![]() This column will explain a few of the techniques and results from that paper. ![]() ![]() Curiously, I soon came across an essay in Aigner and Ziegler's wonderful book Proofs from the Book that addressed just this issue and that led me to a remarkable paper by Aldous and Diaconis that gives an answer to this question. This led me to wonder how many shuffles would be needed to give a good guarantee that the deck had been put in random order. The ordering from the first part of the game persisted after the shuffles it would seem that the shuffles hadn't affected the ordering of the deck as much as we wished. The cards were still grouped too closely by suits that is, in spite of the shuffles, we were still seeing long sequences of, say, clubs when drawing from the pile. During the middle of one game, we went through the entire deck, so we shuffled the cards in the discard pile a few times and started playing again. A month ago, I was playing the card game Crazy Eights with one of my children.
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