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> The State Lottery made a mistake in all this. They listed the odds of winning that was associated with each combination of numbers.

I don’t see why this is a mistake. Every lotto should do it, but I can see why they don’t.

Right, that wasn’t the mistake. The mistake was designing a game that is gave the player the house advantage.
Not really. The lottery organiser didn't lose out on any money here. The total prize money is going to be paid out to someone. In fact, the operators, through this mis-design, might have encouraged more lottery ticket buying than there would have otherwise been (e.g. this guy started buying thousands of tickets) - so this 'flaw' would have made the lottery more money!

It all starts to go wrong when the secret gets out; ordinary lottery players might avoid the game because they see it as rigged, so the revenue goes down. At this point, the lottery organisers have to do something.

It's not a mistake at all, it's an advertising campaign for numeracy.
In a proper lottery (i.e. balls randomly extracted out of a machine), the odds are the same for each combination of numbers, surely...? How did they produce these odds, artificially?
I don't think the game is really flawed, per se. It's just that during the weeks with these roll downs, the expected value of a ticket can be positive.

Effectively, players during weeks without rolldowns are subsidizing excess prizes for weeks with the rolldown rule in play. This is probably a feature you don't want in the game, but it's not too different from games where when the jackpot is particularly high that the EV of a ticket can exceed its price.

That is a dangerous game though: some weeks there are two winners and then the expected value goes negative even though the total payout is more than the cost of buying one of each ticket.
Sure, but that's something that's easy to model in your EV and volatility calculations, too, even though forecasting total sales and the distribution of peoples' number choices (non-uniform == better for you) is a bit of a trick.
Jerry studied those winning odds, and the timing of those Roll Downs. He realized that, statistically, a single one dollar lottery ticket was worth more than one dollar in those final weeks.

The state's error was being too slow with "Roll Downs."

10 years, $26M revenue, $8M profit. $800K/year; I guess taxes were counted in the $18M expenses. Nice "side-gig" to running a convenience store!

[edit: 10 years, not !0 years.]

I’d imagine some of the revenue was their commission from selling tickets.

At least where I am, vendors and their family are basically prohibited from playing/winning after they were found to be winning way too often.

What was happening is they would get to know which players don’t check how much they’ve won and declare you’ve won $100 when you really won $1000. Or worse.

It's not a mistake, it's a legal requirement in some places. It's poor writing.
Question: How can he be right about the estimated value of a ticket when the number of buyers is unknown? Should the game not swing back once the "hack" is made public?
You can estimate the number of buyers.

You can also clock how long it takes to sell tickets at gas stations and calculate a theoretical maximum because you can get all of the selling locations.

It's straightforward to calculate the number of buyers of a lotto given the before and after size of the jackpot, the number of winners of each prize and the formula by which the jackpot increases per buyer. All of this is public information, it's just that it's not known until after the lottery is over. But the number of buyers in the past is a great predictor of the number of buyers in the future for a given jackpot level.
Assuming they sold lotto tickets at their convenience store and that the couple actually worked at the counter, they could probably get a pretty solid gut feel for the relative demand of each drawing based on the number of tickets they sold.
My (general) understanding is in these lotteries, whenever there's a rolldown, all tickets are positive EV, regardless of the number of tickets bought. Although, it certainly would get slim if the number was very high. I think there were three known large scale buying groups for the MA rolldown lottery?

The exciting technique was determining when your buying could trigger a rolldown, possibly without it being previously announced.

> whenever there's a rolldown, all tickets are positive EV, regardless of the number of tickets bought

This is probably likely, but wrong in general. If the tickets cost $1 and the total prize money is composed from e.g. 50% of the ticket prices plus a fixed amount of leftover prize money, when enough tickets are bought for the rolldown round, the leftover prize money isn't enough to cover for the 50% of the new tickets that doesn't go in the pot.

Example: $2m leftover money in the pot, 5 million tickets bought for $1 each. EV = $2m + 50% of $5m = $0.9 per ticket.

Now, if you buy enough tickets to guarantee e.g. 4 correct numbers and know for a fact that due to a rolldown the minimum payout is going to be high enough to cover the cost of that (at least with a high probability), then you're fine. I'd assume that's what the couple in the story did.

So basically you are betting that not many other people have the same winning combination. Sounds like a good deal for the house to me.
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> The math explanation could fill an article itself.

