November 2007 Archives

Filling the space with something . . .


One of the things that is both wonderful and difficult about being the stay-at-home-in-the-morning father of an 18 month-old baby is the kind of "thinking time" you get.

Here's what I mean: hanging out with Zoe isn't like brain surgery. There are no complicated problems to figure out, no serious problems to solve. All of that comes later, I think. For now, we say, "look!" to each other a lot, and roll around on the floor laughing, and carry toys from one room to the next. There's a lot of space in my brain for thinking during these times, though when she's awake, I try to be present as much as possible. Every day is new and wondrous.

But when she goes down for her nap, I have to spring into action. Dishes need to be washed, the animals need food, I have to grab a shower, lunches need to be packed, etc. Again, none of this is like doing calculus, or solving a complicated strategic problem. It's all busy work that just has to get done NOW.

So I tend to play games with myself while I'm doing the dishes or picking up toys. I make up problems—usually ones that grow out of some kind of day-to-day experience I'm having, but not always—and I try to solve them. Anyone who knows me knows that I'm that kind of geek.

The one I did most recently kept me up into the night and required some work in a spreadsheet program, but I solved it. For the pleasure of geeks everywhere, I present it to you now:

The Scenario
You are buying groceries one evening with your family. While checking out, sirens and lights go off everywhere and balloons drop out of the ceiling. The manager of the store comes running out to you and says, "you may have won 1 million dollars!"


He brings you over to the customer service counter, where they've set up a green felt gaming board. You see a stack of red dice on the board.

Here's what the manager tells you:

We're going to roll these dice once to see if you've actually won 1 million dollars. Here's the deal: you decide whether you want to roll 1, 2, 3, 4, 5, 6, or 7 dice. When you've decided on the number of dice to roll, I'm going to grab the same number of dice for myself.
We'll roll our dice at the same time, we'll count up all of the numbers from each of the dice, and whoever has the higher number wins.
But to make it a bit more interesting, and because you are a valued customer, I'm going to give you a tiny advantage: I'll give you a win if we tie.
Go ahead and grab the number of dice you want to roll, and let's see if you walk out of this store a millionaire! Remember, you can choose to roll 1, 2, 3, 4, 5, 6 or 7 dice.

The Question
Here's what I want to know from you: What number of dice gives you the highest probability of winning?

All seven possibilities are better than 50%, simply because a tie goes to you, as the attacker. But I want to know how much better than 50% each of the seven possibilities is.

Everyone will have an intuitive answer, but that's not what I want. Give me the intuition, but I also want to know what the percentage chance is to win for each of the seven scenarios. I'll need to see your work, too. Tell me how you got there.

The Spoils
I don't expect a lot of people to play this game, but post the right answer in the comments first, and you could win something geeky. Maybe a t-shirt, probably a gadget. You'll have to play to find out. But you have to be a complete dork (like me) to want to solve this problem at all, so I know that it doesn't matter what you win. Getting the right answer will be the best reward of all.

About this Archive

This page is an archive of entries from November 2007 listed from newest to oldest.

September 2007 is the previous archive.

January 2008 is the next archive.

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