Buying lottery tickets is smart

Some speculations about fantasy, anticipation, and dread

Midjourney: A path, very minimalist

Many people think buying lottery tickets is dumb. A quick Google search found this article from Investopedia from a couple of months ago.

Betteridge's law is that any headline that ends with a question mark is answered with a “No”, and the law does not fail us here. The article begins with some statistics: Your odds of winning the jackpot in a Powerball are 1 in 292.2 million. It is far more likely, then, that you will die by being hit by lightning (1 in 1,222,000 odds in a given year), die from a hornet, wasp, or bee sting (1 in 57,825 lifetime risk), or die in a cataclysmic storm (1 in 35,074 lifetime risk.)

Given these long odds, the conclusion is that buying lottery tickets is a poor investment strategy. There are better ways to spend your money.

Spending $5 per week on lottery tickets adds up to $260 per year. Over 20 years (a typical long-term investment horizon for stocks and bonds), the total spent on lottery tickets would be $5,200. Putting $260 per year into stocks (and assuming annual returns of about 7% based on equities' historical performance) would leave you with $11,015 after 20 years. But if you just spent the money on lottery tickets you'd only be left with your (likely negligible) prizes won.

This all makes sense. If your goal is to accumulate money, buying lottery tickets is a poor way to do so. What’s worse, some people are addicted, spending more on lottery tickets than they can afford. This isn’t smart at all; it’s sad.

Still, an occasional purchase of a ticket can be reasonable. Not because it’s a wise financial move, but because it’s fun. The five dollars or so you spend provides a path to imagining that your debts are all paid off, you are financially secure for the rest of your life, and you can quit your job, move to a cooler house, and travel the world.¹ You get a period of pleasant fantasizing that will last from the moment you buy the ticket to the moment of the drawing when you find out that you didn’t win.

But why do you need the ticket to fantasize about being a millionaire or multi-millionaire? Why not just fantasize about it? I can pretend right now that I have twenty million dollars and now think about exotic vacations, freedom from financial anxiety, and a house with two squash courts. Why should spending five dollars on a zillion to one shot make any difference?

I think the answer is this:

We imagine something best if there is an easily imagined path to it really happening

Yes, I can simply fantasize that I now have twenty million dollars. But it’s like imagining that I can fly. There’s no conceivable way it can happen. The University of Toronto is not going to give me a twenty-million-dollar raise. I don’t have super-rich relatives, so I can’t imagine them dying and leaving their money to me—and it’s not fun thinking of loved ones dying, anyway.

So I buy a lottery ticket. Now there is a clear path from my life right now to my life as a multi-millionaire. If the right numbers come up, my dreams will come through. Sure, the odds are infinitesimal. But it’s possible and it’s specific—now I know exactly what would have to happen for the fantasy to become real. There is a path from my present to my desired future.

But this just pushes the question back. Why does having a path make such a difference? Here are two ideas.

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Idea 1: A path triggers mental systems for thinking about the actual future, and such thinking excites the imagination

Humans have mental systems that allow us to envision possible futures—different paths we might take from the present. We need such systems for planning. What should I do this evening—go to the gym or stay home and watch Netflix? Where should I go on vacation? Which class should I offer to teach next semester? As we mull over these decisions, we try our best to imagine what these futures would be like—what we would feel in these alternative realities. (Psychologists call this “simulation”).

We can imagine without employing these mental systems. I can imagine a world where I can fly, where Al Gore was elected president, where Earth has three moons, or where I am a brain in a vat. But such imaginations are emotionally weak, nowhere near as vivid as when I think about possible (however unlikely) path-based futures.

Path-based imagination can lead to powerful feelings of anticipation—or worry and dread.

For a couple of years, someone from China has been emailing a set of Yale Professors, including me, saying that he was going to kill us. The threats were vague and incoherent: “Kill Paul Bloom Paul will die at my hands Oh Kill Kill Kill”. Until a few months ago, the emails did not include anything that suggested that he knew anything about me, and made no mention of specifics. They were easy to ignore.

Last summer, I was invited to give a series of lectures in Shanghai. Once I agreed, I got an email from my Chinese correspondent saying he knew about my coming visit and was going to kill me in Shanghai. He was quite specific—he promised to shoot me the moment I got out of the plane.

Did I appreciate that the odds of this happening are extremely low? Yes. He would have no way of knowing when I would arrive, and an airport is a very safe place. On reflection, him killing me after this specific threat was just as unlikely as him killing me in the non-specific phase of our relationship. But it didn’t feel like that. My death was now specific; I could imagine it so clearly. There was a path.²

So many things are like this. Years ago, my younger son went hiking in Nepal, and he was entirely out of touch for about five days. I worried a lot. I saw him plummeting from a mountain and dying. There was a path.

