Expecting Lady Luck.

January 13, 2021 6:09 PM

Maximizing the Expected Value of a Lottery Ticket: How to Sell and When to Buy. tldr: "Powerball tickets bought (under the current sales model) with pool sizes between $775.2 million and $1.6656 billion have positive expected value." But that's before everyone read this. P.s.
posted by storybored (53 comments total)

Don't feed the machine, give me $2 instead and I'll tell you if you won or not. Instant results for $1 more.
posted by Old'n'Busted at 6:28 PM on January 13, 2021 [12 favorites]

Again, there's one really good, totally valid reason, for buying one of the big big tickets, especially in the time of covid:

Best daydreams ever!

Pollytechnocolor utterly realistic, no...yea, hyper-realistic, enthralling hours of pure entertainment. Cheap for $2.
posted by sammyo at 6:37 PM on January 13, 2021 [17 favorites]

Yeah, as a non-buyer I can totally see the appeal of having a few days of happy ideation. Just a few days, that's all. That's all it has to be. That's all anything has to be anymore.
posted by aramaic at 6:39 PM on January 13, 2021 [7 favorites]

Best daydreams ever!
I've heard this a fair amount before, and fair enough, though it does have me wonder why stop at "I have the ticket and imagine winning" and not "The winning ticket comes to me through unlikely circumstances, and I imagine winning"?

I've had birds drop money in front of me a couple times, a dime-bag of weed once even. A lottery ticket doesn't seem out of the question at that point.
posted by CrystalDave at 7:10 PM on January 13, 2021 [12 favorites]

IDK, some lizard brain thing. But I really can't get engaged in that sort of speculation on a hypothetical like I can while holding a ticket.

But on the other hand I get a lot more mileage out of a ticket than a few days. I buy a ticket once or twice a year and that sucker lives in my wallet for months allowing me to speculate before I check it. A $5 equates to a small fraction of a cent per hour day dreaming.
posted by Mitheral at 7:15 PM on January 13, 2021 [15 favorites]

Once upon a time, I was down visiting a friend in Louisiana and bought a Powerball ticket at a convenience store near her place. As I was sitting in the bar she worked at, the morning I was going to fly home, the local news was showing the store because the winning ticket had been sold there. Not me, of course, but that’s a hell of a close call.
posted by notoriety public at 7:49 PM on January 13, 2021 [8 favorites]

Last time I ever played a lottery, I got the first four digits (of six) right. Want to talk about the air going out of your sails as the numbers are announced...
posted by maxwelton at 9:45 PM on January 13, 2021 [5 favorites]

I've had birds drop money in front of me a couple times, a dime-bag of weed once even.

Metafilter's own prophet Elijah
posted by justsomebodythatyouusedtoknow at 9:54 PM on January 13, 2021 [4 favorites]

But on the other hand I get a lot more mileage out of a ticket than a few days. I buy a ticket once or twice a year and that sucker lives in my wallet for months allowing me to speculate before I check it.

Oh heck yeah. I used to call them my $1 daydreams. Back when it was still a buck.

And I drove a friend nuts by refusing to check them in a timely manner. Just knowing I could be walking around as a millionaire and not even know it was absolutely worth the pocket change of getting a ticket.
There was a certain something to carrying it around and every time I opened my wallet thinking “I might be rich right now.” Just a fleeting thought throughout the day. I haven’t done that in a long time but maybe I should, it might be time for some fantasy.
posted by [insert clever name here] at 11:02 PM on January 13, 2021 [4 favorites]

I got the first four digits (of six) right.
Once in a lonngg while, when I'm feeling lucky [punk], I've been known to buy a Lotto ticket. I can't remember ever having one number right and think that The Man should have a misère prize for people who can show a run of such null tix. My demented, ricketty, 95 y.o., father-in-law allocates 1% of his pension every week to this institution. His fantasy, occasionally articulated, is a longish list of folks he's going to take care of with the loot. I find that rather endearing.
posted by BobTheScientist at 11:43 PM on January 13, 2021 [4 favorites]

In the UK I think you have 90 days to claim, sometimes if a winner hasn't appeared and the clock is running down stories appear in local newspapers asking if people have checked all tickets bought for that draw.

