Should you ever buy lottery tickets?

Between Christmas and New Year, a single lottery ticket that sold for $2 in California won a prize of $1.2 billion. That’s an astronomical return on investment (a “600-million-bagger”!). But, even though winning lotteries is rewarding, it still doesn’t make financial sense to buy lottery tickets. Lotteries pay out less in prizes than they collect in ticket sales – in the UK, only about half the money goes on prizes – and in aggregate lottery-ticket buyers lose money.

Despite paying out only half what it takes in, last year the UK national lottery sold over ￡8 billion-worth of tickets. So, even though almost everyone will lose money playing the lottery, many of us do. One of the reasons of course is that dreaming of winning a jackpot is fun. Another reason people give for playing the lottery is that some of the money goes to good causes. However, only about 34p in every ￡1 goes to good causes. If people want to give money to good causes, they would be better off doing so directly rather than via the lottery. The main reason people give for buying lottery tickets, however, is that the potential prizes are so very large. But it won’t matter how large prizes are if your chance of winning them is zero. So, what are the odds of winning the lottery?

There are three main national lotteries:

Euromillions has prizes of up to ￡200 million. Because it is played by people all over Europe, not just the UK, the odds of winning the jackpot are 139-million-to-one. Tickets cost ￡2.50.

Lotto is the original national lottery launched in 1994. It pays out anything up to ￡20 million. Tickets cost ￡2 and the odds of winning the jackpot are 45-million-to-one.

Finally, Thunderball costs ￡1 per ticket, pays a jackpot of ￡0.5 million and the odds of winning it are 8-million-to-one.

Personally, if I’m going to play the lottery, I’m probably going to play Thunderball. At ￡1 each, the tickets are relatively cheap, and I would rather have a slim chance of winning ￡0.5 million than almost no chance of winning ￡200 million. Rather than playing the lottery, however, I’m more likely to buy Premium Bonds. Issued by the government, these enter me into a monthly drawer with a top prize of ￡1 million. I’m unlikely to ever win the jackpot, but on average I can expect to win annual tax-free prizes equal to 4% of the value of my bonds. Unlike lottery tickets, Premium Bonds have a positive expected financial outcome.

Playing Thunderball rather than Euromillions or buying Premium Bonds instead of lottery tickets is my set of preferences. Different people will have different preferences. These different preferences are a result of what economists call utility functions. Importantly, our utility functions don’t just capture expected financial outcomes but also how much satisfaction a choice brings us.

A financial choice that I expect will lose me money can still have positive utility. Insurance is an example of this. I pay an insurance premium to protect my house if it burns down. When I do this, I not only expect to lose money, I hope to lose money – I do not want my house to burn down. Buying insurance, even though a loss-maker financially, provides me with sufficient utility to make it worthwhile – I get peace of mind and I sleep better at night.

Recently, the folks at Elm Wealth calculated whether a lottery ticket could have positive utility even though it’s expected to lose money. They took the example of a US middle-income household buying a $2 lottery ticket for a 100-million-to-one chance of a $200 million jackpot – similar then to our Euromillions. No matter how hard they tortured the math, they couldn’t make the choice by this household to buy a lottery ticket a positive one. And yet, as we know, middle-income households do buy lottery tickets. How can it be explained? One possible explanation is that we are living in a multiverse! It’s not something Elm’s analysis explores but it is something researcher Peter Berezin has considered.

Before I get to that, let me remind you that I am not offering you investment advice. I mean, how could I? I don’t know you, your circumstances, your income and expenditure, your assets and liabilities, your lifestyle, your dependents (if any), your age, or your attitude to risk. Also, I don’t know if you are living in the multiverse or not. If you are looking for financial advice, I recommend you speak to a regulated financial advisor. There are a lot of them out there. Helpfully, the regulator keeps a register https://www.fca.org.uk/consumers/using-financial-services-register.

Now, back to the multiverse (I’ve always wanted to say that), which is the insight from quantum mechanics that the universe is constantly branching. Because I am part of the universe, I too am constantly branching. Therefore, if I buy a lottery ticket, I may not win the jackpot in this universe but there will be some branches of the universe where I do win it. As Berezin writes in his report Life, Death, And Finance in The Cosmic Multiverse, “In a multiverse, the versions of you that lost the lottery would gain some utility from knowing that a few of your twins had won.” Conclusion: in a multiverse buying lottery tickets may have positive utility after all.

Does it make sense to buy lottery tickets? Probably not unless we are living it in the multiverse in which case it does make sense. Historically, I haven’t bought lottery tickets, but I will buy one now. And if you don’t hear from me again, it means we’re in a branch of the multiverse where I hit the jackpot. So, as they say, stay tuned.