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With the empeg, the argument is that the initial random ordering of the shuffle list isn't actually random. I've seen far too many coincidental pairings, but at least it's still what I think is a traditional shuffle mode.

Depending on what you mean by 'actually random'. Arbitrary large shuffle without any perceived 'nonrandomness' (e.g. without two consecutive songs from the same album) is certainly not random. Appearance of any song in, say, position #2 in the list is equaly probable, including the one from the same album as the one in position #1. Forcing the songs from the same album (or any other specific pairs) 'apart' makes the ordering less random, not more.

That is not to say, of course, that what we actually want is mathematical randomness. We want appearance of randomness. Perhaps shuffle function should, after randomizing the running order, make an additional pass and further shuffle those song groups that would appear related (using some kind of proximity function). However, some occasional appearance of remnants of order will be very difficult to remove.

Did anybody measure how random the shuffle really is? (Say, make a short list of, say, 20 songs, two each from 10 albums. Calculate probabilty of songs from the same album appearing next to each other. Perform a large number of shuffles and count actual frequency of such pairs.) Didn't somebody do some kind of similar simulation a few years ago?

BTW, 'total disorder is impossible', as Ramsey theory finds out.
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