I have always found the Spanish approach to lotteries very fair and sensible. There are no really huge prizes, well there are in the Christmas Lottery but the lottery design shares them out, (€200 tickets but you can buy a hundredth share of a ticket giving those share holders a hundredth of the prize). Instead there are lots of smaller prizes with quite a few life changing, but not life destroying, prizes. Better for many people to win a couple million or so rather for one person to win tens or hundreds of millions.
posted by epo at 1:28 AM on January 14, 2021 [11 favorites]

...Not me, of course, but that’s a hell of a close call.

Obvs! Otherwise you wouldn't be seen in a shithole like this
posted by NoMich at 5:18 AM on January 14, 2021

Since most states don't let you collect anonymously, I don't buy lottery tickets because I might win.
posted by Ampersand692 at 5:58 AM on January 14, 2021 [3 favorites]

Deciding how to manage winning a big prize is an entertaining mental exercise. Start a foundation, what to call it? how to find a lawyer, manager, etc. What sort of nifty, sustainable house might I build and where.
posted by theora55 at 6:15 AM on January 14, 2021 [3 favorites]

Idk, even the entertainment angle rings hollow (to me, obv here shows YMMV).

When I was young the toy store dash with the shopping cart looked like fun. Now it looks like mania. Ok, sure, we're in a dead-end capitalistic dystopia, but fuck them. Human imagination that is contingent on 'buying in' and then usually results in 'list of things they tell me I want' just breaks my heart. We should aspire to dream bigger.
posted by Reasonably Everything Happens at 6:20 AM on January 14, 2021 [1 favorite]

A colleague used to tell me that it's better to buy a lottery ticket in the evening, just before the deadline, than in the afternoon.

When pressed to explain, he said, "Well, you might be hit by a bus and killed in the afternoon before the drawing. If you haven't bought the ticket yet, then your heirs get an extra $2 in your estate."
posted by fantabulous timewaster at 6:21 AM on January 14, 2021 [4 favorites]

The cost of each lottery ticket is $2, so we are interested in situations when the expected value of a ticket is greater than $2. For the standard Quick Pick scheme, one can expect to see returns when the jackpot is between $775 million and $1.67 billion. A ticket provides its maximal return when the jackpot is around $1.02 billion, but as the jackpot grows larger and larger, the expected number of tickets to be sold grows quadratically, and hence, the number of collisions overwhelms the returns of the jackpot. It becomes more and more likely that the prize will have to be shared among more people.

OK, so, sure, $1.02 billion. That's the magic point where it makes the most statistical sense to go buy millions of lottery tickets, because each ticket has an expected return slightly higher than its cost. Except your chance of winning the jackpot grows asymptotically, and doesn't hit 100% unless you buy hundreds of millions of tickets, which you'll have to fund upfront. And you're still not guaranteed to be the only winner, so it's a coin toss whether you'll be out hundreds of millions of dollars or not.

I mean, yeah, they did the math. I guess what I'm saying is, this is why liberal arts education has value.
posted by Mayor West at 6:23 AM on January 14, 2021

OK, so, sure, $1.02 billion. That's the magic point where it makes the most statistical sense to go buy millions of lottery tickets, because each ticket has an expected return slightly higher than its cost. Except your chance of winning the jackpot grows asymptotically, and doesn't hit 100% unless you buy hundreds of millions of tickets, which you'll have to fund upfront. And you're still not guaranteed to be the only winner, so it's a coin toss whether you'll be out hundreds of millions of dollars or not.

