There are 2,779 songs on my iPod. Two of them are "Straight Edge" and "Straight Edge (Live)." And they just played back to back. The chances of that are 1 in 7,720,062.

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If you were to try and guess the first song to be played on your iPod, you would have a 1 in 2,779 chance of being right (assuming the iPod's randomization engine is flawless, which it certainly isn't). The second song, however, would have slightly better odds (1 in 2,778 since I believe iPod tries not to play the same song twice in a random playlist). Given that you've already heard "Straight Edge" and are waiting for the next song to play, there's actually closer to a 1 in (2,779 - # of songs already heard) chance of hearing the other Straight Edge (Live) song. In other words, the low probability of having song coincidences like this is greatly improved by the fact that the current song has already "eaten" its probability and the remaining probability required for a coincidence to happen is much less daunting.

It's like that riddle about a room of 25 people and how likely it is that two people have the same birthday. It's actually closer to 50%.

Though... 1 in 2,779ish is still pretty amazing. :) Have you by chance listened to approximately 1,400 songs on your iPod?

Posted by: Erik Benson | April 13, 2004 at 05:27 PM

The seven million number is 2779 * 2778, which is the chance of hearing any two arbitrary songs consecutively.

But, I agree with your math. The chance of hearing two songs that are adjacent to each other alphabetically are 1 in 1,389, considering the song one before and after the arbitrary song. It's actually slightly less because the first and last song are only alphabetically adjacent to one other. So it would be interesting if John Coltrane's "Big Nick" played before De La's "Big Brother Beat" or Björk's "Big time Sensuality," but certainly not blog worthy. Chances 1 in 1390 or so.

But there are not many repeated song titles on my iPod, with the exception of live songs and remixes. Straight Edge, Out of Step, Criminal Minded, Breath Control, and a bunch of Björk and Nirvana MTV Unplugged cuts. A query for "Live" or "Unplugged" returns 18 live Songs with studio counterparts. So there's an 18 in 2,779 chance of getting the first "paired" song and a 1 in 2,778 chance of getting its live companion. So the odds become 1 in 428,892.33.

And regarding your question about volume... this is my fourth iPod (counting my three replacements) so my playlist count isn't pristine (there needs to be a better way to handle this in iTunes) and over the last couple years I've listened to about 20 songs a day, or 14,600 songs. Well over 1,400, but less than 428,892. :)

Posted by: dj | April 13, 2004 at 06:43 PM

It's like that riddle about a room of 25 people and how likely it is that two people have the same birthday. It's actually closer to 50%.Also, I know this riddle, but I've never fully grokked it.

Posted by: dj | April 13, 2004 at 06:56 PM

Here's a detailed explanation of the Birthday Paradox, and here's a simpler one. I tried paraphrasing it but whenever you start explaining something by saying "it's easiest to understand if you work backwards" it's never very easy to understand. Maybe one way to grok it (without getting the math exactly right) is to remember that there are over 300 potential pairs of people in a room of 25 people. Each of those pairs has a 1/365 chance of sharing the same birthday. The chance is small for each pair, but since there are many pairs, the chance that at least one of them will have the same birthday as another is pretty high.

And so yeah, you're right that if you were waiting for those two exact songs to play back to back on the iPod, the chances of living to see the day would be very slim. But if you're just casually on the lookout for any coincidence, there's a much larger chance that you'll find something that had a very low probability of happening (and which is also blog-worthy) simply because there are so many possible coincidences waiting to happen.

I'm glad I could finally put my DeVry University iPod Statistics Degree to some use.

Posted by: Erik Benson | April 13, 2004 at 09:04 PM

I am not so sure about the randomizing algorythems in my iPod or on iTunes. Seems like I hit the same songs more often than not.

Posted by: Mark | April 16, 2004 at 05:03 AM