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This is a question that I have been struggling with for quite some time. I work with kids at a math tutoring center, and one of the things we do is work on the multiplication facts. We use a standard 52 card deck, numbered 0-12, with 4 of each value. We begin by flipping one card face up. This is the number the student will work on. The instructor then flips one card at a time until all 52 cards are used. After doing this for a few days I started to notice that cards of the same value would come up back to back quite often. So I began to wonder...

What is the probability of flipping through the entire deck without ever having 2 cards of the same value coming up back to back?

I believe that the probability is reasonable, because I have flipped through a deck a few times without repeating a value. However, I believe that the probability is rather low.

Any advice on how to approach this problem would be appreciated.

David Roberts
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    See here: http://math.stackexchange.com/questions/310971/no-two-identical-ranks-together-in-a-standard-deck-of-cards –  Jan 11 '16 at 19:25
  • I would say that unless you're really bad at shuffling, you will practically never get any cards back-to-back. The only way to do that is to turn one of the cards over so that its face is where its back should be. :-) – David K Jan 11 '16 at 19:39

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