Here is why it is not completely crazy to buy a lotto ticket

Why people buy lottery tickets has long been argued over by economists. More recent economic theories give fascinating insights into why people play, attracted by the very remote possibility of winning a life-changing sum. When you see a family in north Co Dublin win €175 million, the possibility of winning, however unlikely, is underlined. And this, economists believe, helps people to give undue weight in their decision making to remote odds of winning big.

Whatever the reasons, the lottery is big business. As well as prizes, it supports jobs in retailers and in causes supported by lottery spending. In some ways, the lottery is a kind of incentivised tax collection scheme, collecting funds to spend on worthy projects which might otherwise be supported directly from the public purse. It has even been called a tax on people who are bad at maths.

1. Why do people play?

The idea of people spending cash to buy lottery tickets has been a challenge to economic theory. True, a fair amount of cash is returned, one way or another, in prizes. In total, the National Lottery paid out €452 million in prizes in 2017, equivalent to 56.5 per cent of the amount spent on playing Lotto games. Generally, lotteries across the world return somewhere around half spending in prizes.

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In Ireland, there are two distinct kinds of pay-outs – the small and the very large. A study by economic consultants Indecon published last December found that, between 2015 and 2017, there were 40 winners of Lotto prizes over €1 million , with the average win being €5.6 million. EuroMillions prizes are even greater, with winners across Europe taking on average €40 million.

These are the fantasy prizes which cause people to play, individually or in syndicates, almost no matter what the odds. And the odds are not in your favour.

In the case of the EuroMillions draw, the chances of winning the jackpot after buying one ticket are just under one in 140 million. The odds on an Irish Lotto jackpot win with all six numbers from 47 balls are a bit more favourable, around one in 10.7 million. By comparison the odds in the massive US Powerball game are one in 292 million, yet “lottery fever” regularly sweeps the US states involved as the rollover jackpots move into the hundreds of millions of dollar.

When the Irish Lotto started in 1988, there were 36 balls, leaving the odds at around one in 1.95 million and leading to one successful attempt to buy up all the possible numbers by a massive syndicate. The number of balls has increased significantly over the years.

Interestingly there is some evidence from the US that making the game harder to win and thus leading to bigger rollover jackpots appearing more often are one factor encouraging participation. If it could be guaranteed that there would be only one winner , then a bigger prize obviously makes it a better investment. But the problem is that a higher jackpot, by encouraging more buyers, is more likely to lead to multiple winners. The maths remains against you.

However, there are many more winners of much smaller amounts, either via the Lotto games or scratch cards. So the odds of winning something are a lot better, even is the estimated value of the ticket is less than what you paid. The odds of wining something on Lotto Plus are as low as 10 to one, for example. The motivation for scratch cards, in particular, is probably different, with the incentive of a quick win of a few euro – and significantly better odds, which can be as low as four or five to one.

Interestingly, scratch card winnings accounted for just over a third of all winnings in 2017 and overtook Lotto winnings as the main source of prize money in 2014. Of the 8.354 million prizes won in 2017, 18 were valued at over €1 million – and 8.344 million were worth €1,000 or less – in many cases a lot less.

So with the Irish National Lottery games , if you win, you are either one of the many who win small, or one of the very very few who win big. Yet it is the long odds on winning big – and the decision to play anyway – which has intrigued economists.

2. What is the theory?

The idea of buying lottery tickets seems to go against the traditional economic theory that people act rationally and allocate their cash to where it can offer the best return based on the probabilities.

Economists who look at human behaviour have particular challenges dealing with uncertainty and people’s attitude to risk. Buying a Lotto ticket does not seem a logical response to the remote likelihood of winning.

For years, economists have tried to rationalise this in terms of economic theory, with a famous paper by US economist Milton Friedman in the late 1940s suggesting that people could be attracted to lottery gambling by the chance of transforming their lives and increasing their social standing. In this way, he said, they were still acting rationally.

