Yet tickets are bought so frequently that well-run lotteries are, for the organisers, virtually a license to print money.
All lotteries exploit a simple bias in the way the human mind works called the availability bias (that and people's desperation).
This is the tendency to judge probabilities on the basis of how easily examples come to mind.
Since lottery organisers heavily promote the jackpot winners, people are continually hearing about those who've won big. On the other hand they hear almost nothing about the vast majority of people who haven't won a bean.
So people assume they are much more likely to win the lottery than they really are.
The UK lottery is promoted with the phrase "It could be you", which, of course, is technically true. To tell the whole truth it should read: "It could be you, but it almost certainly won't be."
This bias affects all kinds of judgements we make that rely on memory. Here are a few more examples:
- A doctor who has just diagnosed two cases of bacterial meningitis is likely to see it in the next patient, even though they only have the flu, which it resembles.
- People judge themselves more likely to be murdered than getting stomach cancer, because homicides are so frequently reported in the news (Brinol et al., 2006). In fact it is five times more likely that you will die of stomach cancer (which is already fairly rare) than be murdered.
- The same is true of shark attacks, which people think are relatively frequent because of media reports. In fact you're more likely to be killed by a part that's fallen off a plane, which in itself is unbelievably unlikely (Read, 1995).
- When two of your friends have just had car accidents, you judge the roads are becoming less safe and feel you're more likely to have an accident as well.
And the examples go on.... when information is more obvious, vivid or easier to recall it biases the way we assess the probability of that event.
The reason we have this bias is that some of the time it is an effective way to make quick decisions. For example, memorable events - like getting food poisoning from a bad prawn curry - teach important lessons (about cheap restaurants).
Beat the bias
Often, though, the availability bias serves to make us more nervous than need be. But there is a way to beat it without resorting to a statistics textbook, an actuary and a super-computer. The key is to specifically try and recall instances of the event that aren't so memorable. For example, how many people do you know who have:
- not been murdered?
- failed to win the lottery jackpot?
- not been killed in a shark attack?