Beyond the hope, marketing and the rational realisation that it almost certainly won’t be you, lotteries are about psychology and cold statistics with the power to change your life. Forty-nine numbers. You choose six. You have a one in 13,983,816 chance of hitting the jackpot.
It sounds simple, but when you delve beneath the central improbability of matching all six numbers, lotteries and their variants are fiendishly complex games that have taxed the minds of statisticians, psychologists, and those who seek to game the system.
Now, by doubling another key figure – the cost of a ticket – the dream dealers at Camelot have changed the game for good. Your chances of winning big will always be one in 14 million, but, below the jackpot, where does the new lottery leave those willing to pay two pounds for a shot at riches? And, ultimately, who wins?
David Spiegelhalter is a statistician and the Winton Professor of the Public Understanding of Risk at the University of Cambridge. He knows about numbers, and spent an hour yesterday crunching the tables drawn up for the new lottery.
First, what’s new? From next autumn, the estimated average jackpot rises from £4.1m to £5m on Saturday and from £2.2m to £2.5m on Wednesday. Rewards for matching three numbers will go up from £10 to £25. Four numbers? You’ll get £100 rather than £60. Match five and winnings drop from £1,500 to £1,000, and from £100,000 to £50,000 if you also get the bonus ball. New raffle numbers printed on all tickets, meanwhile, mean at least 50 players will win £20,000.
“Say you buy two tickets a week, for about £100 a year,” Spiegelhalter says. “Currently on average you’ll win £46 a year. You have 87 per cent chance of winning something, while one in 8 people will win nothing.”
After the change, he adds, “if you spend the same amount perhaps by cutting out your Wednesday ticket, one in three people would win nothing, up from one in eight. But now 63 per cent of people will win something, down from 87 per cent, but they will win at least £25.”
In summary, unless you spend more, you’re more likely to win nothing. But if you do win something, it’s likely to be more, thanks also to the new raffle, which Spiegelhalter says increases the chance of winning significant amounts below jackpot level. “If it wasn’t for the raffle the changes would be ludicrous,” he adds.
If statistics govern your chances of winning (or losing), psychology explains why people play a game with such rotten odds. In a recent article in Pyschology Today, Dr Stephen Goldbart, author of Affluence Intelligence, said: “Jumping on the bandwagon is an age-old motivator of psychological behaviour,” adding: “When we have been afflicted by what we have called the ‘financial anxiety epidemic’ in which we feel tired, uncertain of what to do, and disempowered, we may seek a magic pill to make us feel better.
“In reality, buying a lottery ticket is gambling. But in fantasy, it lets you believe in magic: that you will be the one who spent a little and got a lot; that you will defy the extraordinary odds against winning.”
Lottery ticket sales have remained strong despite the recession, rising 35 per cent since the games were rebranded 10 years ago. Around 60 per cent of adults in the UK play regularly, spending more than £6bn a year. Critics accuse the National Lottery of effectively taxing poor people seeking that “magic pill”.
A 2008 study in the US showed the poorest players spend almost 10 per cent of their disposable income on tickets.
Camelot will be aware that many regular players will be reluctant to “give up” their tickets, particularly if they play with the same numbers. “They’re exploiting your potential regret if your miss out,” Spiegelhalter says. “People are very fearful of regret.”
Nonetheless, studies suggest that Camelot is taking a big risk with its price rise. In 2008, researchers at Carnegie Mellon University in Pennsylvania set out to determine why, beyond hope, people with less were willing to spend more on tickets. In the study, published in the Journal of Behavioral Decision Making, some participants were given $1 at a time and asked if they wanted to spend each on a lottery ticket. People in a second group got $5 and were asked how many tickets they wanted to buy. Members of a third group were given $5 and told they could spend all of it on tickets or buy none.
People in the second group bought half the number of tickets as those given a dollar, while 87 per cent of those in the all-or-nothing group bought nothing. The findings agreed with what’s known as the “peanuts effect”.
“There are money amounts that are small enough that people almost ignore them,” Loewenstein told CNN last November, when the US Powerball jackpot had risen above $550m (£345m). “It almost doesn’t feel real. The lottery and penny slots are kind of the sweet spot of risk taking.”
George Orwell gave the bleakest depiction of a national lottery. In 1984, one such game served the dual purposes of raising funds for wars and distracting people from their predicaments (if not the novel’s main protagonist, Winston Smith). “It was their delight, their folly, their anodyne, their intellectual stimulant... There was a whole tribe of men who made their living simply by selling systems, forecasts, and lucky amulets,” he wrote.
“Winston had nothing to do with the Lottery, which was managed by the Ministry of Plenty, but he was aware that the prizes were largely imaginary. Only small sums were actually paid out, the winners of the big prizes being non-existent persons.”
Real prizes paid to real people, however few, have inspired enterprising number crunchers to exploit the system elsewhere. Students at the Massachusetts Institute of Technology discovered that by bulk-buying tickets for the state lottery, a quirk in the way prizes were distributed when nobody hit the jackpot guaranteed them a return of up to 20 per cent if they bought up to £400,000-worth of tickets.
Their scam became so sophisticated that several students stopped their studies to attract investors. They earned more than £5m by 2005. Moreover, they played with the knowledge of the Massachusetts Lottery, which only closed the loophole last year (no action was taken against the students).
In Ireland in the early 1990s, players picked six numbers from 36. Tickets for all possible winning combinations could be bought for less than £1m, guaranteeing a profit if the jackpot were any higher. When the jackpot reached £1.7m in May 1992, a syndicate of 28 players in Dublin, led by Polish-Irish businessman Stefan Klincewicz, had been preparing for such an event.
They spent £820,000 on more than 1.6 million combinations. But they were one of three players to hit the jackpot, and only made up a profit £310,000 thanks to winnings from tickets that matched four or five numbers.
Back in the UK, where the lottery will mark its 20th anniversary next year, Spiegelhalter admits to being an occasional player himself. “I buy tickets for school demonstrations to show children why they shouldn’t buy lottery tickets,” he says. After crunching the numbers following Camelot’s announcement, he adds: “I have some great new material.”