The Improbability Principle: why incredibly unlikely things keep happening

Written by David Hand on . Posted in Features-OLD

David Hand, a former RSS President, has written a new book that asks the question: why do rare and improbable events continually happen in our world? He takes a statistician's knowledge of probability and seeks to answer the puzzle that exists in every walk of life. Here is a brief synopsis of what he set out to explain in 'The Improbability Principle'.

The American author Anne Parrish was born in Colorado Springs in 1888. In the 1920s she was browsing bookshops in Paris with her husband Charles Corliss when she came across a copy of one of the books which she’d loved as a child: a copy of Jack Frost and Other Stories. She showed it to Charles, who opened it, and there, written inside, were the words 'Anne Parrish, 209 N. Weber Street, Colorado Springs, Colorado’.

Here’s another true story. You know how difficult it is to keep track of all the passwords and PIN numbers we seem to need nowadays. One for each internet shopping site, one for each bank account, and so on. So there’s a natural tendency to use the same one each time. Presumably that’s why Kevin Stokes, of Preston in Lancashire, changed his Sainsbury’s bank card to a PIN code he could remember. But then chance began to intervene, making life especially easy for Kevin. When his Barclaycard arrived, it already had the same PIN code. Later Kevin and his wife Anne opened accounts for their pensions - and the random PIN code that Anne’s card had been given turned out to be the same PIN code yet again. Later still, when Barclays sent Kevin a new card, with a new PIN number, guess what that PIN number was. It was the same again.

Working out the probability that Anne Parrish would come across the very copy of a book she‘d owned as a child - many years earlier, in a different city, in a different country - is obviously quite difficult. Working out the probability of getting four identical PIN numbers is not quite so tough - one can find baseline probabilities from which to work. But in both cases, it’s not difficult to see that the chance of these things happening must be very small indeed. So small that you wouldn’t expect to see such things in your entire life, or perhaps in a period as long as the lifetime of the human race.

So small in fact that seeing such things happen might make you wonder if something funny was going on. If, in fact, something more than mere chance is coming into play, making these incredibly unlikely events more probable - or even causing them. It might even make you wonder if there’s some truth to superstitions like bad things coming in threes, or Jung’s theory of synchronicity, or miracles, or magic.

However, the fact is that such pseudoscientific explanations are unnecessary. To see this, the trick is to approach things scientifically, but in the right way.

And the right way is described in my book The Improbability Principle. The book describes a set of five laws, like Newton’s three laws of motion or the four laws of thermodynamics. But instead of being based on the physics of motion and energy, these laws are based on the mathematics of probability.

The book illustrates the laws in action, showing how each of them can lead to the occurrence of an apparently incredibly unlikely event. It describes the underlying principles, and illustrates with many real life examples. Taken alone, any one of the laws can result in the occurrence of events which ought to be so rare that we should expect never to see them happen. Taken together they intertwine to make extraordinarily improbable events commonplace. And that’s the essence of the improbability principle: extremely improbable events are commonplace.

There are five main laws constituting the improbability principle. One of which you might have encountered before is the law of truly large numbers. This is very different from the more familiar law of large numbers. The law of truly large numbers says that, with a large enough number of opportunities, any outrageous thing is likely to happen. Such things as people winning the lottery multiple times (which always seems so unfair, since most people have never one it once) or the same lottery jackpot numbers occurring on consecutive weeks. The impact of the law of truly large numbers is made even more striking when a subsidiary law, the law of combinations, comes into play. You may well have encountered this, in the form of the birthday problem, given the number of people who must be in a room to make it more likely than not that some pair have the same birthday. Feed the law of combinations into the law of truly large numbers, and it’s really no wonder that extraordinarily unlikely events occur.

A second of the five laws which make up the improbability principle is the law of the probability lever. This law can explain financial crashes, apparent psychic powers, how to beat casinos at roulette, as well as a host of other highly improbable outcomes. The other three laws are the law of inevitability, the law of selection, and the law of near enough. The braid they weave together is a rope pulling inexorably towards the improbable.

In addition to describing these five threads of the improbability principle, the book shows how to use the principle to bend probability to your advantage, in avoiding fraud, making perfect stock predictions, winning more on the lottery and even, that holy grail for lottery players, how to increase your chances of winning the lottery. All based on solid underlying science.

But the improbability principle is not merely about parochial human concerns such as lottery wins, gambling casinos, and lightning strikes. Apply the principle in other domains and it explains how we came to be here - and even, the ultimate question, why the universe is like it is.


The Improbability Principle is published by Bantam Press on 27 February in hardback, priced £20.

David Hand Probability

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