Randomness
Since, as mentioned above, an odd number of legs produces an odd permutation and an even number of legs produces an even permutation, a given number of legs can produce a maximum of half the total possible permutations (less than half if the number of legs is small relative to the number of tracks, reaching half as the number of legs increases beyond a certain critical number).
If the legs are drawn randomly (for reasonable definitions of "drawn randomly"), the evenness of the distribution of permutations increases with the number of legs. If the number of legs is small relative to number of tracks, the probabilities of different attainable permutations may vary greatly; for large numbers of legs the probabilities of different attainable permutations approach equality.
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