If you are interested in how exactly he did it, here is a more detailed description:

https://math.berkeley.edu/~kpmann/ellenberg.pdf

The main strategy is the tremendously complicated scheme of "buy as many tickets as you can physically key in, any time the prize pool goes above $x." Everyone who played the Michigan or Massachussets lottery that week was "hacking" the lottery the exact same way!

That's not quite the optimum solution - what if you accidentally played the same numbers a million times, instead of a million different sets of numbers? So you should make sure you spread out your plays. However, I believe spreading them randomly is "good enough": the interesting maths only improves your edge a tiny amount.

>> the interesting maths only improves your edge a tiny amount.

Its only anecdotal evidence, but this would support your idea.

I used to work for a mom & pop company. The owner was really wealthy. He would only play once the pot got to an insane amount (I think it was over $5 or $10 million) and then on his way into the office, would stop at 5-8 places, buying anywhere from $1-$3K in tickets a shot.

I still vividly remember huge stacks of lottery tickets sitting on his huge desk in his office.

He never did win the big pots, but did win a $1K or $2k amounts by matching a few of the numbers. But very clearly, he spent WAY more then he ever won.

> But very clearly, he spent WAY more then he ever won.

Which, in a recreational context, one could argue has more potential upside than a lot of other recreational activities (at least it's on the table, unlike other activities), and a pretty high baseline thrill as well.

You could argue that, but I think it's still a pretty weak argument. Arguments in favor of gambling as recreation are similar to ones made in favor of drugs as recreation where you basically just burn money in exchange for chemicals that make your brain feel good, but with few other benefits.

Whereas other forms of recreation (IMO) give you more in return, such as increased dexterity, increased knowledge, strengthened human relationships, an interesting story to ponder and discuss, etc.

I'm not saying people who gamble or use drugs are bad, I'm just saying the value of a given recreational activity can be measured along more axes than "dopamine yield"

I don't know anything about gambling, but recreational drugs use can certainly strengthen human relationships and generate interesting (or at least amusing) stories
I would not deny this, but it’s worth stating the obvious: most recreational drugs can also have the effect of destroying human relationships and generating stories that are highly tragic.
There isn't a rational way to value "thrill" - each person has a different thing that gets them the thrill.

For you, maybe increased dexterity or knowledge is good, but for another person, that's downright boring.

One other way to "value" thrill is whether it is legal or illegal, whether it damages other people or just a single individual.

In terms of pleasure derived, you can't really say "this is useless entertainment" vs "this entertainment makes you smarter too so it's better"

There is value in recreation that gives you benefits, I agree, but there is also value in recreation for its own sake too. Expecting all of your hobbies to give you some benefit other than fun can lead to them all becoming "work".
I've both made friends and strengthened existing friendships at the blackjack table and craps table. I love gambling for its own sake, but it's still a little sad to me that so much of a casino floor is slot machines which are not social.
True, I shouldn't have put all gambling under the same umbrella. I actually really enjoy poker myself, though I tend not to bet real money, just chips with friends.
Done correctly, it’s investing at an awesome interest rate.

Buying a bond that has a 10x return with a 50% default rate is still a great investment.

>> 50% default rate

If only 50% of tickets are defaulting, there is something very very wrong with that lottery. This is more like a bond that pays a 100x return but has a 99.9% default rate.

That's the beauty of the lottery from the article. I've done the math on my local games and it tips into your favour after the jackpots get high enough. The issue with my local lotteries is that the EV comes partly from the main jackpot, which is a very low occurence outcome. The article has the EV come from the smaller prizes which can be easily won.
I would say something but I'll pass. Working on breaking the lottery at the moment. Could give away trade secrets to make everyone rich.
TFA is, to put it politely, incomplete. They played both the Michigan and a later Mass state lottery. It looks like the Michigan lottery may not have detected them.

https://highline.huffingtonpost.com/articles/en/lotto-winner...

I remember that one. The medium article looks like a summary.
It's worse though. Because it completely ignores the Massachusetts lottery, which was where the MIT team actually came in.
this is the best article on the topic. Probably my favorite article ever, actually. I also like how it frames Selbee as an average joe-turned-convenience store owner with a side interest in math, instead of how TFA frames him as a mathematician.

Previous discussion on the good article: https://news.ycombinator.com/item?id=16494280

Honestly, the currently linked article seems to me like low-effort blogspam.

