Looking ahead to Friday the 13th

Tomorrow is Friday the 13th, and we talk a little bit about the lore of that number in our own Issue 13. But today is a great day to delve a little bit deeper into the math behind the number. A good place to start is with Friday the 13th itself. Here's a question with an obvious answer: how common is Friday the 13th? That obvious answer is that on average, it should occur on average every seven months. Afterall, there are seven days of the week, so there's a one-in-seven chance that the 13th will fall on a Friday, right? And a one-in-seven chance for every other day, right?

Well, actually that obvious answer is wrong.

Over the course of any 400 year period, Friday the 13th will occure 688 times, while Saturday the 13th will occur only 684 times. This means that Friday the 13th occurs, on average, every 6.97 months. Infact, the 13th day of a month falls on a Friday more than any other day of the week. The math is a bit confusing, but in short, it's due to the magic of leap years.