The economics of American lotteries | Hacker News Reader

The economics of American lotteries

economist.com

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When Powerball makes the news for having a huge jackpot, we purchase a few tickets with relevant family numbers. The tickets always generate ridiculous conversations of what we'd do with the winnings, and assessing how those conversations change each time is more than worth the occasional few dollars spent on it.

We're very aware of the probabilities involved.

Exactly. This fun costs as much as a movie ticket or a dinner.

My father, working as an unskilled labourer all his life, always called lotteries "tax on stupidity". Mostly said as he fished out his coupon to check his numbers. Even if it is pie in the sky to buy lottery tickets, the dream it provides is a strong drawn on those that don't have much.

It's more enlightening to think about the proceeds of the funds. If we're taxing the stupid we must be collecting a fair bit of coin, where does the society direct that funding? Education, facilitating children's sports activities, reducing homelessness or allowing the people administering the lottery to buy luxury goods for themselves? The answer seems to depend on which lottery and which country. Some spend this money very wisely.

Almost universally lottery proceeds displace tax spending. For example, in my jurisdiction lottery proceeds go to education. That lets the government spend less money on education and more on the boondoggle of the day.

Morgan Housel in Psychology of Money talks about this. It does make sense, unfortunately, some of these people are at a point where the probability of them living a comfortable life via winning a lottery is higher than anything else.

I'm skeptical those numbers work out. Winning any amount of $ in a lottery is vanishingly small odds.

Even if true, that would imply ANY probability of a comfortable lifestyle is ~0.

>Even if true, that would imply ANY probability of a comfortable lifestyle is ~0.

That is definitely the case, and it's precisely the point that parent was making.

Wondering if this is the same effect which causes people to vote for fringe positions? Because the mainstream options did not work out in the past?

It's a basic result about utility functions really, except it now works the other way around. When any small amount of money just leaves you in more or less the same situation then your utility function stays constant and then increases, meaning it is (locally) convex (as opposed to the usual situation where it is concave).

Hence why in that case the expected utility of a lottery can be greater than the utility of its expected value (which is negative).

I really think its much more about the entertainment value the lottery provides. For most players the utility of playing literally is higher than the cost because of non monetary gains.

What are your assumptions for the chances involved here? It seems intuitive that the "harder" options would still be better odds. Did you perhaps means that it _feels_ like their chances are that low for any other option?

I'm still working through the book but that's the whole premise. It'll be impossible for us to rationally and logically relate to what (in this case) they go through. Logically, to us, it makes no sense to buy lottery tickets. But given the circumstances they grew up in, the lack of opportunities that continue to riddle them, they're willing to take that chance since it offers a higher probability of them leading a comfortable life.

How so? I imagine it would need to be a very specific set of circumstances where money is the limiting factor to living well.

I'm pretty sure in a capitalist society having sufficient money is a requirement for living well, even if that is not all that is required for one to do it.

Also when in a capitalist society when big problems come up sometimes the easiest or perhaps only way to solve those problems would be having enough money to solve them.

There’s also a consideration for the working poor - they’re surviving at some level of surviving. Most people wouldn’t blink at someone spending 5% on entertainment ($600 a year is $50 a month which is a couple of streaming subscriptions), or donating to a club or church.

For most people who buy a lottery ticket they’re really “buying the dream”.

I think you’re onto something but it’s more immediate than a comfortable life. Somebody focused on immediate satisfaction or surviving the next few days is at a convenience store. There’s something they need/want that costs $10, but they only have $2. If getting that $10 item is all that matters to them at that point and there’s no partial substitute they can get for $2, then a $2 scratch off ticket with a 2% of paying $10 may be the highest utility for their money.

> "In the poorest 1% of zip codes that have lottery retailers, the average American adult spends around $600 a year, or nearly 5% of their income, on tickets."

This was really eye opening for me. I knew that those in a low economic class bought more lotto tickets, but I had no idea the amount was that high.

To be precise most people who play the lottery buy more tickets with any winnings they get. So the actual percentage of income will be a bit lower, though doing the math is more complex.

It’s still terribly sad, though it’s arguable that anything replacing it could be worse.

