America's new favorite pastime: The lottery | Hacker News Reader

America's new favorite pastime: The lottery

axios.com

35 pointsgmays91 comments

FYI, if you make a realistic calculation (including tax and multiple winners), the EV of a lottery ticket is still negative.

Depending on your tax bracket, the non-jackpot prizes have about $0.19 of EV.

In a state where you don't pay tax on lottery winnings, like CA, you cash option post-tax is currently estimated at $408,403,045.

My estimate of the multiple winner correction to the EV is 0.8, based on numbers of winners for prizes >$500M.

Your jackpot EV is therefore $1.08 and the total winnings EV is therefore $1.27, meaning the overall EV is -$0.73.

For there to be positive EV, that delta needs to all come from the jackpot, so the headline jackpot number would need to go from $1.1B to $1.8B to get it there.

Great analysis. I want to share my thoughts on EV because they seem to go against what pretty much everyone else is saying. I think even if the EV was >$2, it would still be irrational to play. I say this because I think it's silly to talk about the EV of buying a single ticket when the odds of winning are 1 in 300 million.

Like, you still aren't going to win the jackpot. Your odds didn't improve just because the jackpot got bigger. I guarantee you are going to find out tonight that you wasted $2, just as you would have wasted $2 at any other time when the jackpot is/was smaller.

I think it's just people rationalizing what they know is an irrational behavior. They're fooling themselves into believing they are making a rational choice because they want in on the fun/excitement despite paying the "poor tax."

Anyway, good luck to anyone who decided to buy a ticket and enjoy a few hours of fantasizing about what you'd do with the winnings :)

You could flip the perspective and look at it as helping out the winner.

Still for most people, their biggest return is being able to day dream for 5 minutes what it would be like to win.

Totally. And it becomes a cultural phenomenon - neighbors and coworkers are chatting about it … you want to be part of that moment. Here’s what I wonder - what is the maximum frequency of big media hyped jackpots? Would we all do this again next week, next month? I don’t think so. Maybe next year?

They say you can't win if you don't play (pay). But that's not true! There is an epsilon chance that someone dropped their lottery ticket and the wind blew it away and they gave up in getting it back and while taking your groceries to your vehicle in a parking lot it blows by you and you pick it up. And there's an epsilon prime chance that it will be the winning ticket. So there is an epsilon times epsilon prime chance that you win the lottery without actually playing (paying inti) it. ;)

I like to say that your odds don't significantly change if you pay for a ticket or not. Both non-zero but very close.

Most of what you're describing is captured by the Kelly Criterion: it tells you the "optimal" fraction of your bankroll you should bet to maximize returns given the odds and EV. For a game with positive EV and 1 in 300M odds, you should be betting a very small fraction of your overall bankroll -- well below $2 for anyone not already in the 0.01% wealth bracket. So indeed, it would be irrational (suboptimal) to participate in the lottery unless you were already very wealthy.

Even beyond the Kelly Criteria, you could also tweak your EV based on the marginal utility of a dollar -- i.e. going from $0 in savings to $10M would have a massive impact on your quality of life, whereas 10x'ing from there ($100M) would provide marginal additional benefit comparatively. Thus, (ignoring Kelly) the "quality of life EV" for a $10M jackpot with 1 in 5M odds is vastly better than a $100M jackpot with 1 in 50M odds despite having the same EV.

https://en.wikipedia.org/wiki/Kelly_criterion

Nice, I had heard of the Kelly Criterion before but never thought to consider applying it to this situation. It's fantastic if the mathematically correct amount to wager (for any ordinary person) is less than $2 which rounds to 0 tickets which supports my intuition to not play.

Your second paragraph touches on another thought I had, which is why people think it's only worthwhile to play when the jackpot is $600M+. Any of us would be happy to win just $20M so why not play for every jackpot? Again it comes down to that misleading EV calculation, which I believe doesn't even matter if you are only going to buy 1 ticket only. Wagering based on the EV would only make sense if it was feasible to buy on the order of 100M tickets. Then you'd have a reasonable shot of winning each jackpot. And playing enough jackpots, you would come out ahead.

