Roller Derby is a game of played with dice¹ that develop strategies for winning based on probability. The game can be played by people who already have a solid foundation in understanding probability. It can also be used as a way to introduce probability to support the development of that solid foundation.

The goal is to have students play the and ask them questions to help them develop a winning strategy based on probability.

1. To start, put students into pairs. Each player needs a game board, a pair of dice (number cubes), and 12 markers (pennies, buttons, chips, etc). It can help if you have two different color dice for each player, but it’s not necessary.(The rules and game boards can be found in the pdf link above)

   Here are the rules:

   • Each player takes 12 chips and place them into the columns on their board in any way they choose. (Players can have zero, one, or multiple chips in any column.)
   • Players take turns rolling two dice and removing a chip from the column with the same number as the total shown on the dice. Every roll applies to both players. If the column is empty, the player does not get to remove a chip.
   • The first player to remove all their chips wins
   • Keep track of all rolls in a chart with three columns – Die #1, Die #2 and Sums. (Here’s where it can help to have two different colored dice).
2. Let students play a few rounds.
3. Ask students, “What is a good strategy for placing your pennies (chips, buttons, etc) in the 12 columns on your game board?”
4. After students have shared some ideas, let them continue playing. Have them keep a record of the strategies they use.
5. Tell students they are going to stop playing for a little bit to do some reflection and develop their strategy.
6. Ask students to find a systematic way to list all of the possible outcomes for rolling two dice and the sums for each of those possible outcomes. (There is a chart for organizing all the possibilities in the PDF link above. I suggest letting students try to find a systematic way on their own and reserve the chart for groups that are struggling). A question that is likely to come up is whether rolling a 4 and then a 3 is the same as rolling a 3 and then a four. Again having two different colored dice can help students see that they are in fact different rolls/possibilities. 
7. Some questions you can ask:
   • What do you notice? What do you wonder?
   • What sums are possible when you roll two dice?
   • Which sums occur most often?
   • How many ways can you get a sum of 6? A sum of 2? A sum of 1?
   • Are all the sums equally likely? Explain your thinking.
   • Now that you’ve analyzed the possible outcomes, do you have any new ideas for a winning strategy for Roller Derby?
8. If you have time, let students play again using their new strategies.
9. Another interesting line of question is to give students different scenarios with different arrangements of chips and ask them to predict the winner. For example: Eric put half his chips on 4 and the other half on 11. Tyler put half his chips on 6 and the other half on 8. Who do you think will win? Explain your reasoning.

There are also a lot of questions you can ask students to make connections between these concepts and other areas of math. For example:

• If you roll two dice, what is the probability that the sum will be 4?
• If you roll two dice, what is the probability that the sum will be greater than 9?
• If you roll two dice, what is the probability that the sum will be a multiple of 4?
• If you roll two dice, what is the probability that the sum will will be prime?
• Steven and Tyler are playing a game called Odds and Evens. To play the game they roll two dice. If the sum is odd, Steven scores a point and if the sum is even then Tyler scores a point. Is this a fair game of chance? Explain your thinking.

Questions for further exploration

• What is the best strategy for placing your 12 chips?
• Should you always use the same arrangement of chips?
• Does it matter how the other person arranges their chips?
• Is putting all your chips on 7 a good strategy? Why or why not?
• How does the number of chips affect your strategy?
• What if we played with three dice?

¹ On the standardized texts, students should be prepared to see “dice” referred to as “6-sided number cubes”