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.

Hanna Twining, one of our excellent educators in the Center for School & Community Partnerships, fired off a question to me about the so-called "EmDrive". You may (or may not) have heard about it in the news recently, and she wanted to be ready in case any students asked about it.

Well hold on to your hats, 'cause this one's a doozy.

First, the claims: some folks are building devices ("EmDrives") that bounce microwaves inside of a fancy cavity and say that it produces thrust. Difficulty: there are no holes in the cavity, so how can the rocket...you know, rocket? A couple month ago some engineers at NASA built their own and published a paper measuring a detectable thrust. Interesting.

What's the Big Deal? The Big Deal is that if these claims are true, then momentum is not conserved - after all, how else could a chamber full of radiation start moving around if it's not pushing on anything?

But conservation of momentum is on a pretty solid foundation: everything from General Relativity to Quantum Field Theory *rests* on conservation of momentum. The principle has been tested literally millions of times over hundreds of years.

Yes, of course we could be wrong about momentum. That's life. But given the paucity of evidence, here are the most likely explanations for the EmDrive, in order:

1) They're not measuring anything at all and just fooling themselves.
2) They're measuring thrust, but it's from something mundane like a leak in the cavity or an interaction with Earth's magnetic field. ...
3) Momentum is not conserved in our universe.

I talked about this at length on the November 25th episode of the Weekly Space Hangout (look for it on youtube), and I argue that the big NASA paper is riddled with errors: their estimates of uncertainty are way off and they're not really measuring anything. So I'm still waiting for someone to clear hurdle #1.

In a way, the EmDrive is a boon. If a student asks about it, this presents a great opportunity to talk about momentum, experimentation, and the process of science. Which are great things to talk about!

Last week I talked about John "lucky steaks" Reemtsen and his one-in-three-million chances of winning the big prize three times in just five spins of the wheel. One of my favorite parts about mathematics is that you can prove some pretty outrageous things. And I mean "prove" in a really serious sense: you can get counterintuitive results that fly in the face of common sense but simply cannot be argued against. Go ahead, try. You won't get anywhere.

Take, for example, odds. Every time John spun the wheel he had a 1/32 (or 3.125%) of winning steaks for a year. His chances of winning three times in five attempts were incredibly small. Let's say he had another crack at the wheel - what are his chances of winning free steaks yet again?

One might be tempted to think that there's no way his lucky steak streak would continue. His chances of winning again must be absurdly, pathetically low. One might think that, but one would be wrong. John's chances of winning steaks again are exactly, precisely, provably 3.125% - the same as his first pass.

Flip a coin and get heads 99 times in a row. What are the chances of getting heads on the next flip? 50:50. No better or worse than the last 99 flips, or the thousands of flips that came before you got your hands on the coin.

To think that your chances of winning or losing are based on your past successes or failures is known as the "gambler's fallacy", and it trips up a lot of people, especially when it comes to, well, gambling. But thankfully math is here to set us straight.