About a decade ago Megabucks in Wisconsin (a Wisconsin State pick six game) had a positive EV after taxes were even taken out. I think it was maybe a penny at best. However, buying more than one ticket is still foolish in my book. 1 in 14 million vs 1 in 1.4 million vs ... They're all ridiculously long odds. You more likely to die driving to get your ticket.

In Canada, the Canada Revenue Agency considers gambling winnings to be windfalls that are not subject tax, so any winners receive the full value of the advertised prizes [0].

[0] https://www.canada.ca/en/revenue-agency/services/tax/technic...

We also have a fascinating legal relic called the "Skill Testing Question" which allows for games like Roll Up the Rim or guess-the-jelly-bean-jar to exist without being subject to our otherwise very restrictive gambling laws. I'm not sure how it was decided, but the "skill" being tested is usually order of operations.

https://en.wikipedia.org/wiki/Skill_testing_question

What's funny is that the law doesn't say if you're allowed help, or if you need to answer correctly on your first try, simply that they wrote the correct answer on a receipt which the merchant is supposed to keep. When I worked at McDonalds and it was busy, we were encouraged to just tell people the answer so they could redeem their free muffin and keep the line moving.

Take this for what its worth - there appears to be a relationship between economic downturns / recessions and lottery spend - https://taxfoundation.org/does-lottery-revenue-rise-or-fall-...

Given the current sour economic forecasts and inflation concerns, I don't think the lottery spend increasing is surprising.

And correlation with poverty as well. Rich people don't play the lottery.

Is that true? I remember seeing somewhere that it’s surprisingly flat across income, though obviously a larger proportion of income for lower earners.

Yeah because they don’t need to and the $3 ticket isn’t a noticeable expense if they do.

that is a distorted interpretation of assumptions

it doesn't matter when rich people play the lottery, whereas it does matter when poor people play the lottery as its a meaningful proportion of their available earnings

> Rich people don't play the lottery.

They do. It's called "incorporating a company" or "investing in the stock market" often with leverage.

I would guess that for a regular non-connected, non-ivy league folk the chance of becoming a billionaire is roughly the same creating a startup vs. the lottery.

At that point it makes sense to play the lottery if you are a "swing for the fences" kind of guy, that's because when odds are kinda the same it makes way more sense to throw 500$ monthly in lottery tickets than throwing 14h/6d/52w yearly in precious time to build a company or reading balance sheets of publicly traded companies

> It's called "incorporating a company" or "investing in the stock market" often with leverage.

We were discussing the lottery.

And very strange things like the Dance Marathons of the 1930s: https://www.historylink.org/File/5534

Dance Marathons (also called Walkathons), an American phenomenon of the 1920s and 1930s, were human endurance contests in which couples danced almost non-stop for hundreds of hours (as long as a month or two), competing for prize money."

This was fascinating and definitely merits its own post. There are some pretty clear parallels with today's reality TV.

We’ve got a broad and growing addiction & attention problem in America. Ad-fuelled social media, crypto, day trading and useless financial engineering. A growing fraction of the labor force, moreover, is dedicated to these cancers.

People who learn to resist this onslaught of stimulation targeting our limited attention span will be the winners of the next few decades.

I estimate that about 5% of people aged 20-30 currently have this ability.

> People who learn to resist this onslaught of stimulation targeting our limited attention span will be the winners

I agree. One hopes they have a civilisation to come home to.

>Fantasies of dynastic wealth are one of the few things you can buy with $2 these days — a price that hasn't gone up since 2017.

Yep, I'll probably go buy a ticket today after work. I only buy MegaMillions or Powerball when it reaches these outlandish amounts. Read somewhere in an outdated article that Powerball only reached an expected $2 payout per ticket when it's a +$550 million pot.

That graph of the tickets bought in the article is pretty amazing too. If the pot isn't won tonight I would love to see an update.

The challenge with that hockey-stick graph is that it greatly increases the chance of multiple winners. That kills any chance of a +EV. The best lottery drawing is the one just before the one that makes news; by definition, it had no winner, so if you had just picked the right numbers, you would have won it all.

Also every drawing (twice a week) has had one or more million dollar+ winners

People focus waaay too much on the jackpot!

I love the privilege of not being poor enough to be criticized for buying a ticket.

I pay for a lot of fleeting entertainment. What's a $2-3 ticket? Or $20 worth of those?