> All they’ve done is renovate their house and pay for their 14 grandchildren's college funds.

State lotteries love to go on how their proceeds are used for education. But I bet 14 full rides to college on $8MM is a greater impact on education than what the state achieves with the same amount.

They created 14 college funds because each individual 529 allows a lump sum $150k married gift tax free. With that only totalling $2.1m of tax free income, I’m confident they did a lot more stuff with the remaining $5.9m.

Anyway it’s kind of ironic you are comparing the state’s education spending to a tax avoidance scheme.

I would imagine the price for college exceeds $150,000 in many cases. I have a savings target well in excess of that for my son.
I mean this in the best possible way, try punching "529 Plan" into Google.

The point of the comment, which I'm not sure why it was being downvoted, is why something might sound newsworthy (14 college funds?) when it really has a simple, logical explanation if you're sophisticated with money. And in the same breath, in applause of a guy performing a tax optimization, the original poster shits on the state - did it create this tax loophole? Do you think the people running government want college to be expensive?

Rich people, really everyone with heritable wealth, love the 529 plan. If you understood that it is used to create multi-purpose, heritable investment accounts tax-free in vast excess of the actual cost of tuition - that anyone who would have a hard time paying Harvard's tuition goes for free anyway - you would detect some insincerity in "14 college funds" too!

And maybe consider that this 529 plan remains the status quo, this total tax dodge, because of people who have this romanticized picture of it being used to pay expensive college tuitions. We're talking about a family so sophisticated that it's probably going to change legal guardians on those very same children in order to benefit from free tuition anyway.

It's a great story. We certainly want our brainiacs spending resources "hacking" some shitty institution like the lottery. On the other hand, you think he doesn't take beyond his measure from the government too?

The 529 plan, specifically the prepaid tuition plan, is an amazing option here. Another user has already pointed this out, but I want to add personal direct experience.

We used the 529 plan for our daughter, who will go to college in a few years. Let's say 5 for the purpose of the math. At this year's price her 4 years of college tuition will cost her ~ $48k. This total expected to go up around $10k every year before she gets to college (around $2k annual tuition rise, over 5 years).

So if we paid her tuition when she went in five years, we would pay $20k, $22k, $24k, $26k, for a total of $92k. Instead we pay $50k now, and are guaranteed to not have to pay any additional tuition costs, for a savings of $42k. The tax deferment might be another $8k (spitballing).

Which means the using a 529 plan now you can send two kids to college in 5 years for the price of sending one to college in 5 years and paying for it then.

Yes, there are risks.

* They may want to go to a private school, or out of state. The money isn't lost, but you don't get the guarantee either. You just get the money applied to the tuition.

* Tuition prices may come down and stay down. They haven't yet, and it seems unlikely without major upset. They might come down over the next year, but I suspect they'll go back up.

* Universities may become free, or become extinct in their current form. With any forward-looking investment there is a risk of a true disruption that completely changes the landscape. This would be such a huge change that it's not likely to completely happen within the 9 years until she would graduate, if it happens at all.

Honestly, it doesn't matter how they paid for the college. Even if a 529 could not be used to offset taxes lottery winnings, they could just as easily gifted their grandkids that much money, tax free (federally, at least).

The only irony here is the fact that the grandparents spend a higher portion of their proceeds on education than the state (probably, every state is different), and still had plenty of money left over for vacations and other fun stuff.

The biggest selling point of state lotteries is that the money is is used "for education." Califoria is coming under fire for not giving enough of the lottery money to schools, and they only require 1/3rd of proceeds to go to education, and allow about 1/6th of the proceeds to be used for "administration costs" within the schools.

In other words, these people utilizes more of their winnings for education than the state probably did, despite using the majority of the money for non-education-related expenses. Even though, most lotteries are sold as financing for education. That's what irony looks like.

> fact that the grandparents spend a higher portion of their proceeds on education

$0 has been spent on education so far. $2m has been put into an investment account whose realized gains are tax free. You can bet people withdraw with the 10% penalty all the time to spend that money on whatever they want, not college.

The state also runs its own investment accounts, like this individual does, and spends it on many totally worthy concerns, like paying pensions that are used by beneficiaries to pay for housing, food and indeed, sometimes education, so maybe that's the more appropriate comparison.