Technically winnings should be included as income

Few things are as matter-of-factly depressing as an old person shuffling down into a seat, working blank-faced through a stack of garish little scratch-offs, and then throwing them all away

I assume this number is similar to casino slot play through where gamblers roll winners forward. Put in $50, win $2 or $5 every now and then and just play it again, next thing you know you’ve “spent” around $100 but only put in $50.

They're desperate to change their economic situation.

And their solution is to gamble instead of making a budget? If they have $50/mo to spend on lotto tickets, they have more disposable income than they probably realize.

It doesn't add up. The average income in the poorest 1% of zip codes in the US is over $12000. Now, that's two different averages so you could have one of those statistical paradox things going on, but it's at least very poorly worded.

As another sanity check, if you were to play the biggest lotteries - Powerball and Mega Millions - every time (2x a week each at $2), it would be over $400/year, so $600 is not that surprising.

And we’re expanding sports betting too across the nation.

I was at a wedding recently for a young college age couple and the groom, bride, and the grooms buddies were all placing bets on their phones at the wedding reception.

It was a little disheartening seeing some young folks starting their lives and at the reception throwing what little money they had away.

Notwithstanding the extremely low probability of winning, lotteries aren't even fair, i.e. the ticket price is far lower than the expected earnings. I wonder if it would make sense to democratize cheap high risk, high rewards instruments, for example deep out of the money options, to replace lotteries. At least their prices should be fairer (under the efficient market hypothesis).

Next time you’re in 7-Eleven instead of a scratcher you pick up a put option on the 7-Eleven holding company.

This could be solved by mandating some sufficiently high return say 80%. Still losing proposition, but would make it lot fairer.

In the UK we have premium bonds that largely serve this purpose. You are most likely to win small prizes but £1 million is possible. Average return is around 4% I think.

Expected value on some jackpot lotteries does occasionally go over 1. For example, I did the math on Canada's 6/49 about 20 years ago. Whenever the jackpot was over ~$30M, the expected payout was over 1. If you bought a ticket for every jackpot the expected payout was 0.5, the expected payout of any lottery without a jackpot was < 0.2 in hindsight. For $30M prizes the number of players and the odds of sharing a prize went up, but not enough to compensate.

It would have had to go well above $45M to make the "buy every number" strategy have expected value of > 1 since buying every number increases the expected people sharing the prize by 1.

> Using zip-code-level sales data from 24 states

Gas stations tend to be built near highways. Communities near interstate and regional highways tend to be “poorer”.

Is it possible that data gathering method here is flawed? Joe blow doctor coming off a 10 hr shift just happens to fill up his car on the way home. Exits highway to nearest station. Sees PB sign and decides to toss in a couple of dollars for ticket while filling gas tank.

Rinse and repeat for the many other corporate grinders, day laborers, nurses.

Sales funneled through these “poorer” zip codes simply because it’s on the way. I can’t even recall the last time I went out of my way to buy a lotto ticket.

Sure maybe there are people that impulse buy hundreds or thousands dollars worth of tickets. But that has to be a much smaller portion. Particularly those addicted to gambling.

It is rational in many cases to gamble at low levels of wealth. The difference between $1,000 in net worth and $0, or $10K and 0, is infinitesimal. At extremely low levels of utility, it doesn't really matter.

Kelly criterion only applies if you have a substantial bag already. Then, you can size your bets according to probability.

For the lower wealth strata, they need to target convex payoffs, however. Lottery, meme coins, otm options (like the Gamestop situation) make sense. Things with a more linear payoff, such as sports betting (only double if you win the coin flip), less so.

Depends on what your goals are, I suppose. The difference between $10k in the bank and $0 in the bank is gargantuan when you need to buy groceries for your kids.

This comment is so out of touch that it almost has to be a parody. The people spending money on scratchers instead of buying groceries don’t ever have the option to have $10k in the bank. These people have probably only seen a comma in their bank account once.

What are you talking about?

I'm talking about the comment I responded to??

> The difference between $1,000 in net worth and $0, or $10K and 0, is infinitesimal

I had a discussion with a colleague recently about the lottery. We posed this question: why not instead of a large jackpot with 1-5 winners, you have smaller jackpots with many winners of say, 100k?

Imagine instead of one person winning a 600m jackpot, 6000 people win 100k? 100k isn’t a particularly life changing amount of money but it could help dissuade frivolous spending and make good financial decisions. 100k can help pay off debts, pay off that car, put some in savings, etc for many people.

