Heads. Heads. Heads.

If a coin has landed heads three times in a row, what should happen next?

Most of us feel the pull of an obvious answer: tails.

But the coin doesn't know what happened before. If it's a fair coin, the next toss is still 50/50.

We know this intellectually. Yet our intuition keeps telling us otherwise.

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We are remarkably good at finding patterns, and remarkably bad at recognising when there is no pattern to find. [1]

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How randomness ‘works’

Before we look at why randomness can fool us, it helps to understand what we actually mean by random.

A random event is one where the outcome cannot be predicted with certainty from the information available beforehand. When random events are independent, the outcome of one event does not determine or change the probability of the next.

In other words, a sequence of independent random events has no memory.

A fair coin doesn't remember that it landed heads five times and a roulette wheel doesn't know what happened on the previous spin. Neither is keeping score or trying to restore a balance.

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A random process doesn't keep track of what happened before and doesn’t try to restore balance.

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This doesn't mean that random sequences look evenly distributed in the short term.

Quite the opposite.

A genuinely random sequence can contain streaks, clusters, and apparent patterns that look anything but random.

We are good at finding patterns even when they aren’t there

Our brains are remarkably good at finding patterns. It's one of the things that helps us make sense of the world.

But when it comes to randomness, that same ability can lead us astray.

Imagine flipping a fair coin 20 times. Which sequence looks more random?

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H T H T T H T H H T T H T H T T H H T H

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