> they could just as easily gifted their grandkids that much money, tax free (federally, at least)

I don't think that's true, and your information appears to be the result of doing Google searches on SEO'd tax and accounting law partnership pages.

It seems like there a lot of misunderstandings anyway about how this stuff works. Can they reduce the taxes they would otherwise pay on the lotto income? Of course, creating 14 529 plans (as opposed to say, 1, or 0) is an important part of that strategy. Then there are so called experts working in finance chiming in, which if I could point to anyone being a complete waste of money for baby boomers in the last 20 years, it’s CFAs collecting 1.0-1.5% AUM every year on top of mutual fund fees that all underperformed low cost indices. The kind of assholes who, in the absence of any normative measure, have finally settled on justifying their high fees as “not answering the phone when you want to panic sell.”

It’s infuriating, honestly, the lack of any sophistication whatsoever and the trust put into total leeches like CFAs. And here we are, getting lost in the tax details, from people who would balk at paying a retainer for an ongoing professional opinion instead of a management fee - when those opinions could save them literally millions over the lifetime of a windfall like this - and wind up on SEO’d advice pages googling stuff themselves instead.

A bunch of temporary embarrassed billionaires Googling, shitting on how the state spends money, voting in tax cuts for people much richer than them. I don’t have expertise either, I’m not a lawyer or an accountant ,but consider paying one the pathetically small fee it would cost to get an answer to these questions that make sense for you and your situation.

> $2m has been put into an investment account whose realized gains are tax free. You can bet people withdraw with the 10% penalty all the time to spend that money on whatever they want, not college.

The gains are tax-free iff spent on qualified expenses.

Non-qualified distributions from a 529 pay ordinary income taxes on the realized gains on top of the 10% penalty. As a tax avoidance scheme, this one is pretty terrible.

I worked in finance for awhile and we almost never saw 529s being withdrawn for non-education expenses. When it happened it was for financial emergencies, which presumably these people wouldn’t have.

The rest of the dispute aside, 529s really are used for education.

the federal lifetime exemption for gift taxes is >$10 million (and double that for a couple) so I think it is entirely true.
> I don't think that's true, and your information appears to be the result of doing Google searches on SEO'd tax and accounting law partnership pages.

It's absolutely true. You can give up to $15k a year to anyone. If you gift more than that amount to certain people, you have to file Form 709 with the IRS. Income taxes are due on the amounts after total lifetime gifts to a person exceed the lifetime exclusion limit, which is currently $11,700,000. If married, these numbers are doubled, as each spouse may gift individually.

But even if none of this applied, you can find a list of exclusions right on the IRS website, which states:

    Transfers Not Subject to the Gift Tax

    Four types of transfers are not subject to the gift tax. These are:

    Transfers to political organizations,

    Transfers to certain exempt organizations,

    ***Payments that qualify for the educational exclusion, and***

    Payments that qualify for the medical exclusion.
I'm not some "temporarily embarrassed millionaire" making shit up from a Google search. I have family to whom I gift money, which means I file this form every year. Congress is full of a bunch of wealthy elites looking out for their own interests. Thus, gifting money tax-free is not difficult, at all.

Also, I'm pretty left leaning. My shitting on the state for mismanagement of (and outright lies on the use of) lottery funds is because I want them to be held accountable and live up to their promise.

>> But I bet 14 full rides to college on $8MM is a greater impact on education than what the state achieves with the same amount

When I was in college, I did some pharmaceutical testing with a local company. We had three colleges in the area so it was perfect for recruiting healthy males between the ages of 18-35.

They came out with some advertising showing they paid college kids more money in six months than the state did in tuition support at all three colleges combined. It was enough to get the state's attention and got them involved in how they both could be doing more for the state's college system. I know at one point the company was donating a LOT of money to all three colleges Pharma school and hiring a lot of their students. It provided them a nice pipeline of talent.

EDIT: The company was out of North Dakota. All the stuff we tested was already FDA approved. Most of the studies were companies looking to get less expensive generic forms of those drugs into the market. Here's some of the tests I was in:

- Naproxen

- Sudafed (it was a nasal variety for decongestion)

- Diclofenac

- Zinc Acetate

- Doxycycline

“When I was in college, I did some pharmaceutical testing”

You weren’t the only one.

