7.3 Fair and unfair games

7.3 Fair and unfair games (EMG54)

Do you think games of chance are always fair?

So far all of the games that we have looked at are fair because you have an equal chance of winning and losing. But some games are designed to be unfair. Do gamblers have a good chance of winning? Are you more likely to win if you are luckier?

Many games of chance are designed to make one person have a better chance of winning that the other. Every now and then, the loser will win, which gives them confidence to carry on playing! However, if the game is weighted towards one player, then that person will always win in the end.

When you know the chance of a particular event, then you can make predictions about the probability of it happening. A fair game is a game in which there is an equal chance of winning or losing. We can say that if a game is fair then the probability of winning is equal to the probability of losing.

If you change the rules, you can make the game less fair. For example, if someone wins a game of dice only if they get a \(\text{3}\), is it a fair game?

In the next activity you will make your own simple games and decide which rules give a player a good chance of winning, which games are fair or unfair and why.