Fair games, the stall and the Lotto

A game is fair when every player has the same chance of winning. That sounds simple, but many games that look fair are not, and some are unfair on purpose.

Checking fairness

To check a game, list every outcome and count how many lead to a win for each player. In Winning Differences, where Player A wins on a dice difference of 0, 1 or 2, Player A has 24 of the 36 outcomes and Player B only 12. It looks fair because each player has three numbers, but the numbers are not equally likely.

Why the stall usually wins

Gala stalls and fundraising games are usually set up so the stall wins more often than it loses. That is how they raise money for the school. It is fine, as long as players know the chances and the game is honest. A good stall shows its odds clearly, gives small prizes, and is still fun to play.

The Lotto

Lotto New Zealand draws 6 numbers from 40. There are 3,838,380 different ways to choose 6 numbers from 40, so each line you buy has a 1 in 3,838,380 chance of winning first division. If you bought one line every week, you would expect to wait tens of thousands of years, on average, for a win.

Picking 'lucky' numbers or numbers that have not come up for a while does not help. Each draw is random, and the balls have no memory. Health New Zealand's safer gambling service explains this so that people make informed choices.

Rules for fundraising

In Aotearoa, raffles and games of chance for fundraising have rules set by the Department of Internal Affairs. For example, the money raised must go to a community purpose, not to the person running it. Your gala committee can check these rules.

Designing a fair, honest game is a real skill. It needs clear rules, careful counting and lots of testing.