The National Lottery

Big balls, small chances: Roughly 32 million people play the UK lottery each week.

It could be you... but it almost certainly won’t: the lottery has made a bad bet even worse by adding ten numbers to its draw. The odds will now be one in 44 million. So why do people play?

  • The lottery! My one hope of a life of luxury and leisure...

    Don’t count on it. The chances of winning the lottery have always been stupendously low and from October your odds will get even worse. Camelot, the company that runs Britain’s National Lottery, announced this week that it will increase the number of balls in the draw from 49 to 59.

    That might not sound like a particularly significant adjustment, but its impact is huge. Currently, the probability that any given ticket will win the jackpot is one in 14 million. Once the changes come into place, they will fall to one in 44 million. The chance of winning smaller prizes will fall as well. In fact, the likelihood that you’ll win any monetary prize at all will fall by between 40% and 50%.

  • How can such a small change matter so much?

    That question gets to the heart of how the lottery works and why it is so deceptively difficult to hit the jackpot.

    To take part in the Lotto, a player picks six numbers between 1 and 49 and pays £2 to enter these numbers into a draw. Twice a week, six numbered balls are drawn at random from a pot.

    The first time a ball is drawn, there is a six in 49 chance that it will be one of yours. That means that 43 times out of 49 your bet will fail at the first hurdle. The second time, one of your five remaining numbers must come up out of the remaining 48 — a five in 48 chance. To determine the probability that both events will occur, we multiply them together: 6/49 × 5/48 = 5/588, or just over 1%. The next time a ball is drawn, the odds are lower again: now the calculation is 6/49 × 5/48 × 4/47, which comes to roughly 0.1%... and so on.

    Individually, the chances of each ball being drawn seem reasonable. But when they’re multiplied together, the probability shrinks extremely rapidly. Adding ten numbers makes each one only modestly less likely to occur, but these small differences multiplied together make your chances three times worse.

  • So they’ve just made it far harder to win? That’s outrageous!

    So say many. There is a sweetener, though: Camelot have added an extra rule whereby anybody who matches two numbers wins free entry into the next draw. Nevertheless, mathematicians have confirmed that the odds of winning actual money will be lower.

  • So you’re saying I shouldn’t play the lottery?

    You certainly shouldn’t expect to win. The odds of success are so small that they may as well be zero: you’re far more likely to be struck by lightning. And don’t forget that Lotto is a type of gambling. It can be addictive and a dangerous drain on your money. That’s why it’s illegal to enter the lottery if you’re under 16 — and why you should be very careful about playing even if you’re allowed.

  • But doesn’t the money go to good causes?

    Most of it goes to organisations that work in areas like charity, education, sport, heritage, the arts. So it’s not all bad. Besides, not everyone plays with the illusion that they might hit the bigtime. ‘If you’re playing because you want to donate money to good causes and you want a bit of midweek excitement, that’s great,’ says Mike Ellicock, the head of National Numeracy, ‘but if you think you’re going to get rich, think again.’

  • So, in short: good or bad?

    That’s the big question! To some people, the lottery is a handy fundraiser for charitable causes and a harmless excuse to fantasise about incredible wealth. Others see it as a particularly unfair type of tax, which disproportionately targets poorer and less educated people. There are even those who want to ban it altogether — but that’s not likely to happen any time soon.

You Decide

  1. ‘Playing the national lottery is stupid and irrational.’ Do you agree?


  1. The Day Lottery (not a real lottery) costs £1 to enter. Players choose three numbers between one and 20, then three numbers are drawn at random. If all three match, you win £500; otherwise you win nothing. What is the probability that any given ticket will win? Are players getting good odds?

Word Watch

Smaller prizes
Lotto players can also win smaller amounts of money by matching three, four or five numbers. Still, if you play regularly you will win back only 55.5p for every £1 you spend — and that’s before the changes come into place.
This is the main game run by the National Lottery. There are others (such as Thunderball) but none of them is even close to being a worthwhile investment.
Drawing numbers in a lottery provides an example of dependent events: when one of your numbers is drawn, this reduces the number of options by one and also the number of balls in the pot. However, successive draws are independent events: success or failure in one draw has no effect on your chances next time around.
Struck by lightning
Between 30 and 60 people are struck by lightning in Britain each year. This works out as one in every one to two million people.
Statistically, people on lower incomes spend a disproportionate amount of money on the lottery. And an awful lot of people play — around 70% of the total UK population, according to Camelot.

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The National Lottery
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