When events occur at random times, they will inevitably group in clusters in our minds - unless there is some non-random process that spaces them apart. And so when we experience haphazardly timed events in life, we're liable to think that bad things happen in threes, that some people are born under a bad sign, or that God is testing our faith.

The danger lies in the very idea of "randomness" - which actually is two ideas.

Randomness can refer to an anarchic process which throws up data without rhyme or reason - like the roll of a die or flip of a coin. But it can also refer to the data themselves when they defy simple summary.

For example - "heads, tails, tails, heads, tails, heads" looks random, while "heads, heads, heads, tails, tails, tails" does not because the second can be compressed into "three heads, three tails".

People judge the second run to be less likely, even though every sequence of flips is equally probable. They may even bet that after a long string of heads, the coin is due for tails, as if it had a memory and a wish to appear fair - the infamous gambler's fallacy.

What we often fail to appreciate is that a random process can generate non-random-looking data. Indeed, it's guaranteed to do so in the fullness of time. We're impressed by coincidences because we forget how many ways there are for coincidences to occur.