Blogs | December 18, 2018

What’s a lottery ticket actually worth?

Do we need more restraint when it comes to lotteries? Behavioural economist Jenny Robinson discusses the issues.


Never commute on a Monday morning again. Buy a classic Porsche 911. Take a three-month holiday in South America. If you buy a ticket, there’s just a chance you might one day win the lottery – or so they say.

Lotteries were held at least as far back as 200BC, based on Chinese records of a keno-type game. And they have continued to grow in popularity: the French Revolution allegedly had something of a hiccup when questions were asked about how the people could be trusted to rule themselves when they were so keen on “vices” such as lotteries.

Today, the World Lottery Association reports that $273 billion were spent on tickets for members’ state-run lotteries in 2017. People are certainly putting their money where their mouth is, but is it worth it?

Long odds and small pay-out ratios
Even when government-run, a lottery typically still has to create revenue and pay costs. Typically, this might include marketing costs and even a fee to shopkeepers or other businesses that might sell the tickets. These obviously erode the sums that can be paid out in prizes.

A review of lotteries puts the average pay-out at around 50%. This means that only about half of the money gambled in a lottery is typically returned in the form of prizes. At ING eZonomics, we don’t support gambling in any way – but we should point out that this rate is even worse than what some pundits suggest for other gambling games (compare around 74% in bingo to 98% in blackjack).

Additionally, the odds of winning on the lottery are remarkably small. In a traditional lotto game where six numbers must be picked from 1-49, there is only a one in 13,983,816 chance of picking the correct numbers. If you have to pick from 59 those odds shrink to one in 45,057,474.

Given the small pay-out ratio and the long odds of winning, rational analysis would surely suggest that lotteries just aren’t worth playing.

Understanding the odds doesn’t make you immune to lottery fever, says Jenny Robinson

So why do people do it?
Academics suggest people play the lottery because lotteries are commonplace, so they may not be seen as “gambling”. Instead, people consider lotteries to be fun and sociable, rather than vice.

Secondly, people don’t behave rationally when participating in the lottery. A lottery ticket encourages people to take a punt on a range of prizes; there is a fixed chance of winning. A lottery ticket, in economics terms, should be valued according to the expected return, based on the mathematical probability of this happening.

If the cost of the ticket is less than this expected return, you should take the gamble. However, if the ticket price is higher than this expected return, it’s probably better to go and buy a cup of coffee instead. For many, a lottery ticket looks like a key to the dream of a different life. The chance of this coming true is low; typically, once the draw is made the dream disintegrates.

There is no way to know with absolute certainty the expected return on the gamble, what’s more. This is because this varies by the number of tickets sold. When more people play, the prize fund typically is increased – even before roll-over weeks (when the prize is not won) are taken into account. As psychologist Daniel Kahneman writes in Thinking, Fast and Slow, “the actual probability is inconsequential; only possibility matters” .

Unfortunately, in practice, understanding the odds doesn’t make you immune to lottery fever. Studies suggest that when people learn to calculate the odds and ignore common gambling fallacies, they still gamble just as often. As 18th century English novelist and playwright Henry Fielding wrote in The Lottery, credulity’s always in fashion.

This can go beyond not knowing the expected return on “investment” in a lottery ticket. Researchers in Israel have found that 59% of people given lottery tickets, even if they hadn’t chosen the numbers themselves, were reluctant to swap them even if the incentive was something of greater value – in this case, a different lottery ticket and some chocolates.

Rationally, you’d expect more people to trade because the alternative lottery tickets would have identical characteristics (the same chance of winning), and if they swap they’ll gain because they’ll get to enjoy a guaranteed treat as well.

But the people in the experiment did not. What was behind this result? One theory highlights the endowment effect, where the thing you have is worth more to you than it would be if you had to pay to acquire it.

Another idea is that the people don’t want to regret having swapped their ticket if it turns out to be the one that wins. As at least one study suggests, exchanging a lottery ticket can feel like tempting fate – that a lottery ticket that’s swapped for another is actually more likely to win because you swapped it.

One way to stay irrational
Knowing that behaviour around lotteries is pretty irrational, you might be tempted to prove your own rationality by choosing 1 2 3 4 5 6 as your numbers the next time you head out to buy a ticket. Don’t.

These may be just as likely to win as any other six choices. But it would mean dividing the jackpot among all the other people doing the same thing, with these numbers rumoured to be very popular. So your prize might cover a few bottles of champagne, but that Monday morning commute will be yours for some time to come.

EducationIrrationalLottery

eZonomics team
.(JavaScript must be enabled to view this email address)