If the Expected Value is positive it means it makes as much sense to buy one ticket as it does a million tickets.
posted by JPD at 6:44 AM on January 14, 2021 [5 favorites]

I used to quote the statistician's creed: "A lottery is a tax on people who are not great with math." Then I pivoted to the "buy a ticket if the payout is high enough;" as the cost of daydreaming many have pointed to above. But this seems to indicate "even if we are disciplined enough to only play when the expected value is positive and fortunate enough to be the unique winner when we hit the jackpot, we will have to play" billions of times to have any confidence in realizing a profit. So now I'm back to daydreaming with CrystalDave's method----if I can train my local crows to bring me promising slips of paper, even better: crow army + possible jackpot!
posted by adekllny at 6:58 AM on January 14, 2021 [2 favorites]

adekllny, angrily yelling at crows who just dropped muddy lottery tickets at their feet: "matching only two numbers doesn't win anything, you need at least two numbers PLUS the powerball! Try harder next time!"
posted by AzraelBrown at 7:05 AM on January 14, 2021 [4 favorites]

Although, on further thought: training crows to grab just-purchased lottery tickets out of people's hands as they're leaving Circle K, and deliver them to you in exchange for shiny balls of crumpled tinfoil, is a very cost-effective way of getting large numbers of tickets for little investment.
posted by AzraelBrown at 7:08 AM on January 14, 2021 [10 favorites]

I briefly read that as "cows" and was extremely confused about the sort of environment in which cows can just wander up, manhandle people and take their stuff. Kangaroos, sure, maybe, but cows?
posted by aramaic at 7:46 AM on January 14, 2021 [8 favorites]

You do run the risk of pissing off a bunch of crows.
Probably safer to just rob a local gangster.
posted by fullerine at 7:47 AM on January 14, 2021 [2 favorites]

In the early 1990s, eleven year old me had this bright idea to record the nightly lottery numbers to find out if any were more likely to appear. Each evening I diligently entered the drawing into a Quattro Pro for DOS spreadsheet. With each successive histogram, my ideation ran wild and I started plotting various schemes to convince an adult to be my straw buyer.

And then I learned an important lession about statistics.
posted by RonButNotStupid at 7:52 AM on January 14, 2021 [7 favorites]

I have always found the Spanish approach to lotteries very fair and sensible.

One other difference is that the Spanish lotteries are what we would call "raffles" here. There is always a winner chosen from the range of numbers sold. Your odds of winning the top prize in the Christmas lottery, for example, is 1:100,000 which is actually pretty cool. You might share that prize with an entire town because of how they split up tickets, but still.

It's the Americans that created all kinds of impossible odds and rollover rules that let us get to these jackpots that border on 10 figures. And, sometimes, even the lottery commissions screw that up.
posted by JoeZydeco at 7:54 AM on January 14, 2021 [2 favorites]

OK, so, sure, $1.02 billion. That's the magic point where it makes the most statistical sense to go buy millions of lottery tickets, because each ticket has an expected return slightly higher than its cost.

Isn't this the expected value of a ticket under their improved system which reduces collisions (ie: quick pick with the same exact numbers) , not the existing one that theoretically produces many collisions.

I actually came out of this trusting QuickPicks slightly less. They don't discuss the technology of QuickPicks in the article, but it's theoretically possible that given the same computer parameters for an exact given timeperiod and different locations, multiple QuickPick generators could be dispensing the exact same numbers, which reduces the likelihood that those would be single winners.
posted by The_Vegetables at 7:54 AM on January 14, 2021 [1 favorite]

The high payout thresh-hold never makes sense to me. A few million should set you for life, even factoring for inflation.

But eight or nine or ten figures - that's too much responsibility.
posted by BWA at 8:02 AM on January 14, 2021 [1 favorite]

No worries, I will take on that burden for you!
posted by They sucked his brains out! at 8:17 AM on January 14, 2021 [1 favorite]

I have always found the Spanish approach to lotteries very fair and sensible.

It's more equitable in that there are more ways to win and more people benefit, but that doesn't make it actually fair, sensible or equitable. Just like in Vegas, the house always wins. The purpose of a government-run lottery is always to make money from the government, and it is always a regressive tax. Lower-income people, because they have more need for the money, have a higher propensity to buy tickets and lose more money, per capita, than high-income people who are less inclined to buy. Compounding this regressive skew is the fact that lottery revenues reduce the need for states to tax the highest income earners, so the whole scheme benefits the 1% by reducing their taxes.

