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Game of PIG - Sixes

Stage:3 Challenge Level:

Piggy Sixes

Piggy challenges you to play against her. Just play and have fun - then start to think of the mathematics behind the game. She has a good strategy for this game. Can you beat her? If everyone in the class plays Piggy does she win more games than the class? Why? Can you suggest a better strategy?

You can play this game with your family and friends. It is a game, played with two dice, for any number of people but it is best for 2, 3 or 4 players.

The winner is the first player to accumulate 100 or more points. Players all start with zero points, they take turns and they can throw the dice as many times as they like, adding the total at each throw to their cumulative total. Throwing a double 6 ends the turn and sets the score back to zero. Throwing one 6 ends the turn and nothing is added to the score for that turn.

The art is to decide when to toss again and when to stick. Can you formulate an optimal strategy for the game?

What is the probability of throwing a double six? What about the probability of throwing a double six in two successive throws, or three...? What is the expected score if you throw the pair of dice once, twice, three times...?

Try playing against Piggy. Can you work out Piggy's strategy.

Can you find a better one?