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Why swapping cards at random is not a fair shuffle: Fisher–Yates and the 27 paths
Shuffling three cards by swapping each one with a random card from the whole row looks fair, but it is not. It makes 3 × 3 × 3 = 27 equally likely paths for…
Why seven shuffles are enough to mix a deck of cards
A 52-card deck can be put in about 8 × 10^67 different orders, yet a few quick shuffles leave a lot of the old order behind. In 1992 Dave Bayer and Persi…