Just a thought.

From a policy making perspective, this article is on point. Lottery advocates justify their existence by saying the money goes to a good cause, like education or sports. And sure it does, by taxing the people who can afford it the least. The tax system is mostly progressive, taxing people with higher incomes more. But this is regressive tax that hurts poor people most.

But if you looked at it from the perspective of the people who are buying the lottery tickets, this view is paternalistic. They know that they're unlikely to win, but they buy anyway because it's a chance of winning something big. They're buying hope. And they're doing it of their own free will. Any attempt to "save" them from this regressive tax won't find much support from them.

I wonder what is the hierarchy of gambling in different social classes. From lottery, to betting, to gambling, to option trading, to crypto and general day trading... Not to forget any type of entrepreneurship... Maybe some items I forgot too...

And also collectibles and so on...

Dreaming

People typically talk about how it doesn’t make any financial sense to ever buy a lotto ticket.

But they are missing the point.

An often overlooked aspect of lotteries is … for just $1-2, it gives you the ability to dream “what if I won”.

For many, the escape that dream allows you to have (of what a better life could be like) is well worth the couple bucks.

To be fair, dreams are still totally free, but yes, it infinitely more realistic, after buying a lottery ticket.

I wonder if the (false) sense of agency, of "doing something" - might not be psychologically important. Especially if the only other viable option seem to be in-action and despair?

I just dream I find the winning ticket on the sidewalk. Costs me no money, I have the same dream, and my odds are not significantly different than if I bought a ticket.

I dream that it blows into my open car window so that I don't even have to bend over to pick it up. Might as well dream big.

If you didn’t allow the legal lottery, there would be illegal ones all over. In “The Autobiography of Malcolm X”, Malcolm talks about how he won the local “numbers game” a few times which is how he afforded his first suits. It was sort of like a bank for the unbanked, because the odds were good enough that someone would win eventually and then use it to buy big financial purchases.

Organized crime would run the illegal lotteries.

I wonder how illegal lotteries compare to legal ones in terms of the expected return on a ticket and the frequency/size of winnings. I would expect legal ones can pay out less overall, and that less frequently, with larger (but rarer) prizes because they are better trusted.

https://archive.is/Kuzfv

Note that the alternative to legal lotteries isn't a lack of them, it's "numbers games": https://en.wikipedia.org/wiki/Numbers_game

> Our analysis shows poorer citizens spend a staggering amount on tickets

That is why it is called a tax on the poor.

Lotteries have asymmetrical risk/payout.

Not crazy, if one could allocate a small amount of money to it.

I used to do the lottery, then i stopped. Now i have more money.

Lotteries are the only tax that deep red states are in favor of.

The majority of states without a lottery are red states. The only reliably blue state without one is Hawaii. Purple Nevada doesn't have one probably because they don't want the competition against the casinos. In every state where there is a lottery, purchasing tickets is voluntary, which isn't the case when it comes to taxes.

Nevada reminds that as you cross from California there is a tiny California Lottery store just on the California side.

According to the article, “Some 45 states, and the District of Columbia, operate them”

So a majority of the 5 states without them are red states?

sadly, that is pretty much the american dream now...win the lottery.

Oh brother. You have to have at least some perspective. The American median income is one of the highest in the world (top-3 or top-5 depending where you pull your numbers from) with some of the lowest taxes. You have a huge middle class that lives a very comfortable life. You have millions of people trying to immigrate to your country every year. You have very low unemployment rates. You have a highly diversified economy (from the best tech and financial sectors in the world, to mineral, oil and gas extraction). I get it, it's expensive to own property in California and New York and maybe it shouldn't be ... but you can't have everything!

Fair valid points. But to me I think a lot of the story is "hidden" in the actual value those dollar amounts hold, specifically in America. There's a common theme atm about people not being able to afford homes as an example.

There is a real problem with the cost of housing, but home ownership rates are about 66%, it's hardest on the minority that aren't in that group.

For a dystopian look at the housing market, just look at Canada or Australia. Inflation impacted just about every country. At least in America we have lots of land and diverse housing markets we can choose from.

The American dream is to have a captive consumer or to be a middle man that skims a cut while adding no value.

AKA: Extract a rent!

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