Lowest Number Wins - How Low Can You Go?

Players: The more the better!
Ages: 6 and up
Cost: Free!
Math Ideas: Probability, game theory
Questions to Ask: 
    Why not just pick 1?
    If we played with 100 people, what number would you pick? Why?

This week my family celebrated Rosh Hashanah, the Jewish new year, by having 32 folks over for dinner on Sunday night. It was a glorious, crazy mess, as indicated by this picture of my brain afterward (artist's rendition).

At one point I found myself in a room with kids of all ages who were starting to get very vocal with their predictions about when, if ever, the dessert was going to be served. I realized that I was in a place I've been many times as a teacher: stuck in a room with a bunch of bored, hungry kids with nothing to do.

It struck me in that moment that sometimes parents need a quick, easy multi-age game just as much as I do in my classroom! I've shared a few options in the past, such as the 100 Game or Ultimate Tic Tac Toe. But what if you need something really quick, really easy, and really fun?

Lowest Number Wins is that game.

How to Play

I got the idea for this game from Todd Feitelson, a math teacher who plays weekly with his entire school. He even 3-d prints a custom trophy every week with the winning number and a celebratory M&M inside!

The only thing anyone needs is a blank slip of paper and a pencil.

You give the instructions very simply: "I want everyone to write down a whole number and their name on a slip of paper and hand it to me. The person who writes down the lowest number that nobody else wrote down wins."

Then get ready for the barrage of questions:

Can I write down zero?
Sure, and you better hope nobody heard you say that.

Can I write down decimals? Fractions? Negative numbers?
Nope, nope, and nope. Only whole numbers, the ones you learned in kindergarten, can be used.

What if everyone writes down the same number?
Then everyone loses and dessert is canceled.

Where's the Math?

So how would you pick your number? Let's say you're in a room with ten people. You could pick 0, of course, but look around the room. Nobody else is going to go for that strategy? 

Ok, let's start from a different direction. You could pick 10 and be almost guaranteed that your answer is unique. But you're basically hoping that everyone else guesses 0, 1, or 2 and cancels each other out, leaving you as the winner by default. Just as risky, but in a different way.

No matter your strategy, you are thinking probabilistically. You are assigning a likelihood to a bunch of possible outcomes in your head, then making decisions based on those (very informal) probabilities.

If you allow your kids to talk with each other, then they might get into some game theory as well. What if one kid loudly declares "I am writing down 0, so if anyone else writes down 0, we both lose!" How do you react? Do you trust him? Should you pick 0, just in case he's lying? Has he spent the last few years building up an immunity to iocane powder?

Questions to Ask

This is a game that is more fun with even bigger groups, so it's perfect for family gatherings, birthday parties, or anywhere else that you have a bunch of restless kids and desperately need a Plan B.

I suggest posing questions to the entire group, such as "How do you decide what number to choose?" or "If we were playing with 100 people, what number would you pick?" By fielding lots of responses, you get to hear a lot of perspectives on how kids think about this challenge. 

Not only that, but each new contribution to the discussion will have a measurable impact on the strategy on the next round. It's not uncommon for the winning number to shift significantly from round to round.

You could even make a graph like the one Todd made above, just to show how everyone guessed. Then see how that affects guesses in the next round!