# Unpopular Lottery Numbers

14 January 1995 was an evening that Alex White will never forget. He matched all six numbers on the UK National Lottery, with an estimated jackpot of a massive £16 million. Unfortunately, White (not his real name) only won £122,510 because 132 other people also matched all six numbers and took a share of the jackpot.

There are dozens of books that claim to improve your odds of winning the lottery. None of them works. Every combination of numbers has the same odds of winning as any other – 1 in 13,983,816 in the case of the UK “Lotto” game. But, as White's story shows, the fact that you could have to share the jackpot suggests a way to maximise any winnings. Your chances of success may be tiny, but if you win with numbers nobody else has chosen, you win big.

So how do you choose a combination unique to you? You won't find the answer at the National Lottery headquarters – they don't give out any information about the numbers people choose. That didn't stop Simon Cox, a mathematician at the University of Southampton, UK from trying. Ten years ago, Cox worked out UK lottery players' favourite figures by analysing data from 113 lottery draws. He compared the winning numbers with how many people had matched four, five or six of them, and thereby inferred which numbers are most popular.

And what were the magic numbers? Seven was the favourite, chosen 25 per cent more often than the least popular number, 46. Numbers 14 and 18 were also popular, while 44 and 45 were among the least favourite. The most noticeable preference was for numbers up to 31. “They call this the birthday effect,” says Cox. “A lot of people use their date of birth.”

Several other patterns emerged. The most popular numbers are clustered around the centre of the form people fill in to make their selection, suggesting that players are influenced by its layout. Similarly, thousands of players appear to just draw a diagonal line through a group of numbers on the form. There is also a clear dislike of consecutive numbers. “People refrain from choosing numbers next to each other, even though getting 1, 2, 3, 4, 5, 6 is as likely as any other combination,” says Cox. Numerous studies on the US, Swiss and Canadian lotteries have produced similar findings.

To test the idea that picking unpopular numbers can maximise your winnings, Cox simulated a virtual syndicate that bought 75,000 tickets each week, choosing its numbers at random. Using the real results of the first 224 UK lottery draws, he calculated that his syndicate would have won a total of £7.5 million – on an outlay of £16.8 million. If his syndicate had stuck to unpopular numbers, however, it would have more than doubled its winnings (The Statistician, vol 47, p 629).

So the strategy is clear: go for numbers above 31, and pick ones that are clumped together or situated around the edges of the form. Then if you match all six numbers, you won't have to share with dozens of others.

Unfortunately, probability also predicts that you won't match all six numbers until the 28th century. I bought a ticket using some of Cox's least popular numbers: 26, 34, 44, 46, 47 and 49. Not one of them came up.

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