck by s(M), determine s(M) as M → ∞ (The pairs may overlap. For example, for M=5, we have two successive pairs corresponding to 73452.)

As a bonus, what is the expected number of such successive pairs in an M card deck as a function of M?

 No Solution Yet Submitted by K Sengupta No Rating

 Subject Author Date re: Some thoughts (Spoiler) Finished Jer 2009-12-18 16:37:57 re(3): Recursive two-way formula. Fixed. higher numbers Charlie 2009-12-18 13:44:32 re(2): Recursive two-way formula. Fixed. Charlie 2009-12-18 12:32:22 Some thoughts (Spoiler) Harry 2009-12-18 00:18:57 re: Recursive two-way formula. Fixed. Jer 2009-12-17 10:16:29 re: Recursive two-way formula. Charlie 2009-12-17 03:25:01 Recursive two-way formula. Jer 2009-12-16 18:55:43 re: For M=1 to 10 by counting---plus conjecture Charlie 2009-12-15 12:12:20 For M=1 to 10 by counting---plus conjecture Charlie 2009-12-15 11:52:44

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