## MatheMUSEments

Articles for kids about math in everyday life, written by Ivars Peterson for Muse magazine.

## April 2, 2007

### Weird Dice

The dice game known as Piggy punishes the greedy player. In Piggy, you and your opponent take turns rolling a pair of ordinary dice. Your score is the sum of the face values of the dice, so if you roll a three and a four, you get seven points. The first player to reach 100 points wins.

Here's the fiendish part. You can roll as many times as you want in a turn, but as soon as you roll doubles, you lose all the points you have won in that turn, and your turn is over.

Now suppose that you can choose between using a standard pair of dice or a special pair of dice. Instead of having faces marked with 1, 2, 3, 4, 5, and 6 dots, one of the weird dice has faces labeled 1, 2, 2, 3, 3, and 4, and the other has faces labeled 1, 3, 4, 5, 6, and 8.

Amazingly, your chances of rolling any particular total are the same with either pair of dice.

The chart shows there are only two ways (shaded yellow-green) to roll a sum of three with the standard dice. The same is true of the weird dice. Similarly, with both pairs of dice there are six ways (shaded purple) to roll a sum of seven, and so on.

Would you use the weird dice in a game of Piggy? If you did, your chances of getting a particular total on a given roll would not change. However, if you look closely at the chart, you'll see that doubles come up more often with standard dice than with weird dice. (Doubles are shaded blue.) Since the Piggy player who rolls doubles more often usually loses, you should choose the weird dice.

If you want to try out weird dice with Piggy or a board game, such as Monopoly, you can easily convert standard dice into weird dice. Take one standard die, then cover the 5 with a small sticker and label it 2, and cover the 6 and label it 3. Take another standard die and put a sticker over the 2, labeling it 8.

In a game like Monopoly, where rolling doubles has special consequences, you might find that using the weird dice changes your strategy a little.

Muse, May/June 2000, p. 18.