Randomness doesn’t mean equal distribution

This quote came up in my notes a few days ago, and it felt similar to a post I had recently written about how infinite numbers don’t include everything.

If you have a system that generates random output, there is no guarantee that the results will be perfectly distributed. If you output something random 1,000,000 times, things should end up pretty close but you never know for sure.

In the early days of the iPod, many users were convinced that the “shuffle” feature wasn’t really shuffling properly because certain songs would come up multiple times when others hadn’t been played once yet. The New York Times ran an excellent article about it, and Seth Godin summarized it in “All Marketers are Liars” like this:

The article was about people who were convinced that they shuffle feature on their iPods was broken. They were certain their iPods favored some songs over others. But randomness doesn’t necessarily dictate that the songs be distributed evenly.

In a way, this links back to the Baader-Meinhof phenomenon, which ties into why people think that Facebook and Google are listening to them. They’re not, but when “random” ads seem to show a close resemblance to something you recently said out loud, it sure feels like they were listening.

Remove the winners

The solution for this is to remove each item after it’s shown up. In the case of the iPod, that would mean that the shuffle feature would only shuffle songs that hadn’t already been played.

Not long ago, the spouse of a coworker was in a drawing at work where they drew two random names to give out prizes — and she won both drawings. The company remedied that, but the preventative solution would have been to remove her name for the second drawing after she won the first one.

In most cases, though, it doesn’t really matter. Enjoy those songs a second time and know that it doesn’t necessarily mean that the shuffle wasn’t random.