Is there a way to flip lotteries from regressive to progressive taxes? I'm not finding any suggestions out there for how that might be done, as long as purchasing is a voluntary thing.
posted by beagle at 8:23 AM on January 14, 2021

Yeah I disagree on the extreme wealth front; if you live in a state where you can't claim the prize anonymously, you don't really want to end up with less than $20 million after tax. I mean -- if someone said I could have $4 million dollars flat out, with the caveat that I would have to deal with a lot of scammers, I probably would take it. But that feels less like a windfall and more like a sadistic reality show plot. And then I really don't like to buy a ticket just to see the pot roll over to another week, so I really only buy when the jackpot is properly over $400 million and I know lots of other people are playing, too. I've always thought that was just my weird brain wanting someone to win, even if that someone isn't me. But apparently...that's just maximizing the expected value of a lottery ticket, so, uh, it's good math.
posted by grandiloquiet at 8:26 AM on January 14, 2021

if you live in a state where you can't claim the prize anonymously

In many (most?) of those states you can still claim anonymously, but you have to plan ahead -- once you win, you establish a South Dakota Trust, and then the prize is claimed on behalf of the trust (assuming you have not made the mistake of signing the ticket in your own name first. Someone acting on behalf of the trust would sign).

South Dakota enforces pretty good secrecy on trusts, which is one of the reasons why the hyper-rich love it so much (wanna take action against the global elite? Then disable the South Dakota Trust system); if your state allows a trust to claim the winnings you'll be pretty darn anonymous and your assets will be almost completely bulletproof (SD also has extremely strong asset protection for trusts, so almost nobody will be able to sue your trust for "your" money).

[seriously, someone do something about South Dakota]
posted by aramaic at 8:39 AM on January 14, 2021 [8 favorites]

We like to call the powerball "Our Retirement Plan"
posted by Mchelly at 9:01 AM on January 14, 2021 [1 favorite]

(assuming you have not made the mistake of signing the ticket in your own name first. Someone acting on behalf of the trust would sign).
Seriously - don't sign the ticket until you speak to a lawyer.
posted by soelo at 9:26 AM on January 14, 2021 [2 favorites]

Here is how I maximize the actual value of lottery tickets for me. I buy maybe three to five tickets a year on a near random schedule but only when the net cash out jackpot is over $200 million. This low level purchasing buys me the ability to pull up an "If I won the huge lottery jackpot" daydream for the entire year whenever I am stressed/bored/or whatever because my infrequent purchases lend me just enough plausibility to give the daydream some juice but it really doesn't cost me much at all. I don't kid myself that I am going to win though. I never believe that. I'm just buying the daydream so I never need multiple or regularly purchased tickets for that.
posted by srboisvert at 9:40 AM on January 14, 2021 [2 favorites]

Yeah I disagree on the extreme wealth front; if you live in a state where you can't claim the prize anonymously, you don't really want to end up with less than $20 million after tax. I mean -- if someone said I could have $4 million dollars flat out, with the caveat that I would have to deal with a lot of scammers, I probably would take it. But that feels less like a windfall and more like a sadistic reality show plot. And then I really don't like to buy a ticket just to see the pot roll over to another week, so I really only buy when the jackpot is properly over $400 million and I know lots of other people are playing, too. I've always thought that was just my weird brain wanting someone to win, even if that someone isn't me. But apparently...that's just maximizing the expected value of a lottery ticket, so, uh, it's good math.

I know that happens to a lot of people who win the lottery but ultimately there's nothing that stops you shoving it all into an index fund and then ignoring anyone that wants to talk about money.

All of this assumes that there is no such thing as diminishing marginal utility of money, but there is. Winning $10bn is not a billion times better than having $10. Especially if your total income is low, the marginal utility of the next $10 might be making or not making rent. If the average American won $1m, they could live in comfort forever without working another day, if they won $2m... they could do the same thing in a slightly bigger house, maybe buy a holiday house? The difference in lifestyles being having and not having to work is obviously much bigger than anything that comes after that. By the time you're a billionaire you're literally just funnelling money into inflating the price of art because why not?
posted by atrazine at 9:54 AM on January 14, 2021

The high payout thresh-hold never makes sense to me. A few million should set you for life, even factoring for inflation.

