James and Katie play a board game online which uses two dice to move around the board. Katie doesn’t have two dice, so uses a 12-sided spinner instead. The rules say that each player moves along the board the number of spaces shown on the two dice together. For example, throwing a 3 and a 6 means the player can move 9 spaces. An extra go is awarded each time the player rolls a double-six – James and Katie agree that Katie earns her extra ‘roll’ if she spins a ‘12’.After playing several games, James claims that Katie must be cheating because she gets many more extra ‘rolls’ than him on every game.
• Try to decide whether James is right. Must Katie be cheating, or is there some other explanation for her luck?
• Use probability to explain why this problem has arisen
• Try to devise a fairer way to play the game.