From the Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/
© Education Queensland, 1997

Dice Difference

In this game, you will play against a partner. One player is the Low player, and the other is High. Each pair of players needs two dice.

You will throw two dice, and subtract the smaller number from the larger. The answer is called the ‘Dice Difference’. The smallest difference is 0, if the two numbers are the same. The largest difference is 5, if the numbers are 1 and 6.

If the Dice Difference is 0, 1 or 2, the Low player wins. If the Dice Difference is 3, 4 or 5, the High player wins. For example, if the two dice are 5 and 2, then the Dice Difference is 3. The High player wins one point.

Investigation

1. Play 25 rounds against your partner. Record who wins each round, and who wins overall. Does the game seem to be fair to both players?
2. By drawing up a grid or otherwise, determine the theoretical probability of each player winning.
3. It turns out this game isn’t fair to both players. Explain how you could change the rules and make it fair. Justify your rule changes.