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Law of truly large numbers


Think about something happening that's a million to one shot. Winning the UK big lottery prize perhaps (1 in 14 million actually), but what about consecutive lottery draws being identical? If that happened it must surely be a fix! It happened in Bulgaria in 2009. Statistician David J. Hand calculated the chances of the same 6 Nos. being drawn again were greater than 50 per cent by the 4404th round. To happen in the very next draw was significantly less likely but given the number of 6-ball lottery draws happening around the world on a daily basis, it is not impossible it would happen somewhere. That seemingly impossible odds are overcome is the Law Of Truly large Numbers.

In a population of 6 billion, million to one chances are commonplace. This fallacy is often at the heart of many pseudoscience claims: "It couldn't just be a coincidence" or "That's just too weird, it must have been meaningful". Imagine how many dreams people have across the world every night, imagine then how many of those people dream about a plane crash before their flight the next day, imagine then how many actually experience a place crash. Though that last number may be very small, the first number is astronomically big. Because your sample size is massive, the chances of the event occurring approaches 1.

It is why science doesn't just accept that coincidences are proof of anything, no matter how rare. One-off or rare events have to be measured against the sample size and repeatable, but ironically, such events are only meaningful because they stand out from the common events. We ascribe meaning to them only because they seem unique. Magician Dave Alnwick often selects and holds up the back of a card selected at random from a deck, he then asks an audience member to shout out a random card. He then turns his selected card around to show a different one (usually). "One out of 52 shows I'll get that right and seem like the world's most amazing magician" he quips.

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