Teaching mathematics
Teaching mathematics

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4.2 Gambler’s fallacy

‘Later events may be affected by or compensate for earlier ones.’

Many people hold the incorrect belief that dice or coins have memory. When playing games or placing bets, people often believe that their luck is about to change because ‘a 6 is due’ or ‘my numbers must come up as they haven’t come up yet’.

In fact, when using a dice, coin, lottery machine, etc., the probability of an event occurring is irrelevant of the previous results. For example, Chloe says:

‘I have thrown a dice 12 times and not yet got a 6. The probability of getting a six on my next throw must be more than one divided by six.’


Chloe believes that the events that have occurred already have some kind of effect on future events. In fact, while it might seem unlikely to throw a dice 12 times and not get a 6, the probability of getting a 6 on the next throw remains one divided by six.

A photo of a hand holding a pair of dice.
Figure 30 Hand holding dice

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