The math for the expected payout reaching $2 per ticket was only for the jackpot. The lesser prizes and bonus modifiers are the losing propositions that get you into a gambling addiction.

I expect a negative expected value game, and I get a negative expected value game.

The first sentence of the article is not necessarily correct since anyone worldwide can legally buy tickets though a ticket-purchasing service.

For example, in 2015 a man from Baghdad bought a ticket through a service and won a $6.4m lottery without leaving Baghdad.

The article assumes everyone buying tickets is an American, which is not true.

I've always found it funny when sales skyrocket when the jackpot is unusually high. 10M isn't that appealing but suddenly 1B is?

I understand the lizard brain mentality, not trying to knock anyone, I just get a little chuckle out of it

You're surprised that sales increase when the EV increases?

EV decreases as sales increase though

I don't care what the EV is, when your chance of winning is 1 in 302,575,350 you're better off selling your house and betting it all on black

No, because you're not homeless if you don't win the lotto. Definitely not better off doing that.

Pfft, there's only a 52.6% chance of losing a bet on black, which means there is 47.4% chance the you could win and end up with two houses minus real estate transaction costs. And that's without going to Monaco where you can play on a 37 pocket wheel.

Personally yes. I am a realist where I know the odds are almost 0 and wasting my money on an almost 0 percent chance doesn’t make sense at all.

But when it’s 1B I still know I won’t win, but it’s also an amount where I at least feel like I should put my name in just in case. Not a lot of tickets but maybe like $10. Seems irrational but I believe that’s what most people are thinking.

That my whole point though. 10M isn't worth putting your name in "just in case"? That's why it's funny to me. It's like saying I wouldn't cross the street to pick up $10M but I would for $1B.

$10 is still a lot of money and that’s why you still see enough people buy lottery tickets.

But $1B brings in casuals from all over the place that usually don’t buy lottery tickets. For some it’s the entertainment value, for some it’s “ohh might as well”.

Well you'd be putting your name in almost every night then, because it's always at least $10 million in one of the lottos (pretty much). $10 * 365 days a year is $3650. That's a big sink of money for something you know for almost certain you're not going to win. But $10 three times a year you're also almost certainly going to lose, but you're only out $30.

> 10M isn't that appealing but suddenly 1B is?

From the article, it sounds like the probability of winning is independent of sales (in a single game)? If that’s true, it’s rational—ticket price and win odds held equal across games—to respond to a larger jackpot.

There's a cost to winning the lottery. Everyone knows you won. In most states, at least. If I'm going to put up with the hassle of losing my privacy, dealing with stalkers, family members begging, friends begging, etc ... then I want it to be a really big win. Then I can give away a relatively large amount of it to my friends and family, maybe even enough to keep a few of them as friends, and buy sufficient protection and anonymity for myself and my family so we can stay safe.

$10M is going to be $5M in a lump sum, and maybe $3M after taxes. That's a sufficient amount to live a comfortable-but-not-exotic retirement for however long you live. You'll still have all the bad parts of winning a jackpot, but insufficient resources to really deal with it.

Two of those dollars are mine. When the jackpot is over a billion dollars, I easily get two dollars of entertainment value from buying one ticket.

Exactly, there’s a big difference between “I’ll grab a ticket at the gas station as a laugh” and poor pathetic exploited gambling addiction.

I used to sell tickets at a convenience store and I’ve seen some pathetic people for sure. But for these mega jackpots I think it’s mainly casual people buying a fantasy for a couple days of day dreaming.

My SO and I used to travel to see family (they've moved) and there's a fillin' station on the way that we'd stop at. We always bought a single ticket just for kicks. It broke up the drive and got us talking and laughing for the second leg of the trip. I totally get the entertainment value.

My SO and I often buy the Crossword scratch cards. It's not because we ever think we'll win (we're definitely in the minus), but because we scratch two letters at a time and pass the card back and forth. It's a mindless game that only costs us $3 to play, and we get a lot of conversation in - often influenced by words in the game or letters like J that nearly never complete a word.

We spend a lot more than $3 on our other entertainment outlets, and its better for the relationship than retiring to the living room to stare at a laptop screen. So we get what we pay for with scratch tickets.

Road trip scratchers!