I wonder if the notion of a path can explain some otherwise mysterious activities. Some people write letters to famous people, asking the celebrity to be their prom date, give them a million dollars, or marry them. Much of this is probably grounded in an overestimation of how likely it is that the celebrity will comply. But I wonder if some of it may be a tool for fantasy, with the letter serving the same function as the lottery ticket. If I don’t write to him, Elon Musk won’t send me a million dollars to start up my new company; but if I do, he might read the letter and do what I ask. Sure, the odds are very low, but now it’s part of my possible future—there is a path—and I can pleasantly fantasize about opening my email and getting some excellent news.

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Here’s a different, though compatible, proposal.

Idea 2: Imagination based on a path forces one to think of a tightly constrained future, which is more fun

In Ulysses Unbound, Jan Elster writes

In a wonderful phrase by George Ainslie … daydreams have a “shortage of scarcity” that makes them intrinsically unsatisfactory.

Building on Ainslie, Thomas Schelling, and others, Elser argues that the problem with daydreams is that you can conjure up any conceivable future, and this omnipotence takes away all the pleasurable feelings of surprise, suspense, and challenge.

Suppose I choose to daydream that I have twenty million dollars. Here goes:

I buy a beautiful house in my favorite neighborhood in Toronto, a penthouse apartment in New York City, and a lovely beach house in Mexico to spend my weekends. Very nice. Actually, when you add it up, twenty million isn’t enough for all this, so make it fifty million. No, five hundred million. No, a billion. It would feel great to leave Toronto on Friday and wake up in Puerto Vallarta the next day, but I don’t want to fly commercial, so I’ll buy a private plane, But that’s still an annoying trip. As long as I’m fantasizing, why not teleport back and forth? Actually, if I can teleport, let’s put the beach house in Thailand. No, Mexico and Thailand. No, a thousand houses on a thousand beaches. I don’t want to be lonely, so I’ll have my friends and family hang out with me. But what if they have better things to do? Well, I’ll just make it that they always want to be with me …

Gaaahhhh. This is too boring to go on. It’s too easy. It bears no resemblance to real-world pleasures. Omnipotent imagining has at least three problems:

1. there is no challenge, no struggle, and no potential for surprise.

2. whenever I think of something there’s always the disappointment of knowing that I could have thought of something better.

3. my omnipotence turns me into a God, but I don’t want to experience my fantasy as a God; I want to experience it as me.

For daydreaming done well, check out Rub, from Richard Russo’s Nobody’s Fool.

“You know what I wisht?” Rub said.

Since he and Sully left the OTB, Rub had already wished for a new car, a raise for himself and a raise for Bootsie, who worked as a cashier at Woolworth’s and hadn’t had a raise in over a year. He’d also wished some big ole company would build a big ole plant right in Bath and make him a foreman at about fifteen dollars an hour. He’d wished it was spring already and not Thanksgiving, that California would just go ahead and fall into the ocean if it was going to, that the climate in upstate New York was more tropical, that someone would die and leave him a big ole boat he could sail down to Mexico, that the Royal Palm Company would start making that red cream soda again …

… The thing that always amazed Sully about Rub’s wishes was that most of them were so modest. After wishing a whole company into existence, Rub would settle for a forty-hour-a-week job at union scale, as if he feared some sort of cosmic retaliation for an arrogant imagination. Sully tried to explain from time to time that if he was going to wish an entire corporation into existence, he might as well wish he owned it and had somebody else to do the actual work. But Rub didn’t see it this way. He liked the smaller wishes and he liked to wish them one at a time.

Sully is wrong. This is wishing done right. It’s constrained and modest and enjoyable.

If you lack the self-control of Rub, set up a path to an enjoyable future and imagine what would happen if you are lucky enough to go down the path. And then stop; that’s your fantasy; nothing else about you or the world changes.

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Investopedia knows a thing or two about fantasy

I bet the writers of the Investopedia article³ appreciate the pleasure of the path; they know how much fun it is to use a lottery ticket as a ticket for fantasy. After going on about how irrational it is to buy lottery tickets, they have a section called

And then there’s this

A bit hypocritical, no? After telling you that the lottery is a tax for idiots, they now advise you on what to do if you win one. (Imagine a non-smoking campaign for children ending with “But if you simply try cigarettes, here’s how to blow the coolest smoke rings.”)

The thing is, this part of the article is really fun. It helps with the fantasy: If you win, these are the choices you have to make. You wanted to be rich; now here are your rich person’s problems. It helps make the fantasy pleasantly real.

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Summary: Lottery tickets—Poor investment strategy; Excellent tool for fantasy.

1. It’s often said that winners of lottery tickets become miserable, but this is an urban legend, based on a small and non-replicated study. Most research shows that they become happier (see this study, for example).

2. He did not shoot me in Shanghai. Possibly embarrassed, he hasn’t written to me since.

3. The writers are identified only as “the Investopedia team”, and I do wonder if someone on the team is ChatGPT.