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The Improbability Principle: Expecting the Unexpected

29/05/2015 18:54 BST | Updated 29/05/2016 10:59 BST

My bet is that you've never won a lottery jackpot. Few people have. After all, for example, for a ticket in the UK national lottery there's only a 1 in 14 million chance of winning. That's like getting 24 heads in a row when tossing a fair coin: you wouldn't want to hold your breath!

And yet - people do win the lottery. Indeed, most weeks the newspapers or the television contain reports of some lucky person whose life has been transformed (not always for the better, though, as later stories sometimes tell). Indeed, there are also stories of people who've won the lottery twice, such as Evelyn Marie Adams, who won the New Jersey lottery twice.

Lottery wins are a familiar example of highly improbable events which occur - and occur repeatedly. But every week the media describe other such things: Alex and Donna Voutsinas discovering that, when they were children and long before they met, they'd been taken to DisneyWorld at the same time (the photo of Donna proved it - there was Alex, in his stroller, in the background). Financial crashes, which the experts calculate should occur about once every 20 billion years, occurring time and time again (to give some perspective, the universe is only 14 billion years old). The classic case of 10 year old Laura Buxton releasing a balloon, with a message saying "if found, please return to Laura Buxton", and giving her address, and the balloon being found by another Laura Buxton who lived 140 miles away. And so on.

This is all very puzzling. If these sort of things are so incredibly unlikely, how come they keep on happening?

The answer lies in the so-called improbability principle. This simply says we should expect highly unlikely events to keep happening. The improbability principle also explains why we should expect these things to happen, which is just as well since, when put bluntly like that, it sounds absurd. After all, surely by definition highly unlikely events must be very rare.

The improbability principle consists of five scientific laws, which weave together to make the improbable almost inevitable.

The law of inevitability says something must happen. When you toss a coin, you know for sure that it will come up heads or tails or that it won't show either - because it falls through a crack in the floor, or ends up leaning against the wall for instance. There are only these three possibilities. It's inevitable that one of them will occur. Likewise, if you buy tickets for all the possible 14 million lottery results then you're guaranteed to hold the jackpot winning one (though, as you'll have spotted, you're not guaranteed to make a fortune - somebody else could buy the same numbered ticket as you).

The law of truly large numbers says that, if you give a highly improbable event enough opportunities to happen then it becomes almost certain. Keep looking for long enough and you will find a four-leafed clover. If enough people each buy one lottery ticket then it becomes almost certain that someone will win. This explains why someone wins the jackpot most weeks, but it is very rarely you!

The law of selection says that if you change the collection of things you choose from, you can change the chances. This law explains why, looking back in time, it might seem obvious what would happen, whereas predicting the future is so tough: there are so many ways that the future can pan out, but only one way that the past did. More subtly, it also explains why speed cameras are effective at reducing accidents, but not as effective as seems from the raw numbers.

The law of the probability lever says that if you change the conditions, you can dramatically alter the chances. Casinos are based on this principle: the slight odds in their favour mean that, over time, they are essentially guaranteed to win.

The law of near enough says that if you relax your definitions you can almost guarantee coincidences. Mike McDermott was reported as winning the lottery twice, first winning £194,501 and then winning £121,157. But both these "wins" were second prizes, not the jackpot - the definition of "win" had been changed. The chance of winning a second prize is much greater than that of winning the jackpot, so the chance of winning twice is also much greater.

As the examples above show, unlikely things happen when the laws work alone, but often they work together, combining synergistically, so that even more surprising things occur. The improbability principle is a rope of chance, formed by braiding together its five laws, and it tells us why such extremely improbable events happen every day.