Yeah I think this is incorrectly assuming that the value of money is linear. Your first dollar changes your life a lot more than your 200,000,000th dollar.
posted by aubilenon at 9:56 AM on January 14, 2021

TFA is all about a new way to generate quick-pick numbers that the authors propose is "more random" and therefore reduces "collisions" (more than one ticket with the same number). The only useful takeaway for today's players is their assertion that in the current system a ticket's expected value would be above $2 when the jackpot is $775 million and $1.67 billion.

The reason that there is an upper bound on the "range to buy" is that due to higher ticket sales (TFS states that ticket sales grow quadraticaly with jackpot value) you are more likely to share the jackpot, which means that the "expected value" of an individual ticket falls below $2.
posted by achrise at 10:11 AM on January 14, 2021

What they ought to do is raise the price of the tickets as the value of the jackpot increases. That way you ensure more participation early on, as well as spurring a robust secondary market.
posted by Faint of Butt at 11:03 AM on January 14, 2021

Although this central server idea appears to be optimal in terms of preventing collisions, it requires constant communication between each sales terminal and the server. If this connectivity is lost at any point, tickets cannot be dispensed.

Hmm. If you trust the machines, you could just distribute a unique list of non-duplicate random picks to each machine ahead of time and cross them off as you go. If you don't trust the machines, then both the paired and the independent PRN scenarios don't work either.

I think I must be missing something. If the set of all possible numbers is large and sparsely picked, which seems a requirement for the existence of large jackpots. . . why bother with the complicated pair thing? It gives you a factor of less than two in margin for unexpected large buys compared to unique lists and makes things a lot more complicated. Just give every machine a list that's twice as long. If you're regularly selling more than half of all tickets, then the paired approach seems like it will need networked intervention to avoid failure anyway.

I'm also surprised that only 30% of people pick numbers themselves. When my grandparents died, they left behind notebooks filled with decades of lottery winning number tabulations which allowed them to pick the ones that hasn't come up in a while. (I doubt they had a coherent mechanism in mind for how that would have been true, even given rather a lot of incorrect beliefs about the world. But, they put significant effort into it.) Then again, one of the same family members sincerely believed they had a winning strategy for casino Craps. Surprisingly, they did not become wealthy as a result.
posted by eotvos at 11:18 AM on January 14, 2021 [2 favorites]

The thing that always stumps me is who do you go to for advice?

Your hometown lawyer? The H&R tax guy on the corner? The local financial planner?

Or is a trip to someplace like NYC warranted?
posted by Fukiyama at 11:29 AM on January 14, 2021 [1 favorite]

The thing that always stumps me is who do you go to for advice?

Your hometown lawyer? The H&R tax guy on the corner? The local financial planner?

Or is a trip to someplace like NYC warranted?

The fancy part of your city probably has some wealth management firms. They generally won't even really speak to you if your net worth is less than double digits worth of millions.
posted by The_Vegetables at 11:35 AM on January 14, 2021

The thing that always stumps me is who do you go to for advice?

Specialists who already do this kind of work, and are duly certified -- a CPA used to dealing in large sums, estate-planning lawyers, banks with "wealth management" divisions, that sort of thing. You'll want a team of advisors, but finding one of them can usually net referrals to the rest (a competent specialist will say things like "while I am capable of setting up your trust arrangements, questions regarding citizenship diversification should be referred to a competent firm, I suggest someone like Henley & Partners").

People who hire "friendly local folks" tend to be the ones who later discover their nice cheerful money person has been embezzling the funds, and then someone ends up buried under a concrete slab (this has literally happened).
posted by aramaic at 11:41 AM on January 14, 2021 [2 favorites]

When I was young the toy store dash with the shopping cart looked like fun. Now it looks like mania. Ok, sure, we're in a dead-end capitalistic dystopia, but fuck them.

I haven't thought about those since I was a kid. At the time, I had vague but exciting plans to fill the cart with the smallest and most expensive items in order to re-sell them. Which may be even more ugly and dystopian, especially for a nine year old, but is also not a bad choice. I'm not sure what the right items would have been at the time. It was a bit before Pogs or Magic the Gathering. Lego is expensive, but bulky. Video game cartridges? Model rocket engines? Model airplane engines and rc components? Pewter figurines? Really fancy chess sets? (In the days before eBay, figuring out what anything was actually worth was harder, of course.)

