"The steaks were too high"

Yup, I made a mistake. In my calculations of John Reemtsen's odds of winning three times out of five spins of a wheel to get way more steak than he could possibly need, I forgot a crucial detail. Huge thanks to David Weinberg, chair of OSU's Department of Astronomy, for pointing me in the right direction.

I was correct in figuring that there were 10 different arrangements of winning three times out of five. For example, he could've won on his 1st, 2nd, and 3rd attempts, or on his 2nd, 4th, and 5th attempts, and so on. And the process for figuring out John's odds are still the same: count up the total number of ways he could win, and divide that by the total number of all possible combinations.

So far, so good. But here's where I miscounted: there were 32 positions on the wheel, which means there isn't just one way to lose, but 31! Let's say John won on his first three attempts. For the next two spins, there are 31*31=961 ways to *not* get the steaks.

This means that there are many more than 10 arrangements of wins for John to get his juicy steaks; there are 10*31*31, or 9,610 possible winning combinations. This increases his odds of winning from one in a million to one in 3,491.

John is still very, very lucky, but maybe he doesn't owe me a free steak any more.