Subsequent work in behavioural economics has developed a new approach, which has much of its basis in psychology. Pioneered by Nobel prize winner Daniel Kahneman, the Prospect Theory takes a new approach on how people look at risk, arguing that they are more influenced by the scale of the gain or loss than the probability of it happening.

People’s decisions are not always driven by an accurate assessment of the probabilities of the event – good of bad – happening, according to Kahneman. In particular people tend to provide a lot more weight than justified to small probabilities of making big gains – or significant losses.

People are averse to even a small risk of a big loss and will take often unreasonable risks to try to avoid it, Kahneman argues. The flipside is that the scale of a lottery win attracts people to buy tickets, no matter what the odds are.

In his best-selling book, Thinking Fast and Slow, Kahneman called this the possibility effect – the attraction of the chance of winning. He wrote: " When the top prize is very large, ticket buyers appear indifferent to the fact that their chance of winning is minuscule. A lottery ticket is the ultimate example of the possibility effect. Without a ticket you cannot win, with a ticket you have a chance, and whether the chance is tiny or merely small matters little.

“Of course, what people acquire with a ticket is more than a chance to win; it is the right to dream pleasantly of winning.”

His research also points to the importance of people seeing examples of Lotto winners – emphasising the “availability” of the prize. “It could be you”, to borrow the marketing slogan. The “framing” of the proposition to people is vital, he says – and there is much in his work in this area relevant to how businesses interact with consumers. Lotteries attract people by focusing on the prize.

In this way, while buying a lottery ticket may not be a rational economic decision on purely financial grounds, it is justified by other factors. It is fun, in other words. And it is nice to dream of winning.

3. What is the bottom line?

The National Lottery, run by Canadian-owned operator Premier Lotteries Ireland (PLI), is a big business in Ireland, representing around 13 per cent of the total betting market and with a significant economic impact. The study by Indecon consultants estimated that, taking account of all its economic impacts – the spending of prizes, jobs in the retail sector and the spending on good causes – it adds close to €2 billion to consumer spending and directly supports over 17,000 jobs.

Over €5 billion of lottery funds has been spent supporting projects and activities around the State since its establishment in 1987 and €8.8 billion, or 53.5 per cent of sales, has been returned in winnings.

Annual sales are now in excess of €800 million, having recovered from a dip during the economic crisis, the first fall-back since the foundation of the organisation.

The main Lotto game accounts for half of sales since 1987, though recent years have seen the introduction of more games and, of course, the EuroMillions. In 2017, the main Lotto game accounted for just 29 per cent of total sales, similar to scratch cards, with EuroMillions at 22 per cent.

There has been controversy in the US in relation to spending by less well-off sections of the community – with one piece of research showing that people with incomes of less than $10,000 spent an average of almost $600 a year on lotteries. Here, the Indecon research suggests that participation in Ireland is roughly in line with the overall population in terms of social class, though players tend to be a bit older and are a bit more likely to be male.

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The bottom line is that lotteries have provided a fruitful area for economic theorists, with a marriage of psychology and economics now leading to the more plausible reasons of why people play, even if financially it is not the best use of their cash.

And of course people are always wondering can they improve their odds. This has led to a lot of “gamblers’ fallacies”. Some people try to pick numbers which are more regular winners, and others go for those which have not come up recently. Neither course of action is logical. Nor is the idea that that if you keep gambling, your odds improve – the money you have spent already is gone and your odds remain the same.

Of course, buying more tickets improves your odds – and participating in a syndicate that buys a lot of tickets will improve the odds of winning, but also cut your pay-out. Interestingly, people also tend to stick with syndicates because they would hate to be the one who missed out. Some people advise that it is better to pick at least some higher numbers, above 30, as people tend to pick based on birthdays and anniversaries and going higher might cut your chances of having to share.

And of course the most common behaviour is to buy when the jackpot rolls over to something really huge. This does make a more attractive pot but high participation also increases the risk that if you did win you would have to share.

For this week’s EuroMillions winner, however, the money was all won by just one ticket.