How the brain misleads our intuition about chance

The mental shortcuts that help us make quick decisions often let us down when chance is involved. They lead us to expect results to ‘even out’, spot patterns where there are none and trust what we can easily remember more than what actually happens.

The imaginary balancing act

After five tails in a row, we feel that heads is due. But the coin has no memory: the chances are still fifty-fifty. This is the gambler’s fallacy.

What ‘looks’ random

If we ask someone to make up a random sequence of heads and tails, they almost never include long streaks. Yet streaks crop up very often in real sequences. Our idea of randomness is far too tidy.

What we remember

Striking events are easier to remember. An incredible hand sticks in our minds; a hundred ordinary hands don’t. That’s why we overestimate how often rare events happen. We see this in impossible coincidences that really can happen.

How to avoid these traps

• Think in numbers, not feelings.
• Remember that with cards, what has already come up does matter, but with dice it doesn’t.
• Be wary of the phrase ‘I’m due a win’.

To practise with simple calculations, read probability for beginners using cards.