> dreaming of what they would do with a post-tax lump sum estimated at more than $600 million.

Post-tax lump sum would be closer to $450M for a solo winner whose state does not tax lottery winnings.

> Statistically, that means this drawing is a rare positive-sum game...

Not unless you are exempt from federal income tax.

> ...if at least one person wins the jackpot.

That's not how statistics works.

Yeah, I know the expected value is negative. But the variance is what makes the occasional purchase worthwhile.

Of course there's always the chance that there are multiple winners which affects either it's expected positive roi

That is in the article, which mentions there's a 50% chance you're going to share the prize.

So let's do the math. 35 cents go to non-jackpot prizes, so the ROI on that is 35 cents, leaving 1.65 for the jackpot. ROI on the jackpot is $1B / 400M odds. That's $2.50 shared amongst the winners. 50% of that is single winner, 50% is shared so $1.25 + $1.25 / 2 = $1.875. $1.875 is greater than 1.65, so the ROI for this lottery is slightly positive. (I don't have the numbers on odds of 3 or more sharing, so the ROI is actually slightly less than $1.875, but it won't be much of a reduction).

Article also said only 75 cents go to the jackpot. the rest goes to the government

The jackpot accumulates. It grew so high because there are many weeks worth of 75 cents. It's an average. Most weeks 0 cents goes to the jackpot because nobody wins, so on the weeks somebody wins, it's often significantly more than 75 cents.

This is obvious because they're selling $400 million worth of tickets to a $1B jackpot.

> The jackpot accumulates. It grew so high because there are many weeks worth of 75 cents. It's an average. Most weeks 0 cents goes to the jackpot because nobody wins, so on the weeks somebody wins, it's often significantly more than 75 cents.

This sentence does not compute. If nobody wins for a week then however many tickets that were sold times 75 cents get added to the jackpot. If somebody wins, the jackpot is reset to $0.

> This is obvious because they're selling $400 million worth of tickets to a $1B jackpot.

$400M this week? Because they should have sold about 1.33 billion $2 tickets without a winner to reach a $1B jackpot, however many weeks that takes.

But I'm not buying tickets on the weeks with low jackpots, just the weeks with billion dollar ones.

Lotteries are criminally stupid, and running them is criminally evil. Shame on all governments that do so, including mine.

Alternative take: there's strong demand for numbers games, and the government, whose spending is at worst weakly correlated with social goods, and who is not profit-motivated and therefore will do less to encourage problem gambling, is better than the alternative in practice.

It would be nice to end the drug war and put lotteries under the same management as Portuguese-style state drug distribution.

Also nationalize coffee chains for same reason lol.

The government may not be profit-motivated (debatable), but it is still cash-motivated. Lottery money in many states go to a variety of services, like education and state parks and such. This does create a motive to encourage spending on the lottery as those services end up relying on the lottery earnings as much or more than conventional taxes and fees for their funding.

> and who is not profit-motivated and therefore will do less to encourage problem gambling, is better than the alternative in practice.

When a government taxes vice its now depending on those revenue streams. It creates an incentive system where the regulator for advancing social good is depending on tax income from the failure of regulating.

Illinois is doing this right now with their gambling industry. Those little gambling machines are in every restaurant and there are dedicated e-gambling buildings everywhere in Springfield. You see folks go in and dump their life savings into those machines. I know a restaurant owner who has customers park out back to hide their gambling from their spouse.

But gambling tax revenue is bailing out the failing state. At the end of the day, it seems like the government of Illinois is the true addict.

I just think it's ok for the government to run a lottery and not advertise it. Allowing gambling machines in restaurant is a whole different story. I think conflating the two is a slippery slope fallacy.

The ethical optimum seems to be:

1) Government run lotteries. Otherwise there will be shady illegal lotteries instead.

2) No skimming funds. 99.8% of what goes into the lottery tickets gets paid out to winners, taking only enough to fund the lottery itself. Otherwise you're taxing the poor, and their lives are hard enough.

3) No advertising. To prevent big stories about the "mega-billions" jackpot, cap and split jackpots. So if you have enough to do a 10 billion jackpot, instead offer 100 million jackpots for a while, until the funds are used up.

