Dueling Dice
How it works
Imagine we have two unusual dice:
- One has 3 dots on every face
- One has 2 dots on four faces and 5 dots on two faces
If we roll these two dice against each other 1000 times, which one do you think will win more often?
In this activity, students start by exploring this question. First they make a prediction, then they run a computer simulation to test their prediction.
When they've found which die wins more often, they try to design a die — deciding how many dots to put on each face — with the same total number of dots that beats this die more than 50% of the time. Then they examine whether their die also beats the other die more than 50% of the time. The answer might surprise them!
Why we like this activity
- It’s fun! Students enjoy predicting which die will win, using simulations to test their predictions, and designing and analyzing their own dice.
- It helps students develop probabilistic and statistical reasoning.
It requires students to engage in mathematical habits of mind:
- Comparing and contrasting / making and testing predictions when trying to figure out which die will win more often.
- Finding and using strategies to design a die that wins more than 50% of the time against another die.
- It has a low floor and a high ceiling: It's easy for students to get started making and testing predictions, but designing and analyzing dice can be quite challenging.