Steve West - Permutations and combinations

MARY REICHARD, HOST: Today is Tuesday, January 11th. Good morning! This is The World and Everything in It from listener-supported WORLD Radio. I’m Mary Reichard.

NICK EICHER, HOST: And I’m Nick Eicher. Here’s WORLD commentator Steve West on calculating probabilities in dice and marriage.

STEVE WEST, COMMENTATOR: My wife is a gamer. I mean that in a very limited way. She doesn't binge in front of the Xbox, playing Call of Duty: Black Ops, though I expect she would do quite well. No, when we go out to lunch or dinner and wait for our meal, the backdrop of our conversation is often a game of Yahtzee played on my smartphone. Pass and play. She's competitive and yet gracious, whether winning or losing. I'm not … competitive that is. I lose too much. I do try to be gracious.

“Hey, you're almost winning,” I say, as we wait on pizza.

“What do you mean? We're tied.”

“Well, you’re almost winning. One more point and you will win. I'm almost winning too.”

She smiled. The man and woman in the next booth stare at us. They are sitting on the same side of the booth, unusual, and they are not smiling. I look back at the game.

On the hundreds of occasions we have played this game, the words “permutations” and “combinations” always come to mind. A door opens on my 10th grade algebra class in which I studied these concepts. My eyes sweep the class and go right to the large and open windows that look out on a flagpole. It’s rope snaps in the wind, and the ring that holds it clangs against the pole. I have only the vaguest notion of what the words mean. I think the sound of the phrase, permutations and combinations, was what I enjoyed, its assonance.

“Your turn,” my wife says.

I roll a six, five, three, two, and six. I'm thinking … what are the odds I will roll another six to give me three of a kind? But I have two rolls. If I save the two sixes and roll again, what are the chances that one of my three rolling die will be a six? What are the chances that all will be sixes? Should I save the two sixes or roll all five of them again? My head hurts.

“Are you going to roll?” she asks.

I'm thinking this has something to do with permutations and combinations, but I have no idea. I roll all five die. Hmmm. No sixes at all. What are the odds?

Soundly defeated, I vow to look up permutations and combinations when I get home. Turns out, Yatzee has nothing to do with permutations, where sequence matters. But it has everything to do with combinations, and probability. For example, the odds of rolling all of one number on the first roll of five dice (you yell “Yahtzee” here) is 1/1296. That’s discouraging, of course, and utterly useless.

Mr. Wizard is not playing Yahtzee. Besides, the pizza is here. A few mouthfuls later, she won. Again.

“You almost won,” she generously said. “Essentially, we tied.”

I smile. She won by two points. I think that unwillingness to trumpet victory is called parity of hearts or, maybe, oneness. What are the odds of that?

I’m Steve West.

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