They pay for college tuition and books in my state.

https://en.wikipedia.org/wiki/HOPE_Scholarship

Edit:

> As of 2006, more than $3 billion in scholarships had been awarded to more than 900,000 Georgia students. As of 2018, HOPE has already helped around 1.8 million students from Georgia enroll in college.

One negative externally that would happen anyway (eg. sports betting) turned into a positive one.

Except it hasn't kept up with rising tuition or many "fees" added since 2008.

Thats typically how they get approved.

State argues they'll use it to fund education, people thinks thats a great idea so it has widespread approval. Later the state decides they'll change the rules to allocate the funds in more ways.

Would you prefer they just raise your tax by a dollar instead?

I used to think the same thing but I've come full circle to believe that any behavior humans take place in, regardless of the consequences, should be legal and regulated opposed to banned/illegal. Money just ends up flowing to cartels and much more unsavory/unethical organizations.

Drugs, prostitution and even gambling fall into this category. It's certainly the lesser of two evils and not perfect. As others have pointed out I'd much rather live in a world that treats prostitution like Amsterdam or drugs like Portugal than the current war on drugs, police militarization, security theater surveillance state we are in right now.

Or alternatively, they're the most ethical form of tax ever -- a voluntary tax.

Without state lotteries they’d still exist, and be far more likely to be crooked even with heavy regulation.

Thought experiment: add more numbers.

We get these huge jackpots because the odds of winning are so low. What happens if we add more numbers so the biggest jackpots end up at $10 billion... Or $100 billion or $10 trillion?

When do things start to break? And what breaks?

Does Lottery Revenue Rise or Fall during Economic Hardship?

https://taxfoundation.org/does-lottery-revenue-rise-or-fall-...

The lottery = Poor Person’s Tax

True, but it's kinda fun too. Buying the ticket and letting yourself fantasize a bit is part of the 'joy' of it. Could you do it another way? Of course. But actually plunking down $2 and dreaming about the winnings in the car feels more 'real'.

To me, it's fairly harmless fun, probably for most people too.

Edit: Also, it's a voluntary tax.

A guy I knew was a statistician for Loral. He always bought a lottery ticket.

He knew the exact odds and expected value and played anyway.

I wonder how that compares to all of the sports gambling going on these days.

All you need is a dollar and a dream. Or in this case, two dollars.

Dang it, not even close.

Any way to hack the $1bn lottery prize?

Buy more tickets /s

Are you aware of any syndicates?

https://www.cnbc.com/2017/06/30/mastermind-of-lottery-fraud-...

https://en.wikipedia.org/wiki/1980_Pennsylvania_Lottery_scan...

You need to be in the business. I think every drawing uses new numbered balls, maybe go for the supply chain if you can't get in the lottery organization itself.

if we were in a recession maybe this would make sense but I've been told we're not so this is completely baffling

Silence, pleb! Don't question the authorities.

I don’t think it’s particularly baffling to believe that potentially winning $600mm is attractive to a lot of people in a country where the top 1% control 15x the wealth as the bottom 50% in sum and where wages have stagnated to such a large degree.

Right because 600m wouldn’t be attractive elsewhere.

Gp is referencing US political slap fights from the last week (Biden admin declaring US is not in recession).

It’s a joke comment.

in the words of a wise man, "not a joke"—I truly thought we were in a recession, but the updated definitions and Wikipedia article lock proved me wrong!

Recession is one of those words like Abortion where everybody has their own definition.

The US officially [1] goes by what NBER says and NBER doesn't call recessions/etc until several quarters after it starts. So any talk right now is speculation and you may speculate correctly but you might not.

[1]: https://www.bea.gov/help/glossary/recession

I didn't realize the definition of "abortion" was up for debate, I thought merely the parameters defining when it should or shouldn't be allowed were.

The Q2 GDP estimate came out on Thursday. Nobody said we weren't in a recession following that, only that the current economy is not like past recessions. If you try following the news, you might be less confused.

> Nobody said we weren't in a recession following that

https://www.cnbc.com/2022/07/29/white-house-goes-on-offense-...

https://en.wikipedia.org/wiki/Gaslighting

They said that there are reasons NBER might not call it a recession when they make their determination. They did not directly say that we aren't in a recession, by the two quarter rule or otherwise.

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