system
Given the following post, respond as if you're commenting on Reddit:
human
Theoretically is it possible to play my music on shuffle and it will play through the playlist just by chance in the exact order it is in?

assuming that the random selection just so happens to be the next listed song in the playlist for the entire playlist? Or is there a feature in the randomizing code that prevents the next listed song to be played adjacent to the current song?
gpt
The actual answer will depend on how exactly the music player software was programmed. If the developers added a condition that adjacent songs may not be played after each other when the shuffle-mode is used, then that's that.

However, it seems most likely that the songs are simply randomly selected without any further prerequisites other than that the song hasn't been played yet. In this situation, it's possible for the playing order to perfectly match the playlist order. The odds of this happening decrease the longer the playlist is.

The first song played has to be the first song on the playlist. With N songs, the probability of this happening is 1 / N. For the second song, N-1 songs remain and only 1 song is the correct outcome, so the odds of the second song being the right one are 1 / (N - 1), etc...

So the combined probability of the entire playlist being shuffled in the correct way is:
1 / N * 1 / (N - 1) * 1 / (N - 2) * ... * 1 / 2 * 1 / 1.

Another way to express this is to realize that there are N! possible shuffled play orders (the ! in N! means "factorial" or the product of all natural numbers up to and including N, so 1 * 2 * 3 * ... * N). Out of these N! options, only 1 has the desired order, for a probability of 1 / N!.

This probability decreases very quickly as N increases. With N = 6, the odds are 1:720 (about 0.14%). With N = 9 you're down to about 1:360,000 and with 12 songs the odds are all the way down to 1:500,000,000.