In the supermarket version, I suspect the optimal choice is to empty the spice aisle and pick through the over the counter medicines, then go for top-shelf liquor. Unless you're at a fancy supermarket with good cigars.
posted by eotvos at 11:41 AM on January 14, 2021

The thing that always stumps me is who do you go to for advice?

A large bank or Trust company like Fidelity or Schwab that are established and have a fiduciary responsibility to their clients.

Take selfies with the slip **do not post anywhere** then put the slip in a safe deposit box. If you want to be anonymous don't sign it yet, it's possible in some states to set up a trust that keeps you hidden. Do not tell anyone except spouse.
posted by sammyo at 11:54 AM on January 14, 2021

Office pools are a serious contract that require planning.

Looks treacherous and a lot of work for someone. What they didn't mention is that someone could make an online office group or email thread and have anyone post their own ticket numbers to the group. The terms are that any wins are divided by individual ticket stake. So, if I post 10 tickets out of 200 total, I could expect a 5% payout.
posted by Brian B. at 11:58 AM on January 14, 2021

Don't feed the machine, give me $2 instead

what upsets me is, here in NC, they sell scratch-off tickets now at $5, $10, and even $20, I think, price points.

there's probably no way to say this in a way that won't rile up one of you good people, but the folks I see buying scratch-off tickets don't normally look like they have $20 to just piss away on gambling in one go. They'd be far better off saving for a bus trip to a casino, if they were determined to put that $20 in the gambling budget.
posted by thelonius at 12:06 PM on January 14, 2021

Don't go to the friendly tv "lottery lawyer"
posted by grandiloquiet at 12:28 PM on January 14, 2021

I have some family friends who won something like $7 million in the 90s. They pretty much became hermits after that. We'd see them once in a while and they'd act the same, and were always very nice, but they wouldn't come to most social gatherings anymore. I remember running into one of them a couple of years ago and finding out that he named his son after my dad. Like why not drop by for a cup of tea sometime then?
posted by any portmanteau in a storm at 2:07 PM on January 14, 2021 [1 favorite]

We like to call the powerball "Our Retirement Plan"

Oddly enough, the people who run the lotteries call your tickets "Their Retirement Plan".
posted by They sucked his brains out! at 2:49 PM on January 14, 2021

Like why not drop by for a cup of tea sometime then?

Probably burnt out by all the shirttail relatives and acquaintances that didn't waste time hitting them up for money.
posted by Halloween Jack at 2:50 PM on January 14, 2021 [3 favorites]

We should aspire to dream bigger.

Everything I won besides enough for a 70-80K annual salary would be used for providing quality, high efficiency, accessible low cost housing. I want to build homes for the disadvantaged and 10+ million dollars would let me.

What they ought to do is raise the price of the tickets as the value of the jackpot increases. That way you ensure more participation early on, as well as spurring a robust secondary market.

So a regressive tax made more regressive by allowing capital holders to skim off profits that would otherwise go to the state?
posted by Mitheral at 6:08 PM on January 14, 2021 [1 favorite]

I'm glad to know I'm not the only person with lottery daydreams. Like, way too many of them, actually. I only started buying tickets a few years ago, when I saw some lottery winner with an obscene amount of money and it clicked with me: that guy had just as much chance as I would have had I bought a ticket...but I didn't buy a ticket.

I know I'll almost certainly "lose" when I buy a lottery ticket, but I buy one for the participation. I buy one just so I won't feel that "damn, I could've bought a ticket but didn't!" feeling. So really it's hedging against future regret.

I'm in Japan so no massive Powerball lottery. There are Jumbo lotteries about three times a year, and the big jackpot is "only" about 10 million (USD equivalent). One neat thing about Japanese lotteries is they are tax free: the amount you win is the exact amount to you take.
posted by zardoz at 7:07 PM on January 14, 2021

that guy had just as much chance as I would have had I bought a ticket...but I didn't buy a ticket.

That is the Iowa Lottery's motto: "You can't win if you don't play!"
posted by Fukiyama at 8:46 PM on January 14, 2021