Why on earth is there a stock photo of a "High Class Mature Man", captioned as "Author" opening the article?
I think that's what we in the business call a "joke"
I think the funniest part is the original (stock photo listing) caption: "high class mature man"...
Probably an elaborate ploy by the subject of the photograph to generate positive AI bias for himself.
This article was written by someone who doesn't understand math or the history of people beating lotteries.

There are many lotteries that have times with an expected positive payout. The key is that the payout can't be shared. Most of the big lotteries have times like this but the chances of having to share it ensure the payout is never positive.

I love that this guy pulled this off. It's a great story.

I was reminded of the story of Mohan Srivastava[1], an MIT/Stanford-trained statistician, who found a flaw in the Ontario Lottery's "Tic-Tac-Toe" instant game. There's a great quote from Mr. Srivastava re: his morality and exploiting the flaw he found:

"People often assume that I must be some extremely moral person because I didn't take advantage of the lottery," he says. "I can assure you that that's not the case. I'd simply done the math and concluded that beating the game wasn't worth my time."

[1] https://www.wired.com/2011/01/ff-lottery/

I have a different reaction: it is not an ethical thing to do. There are lots of things people can do to get money - but this doesn't mean people should do them. Isn't the ethical thing to do to report the problem so that the system can't be gamed by others?
I consider gambling unethical, and thus all forms of cheating are the only ethical way to play such games.
Where'd you come up with this logic? It's similar to saying I find modern banking unethical, therefore its only ethical that I hack in and steal both the depositors and the corporations money.

Also why do you find gambling unethical? Do you also find poker unethical? What about trading stocks?

> Where'd you come up with this logic?

Maybe because gambling companies whole purpose in life is to rip people off, so it's fair play to do that back to them? :)

> He buys a full $8,000 in tickets

An average person will NOT do it.

Is it really a hack? I believe he increased his probability of winning chances

I don’t understand why the state would care. They take their cut off the top. If there is excess unclaimed jackpot money that accumulates week to week until expected values go positive why does that hurt them?
The house hates it when people hit them for big wins.
Most of the "houses" you reference don't have the privilege of paying you for your winnings and then taking a large percentage back as taxable income.
No, the house loves it when someone takes a big win. They have already made their money, the winnings is something they have already budgeted to pay out so it isn't even a loss to them. The big winners tend to brag about their winnings and this free advertising is worth a lot to them.
Old person here. Why is "elderly" sufficiently germane to appear in the title?
He won $26M but spent $18M to do so. Still very impressive, but not quite the impression given by the headline.

> But at this point, Jerry had won more than $26 million dollars from the state lottery. After deducting for expenses, they took in more than $8 million in profit.

A lot of gamblers ignore the "expense" column when talking about their winnings. I had a friend would would go to Reno 2-3 weekends a month and brag about winning $500 or 1000. He never really talked about the fact that on most weeks he came home with empty pockets.
Most true even with stocks
Here in NL it was the state that hacked the lottery. They did not advertise the fact that all the unsold numbers competed for the prize as well and inflated the number of tickets to ensure that this was very often the case.
That's all of a piece with the other state "hack" of advertising one "prize" and actually paying an annuity based on that amount (or the value of the annuity).
So this is basically like old black jack card counting but on a lottery. Wait till the deck is hot and then play, play, play. What a great story!
This indeed reminds me the blackjack movie 21
They didn't "hack" anything. They used math and knowledge of statistical probability.

I don't think the headline "Old man used math to win $26M" would've fared worse.

He wasn't a mathematician by trade, and the ageist term "elderly" bothers me. He was 62. That's 4 years older than I am.
How is gaming a lottery a subject for a founders handbook? That seems like over emphasis on the role of chance in starting companies and arguably the opposite of achieving market fit.
I remember one of my math professors ranting about lotteries being an "idiot tax" and that you should never play them. Seems like he should have tried gaming the lottery instead of ranting against it.
Dispensing with all the folksy prose, buy enough lottery tickets and you'll win on the lower draws.
how is this not random feel good advertisement? people always assume that when an entity momentarily loses that it was gamed, while that entity may profit in the long run from allowing to be occasionally gamed, which then after the fact spreads like wildfire and while most readers eventually give up trying to find a flaw, it did succeed in obsessing them for a prolonged amount of time that they just roll with it and go out to buy some tickets even though they didn't succeed in finding a flaw...