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 :)
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.
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.
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. ;)
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?
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].
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.
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.
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."
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 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
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.
>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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
> 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 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.
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.
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.
> 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.
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.
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?
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.
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.
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.
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.
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.
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.
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.