During the week I attending a neat talk at Harvard given by Tim Gowers. The talk was about a intransitive dice. Not all of the details in the talk are accessible to kids, but many of the ideas are. After the talk I wrote down some ideas to share and sort of a sketch of a project:
One of the Gowers’s blog posts about intransitive dice is here if you want to see some of the original discussion of the problem:
We started the project today by reviewing some basic ideas about intransitive dice. After that I explaine some of the conditions that Gowers imposed on the dice to make the ideas about intransitive dice a little easier to study:
The next thing we talked about was 4-sided dice. There are five 4-sided dice meeting Gowers’s criteria. I thought that a good initial project for kids would be finding these 5 dice.
Now that we had the five 4-sided dice, I had the kids choose some of the dice and see which one would win against the other one. This was an accessible exercise, too. Slightly unluckily they chose dice that tied each other, but it was still good to go through the task.
Now we moved to the computer. I wrote some simple code to study 4-sided through 9-sided dice. Here we looked at the 4-sided dice. Although it took a moment for the kids to understand the output of the code, once they did they began to notice a few patterns and had some new ideas about what was going on.
Having understood more what was going on with 4-sided dice, we moved on to looking at 6-sided dice. Here we began to see that it is actually pretty hard to guess ahead of time which dice are going to perform well.
Finally we looked at the output of the program for the 9-sided dice. It is pretty neat to see the distribution of outcomes.
There are definitely ideas about nontransitive dice that are accessible to kids. I would love to spend more time thinking through some of the ideas here and find more ways for kids to explore them.