QUOTE(Jojo @ Jan 14 2005, 11:49 AM)
But let's say I have 5 songs in one playlist and play that playlist over and over again without letting it fully run through, every song should have been played equally.
Yes, if you play it all the way through, because a shuffle is shuffling the playlist, so no matter how you shuffle it, every song will be played once.

But generally you don't play the entire playlist all the way through, and that's how you get varying results. So let's say you only play the first X songs out of Y total songs in the shuffled playlist. This means that those X songs get incremented, but the rest don't. Now, over time, as you shuffle and play the list repeatedly, you get different sets of X songs that are incremented. And you'll tend towards equal, but it will not actually be equal.
QUOTE
Besides that, iPods's random mode won't play a song twice from the same playlist...so if song_A has been played it won't play again unless you restart the playlist...sure, this is a good thing, but this takes away a bit randomness

Not really. Even though the playlist is shuffled at random and then static after the shuffle (until you reshuffle), you don't play everything in it. This is basically equivalent to repeatedly picking one song at random from a set of songs, and keeping a count.
The songs will tend to be picked equally, but the fact is that they will not be picked equally, over any amount of time. That would not be random at all.
QUOTE(Jojo @ Jan 14 2005, 11:49 AM)
however, in a real random mode, every song should be distributed the exact same ammount!
Totally false. Let's simplify: You flip a coin repeatedly. Let's say it comes up heads three times in a row. What are the odds that the next one will come up tails? Past performance does not control future results. Getting 4 heads in a row is just as equally likely as getting 3 heads then a tail. The odds are still 50/50.
Random choice has a tendancy to even out over time, but this does not indicate that it always will do so. Now, getting an equal distribution is more likely over time because there's more ways to get even distributions when you ignore the ordering of the results, but this doesn't mean that the distribution will always be exactly equal. When picking from a set of a large number of items at random, there's a much wider possible set of distributions. If I'm flipping a coin, then I have 2 possible choices, and the set is small. This means that I reach a high probability of equal distribution fairly quickly. But if my outcome set is large, say, 500 possible songs to pick from, then it will take a very large number of trials before I have anything more than an very small difference in probable outcomes. You'd have to make that decision 500 times before a possibility of equal probabilities occurred, and at least another 500 before there was any difference in distribution probabilities at all. And it's a very, very slight difference even then.
So really, unless you've shuffled that playlist at least 10 or 20 times the number of songs actually in it, you really can't make any visible or noticable call on the randomness of the randomizer function being used.