"More fun with numbers"

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.