Shuffling arrays: Appearances may be deceiving

Random permutations of arrays are widely used in experimentation and simulation, and most arrays are shuffled by means of a computer-based algorithm. In this paper, I show that despite theappearance of a random process, a shuffling procedure must be carefully scrutinized to determine whether it actually does produce random shuffles. A general sequence-transformation procedure is developed for evaluating permutation and shuffling schemes. Applying the transformation procedure and using the criteria that all possible sequences must be equally likely and that each object in a shuffled array must be equally likely to occupy each possible position in the shuffled array, we see that one algorithm meets the criteria, while another seemingly adequate algorithm fails to meet the criteria and, in addition, exhibits systematic deviations from randomness.