The biggest problem with shuffling algorithms (not just Fisher-Yates) is the imperfectness of the RNG. The sequence of numbers it returns is determined by the seed, and only by the seed. And if from the seed only 32 bits are being used, there will be at most 2**32 different sequences. Which means that for a deck of more than 2 cards, Fisher-Yates cannot be 'fair', as N! won't be a divisor of any power of 2. Furthermore, 13! > 2**32, so even if you shuffle a deck of 13 cards, some permutations will *never* be selected, no matter how many times you perform the shuffle.

This was pointed out by R. Salfi: COMPSTAT 1974, Vienna: 1974, pp 28 - 35.

See also the documentation of the Shuffle module on CPAN.

Abigail

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