The paper's reporting revealed that two groups were dominating Cash Winfall: the Selbee gang from Evart, Michigan, and their competition, a syndicate led by math majors from MIT, the Massachusetts Institute of Technology. These were kids young enough to be the Selbees' grandchildren.
Incredibly, the MIT group bet between $17 and $18 million on Cash Winfall over a seven-year period, earning at least $3.5 million in profits. Almost the exact same rate of return as the Selbees.
A nice illustration of the fact that there is only one mathematics, and it's equally available to everyone!
Based on the numbers alone, that's about a 20% return for the MIT group, for an annualized return (not considering compound interest) of less than 3% per year. Does this suggest that those trying to game the lottery should just turn to investing in the market? It's amusing to see that the market, which is less structured in probability and more volatile, outperforms the lottery in this aspect.
Um, needing millions to risk on this means it isn't "available to everyone".
And yes, it is a risk, even if your mask is solid. There's always the risk that the lottery commission could say "oh, come on, the terms and conditions prohibit this kind of thing", leading to a protracted legal battle.
To all the folks saying, "how did the State not know the odds?", a lot of gambling games come out without anyone running the odds. A great example is blackjack switch [0]. The game was invented by an ex-gambler and he never really knew the odds of the game. He just convinced some casinos to try it and would advertise what their average take was. Because most people are bad at math and wouldn't play well, it was always bigger than the actual house advantage anyway.
It was only years later that someone finally ran the numbers and figured out the actual house advantage of the game [1], but no one cared because everyone who had a table was making money on it. Even with regular blackjack, the casinos always make way more than the statistical house advantage because people play poorly.
It was probably the same deal here. The State didn't care what they actual odds were, they just cared that they were making money on it.
I work in the gambling industry and live in au. From my perspective this is super strange. By law vendors have to publish the odd (and on some games the EV).
I think these people just didn't read the article. Given the state made money, it knew what the odds were. It seemed the only reason there was an investigation was to see the real world outcome of how the game was setup. What may be more remarkable is that the state didn't have the analytics to notice this trend before-hand.
The title is misleading. There was no loop-hole. There was simply a structure of the game and the people in the article were able to exploit that structure. They were playing the same rules as everyone else. Buy tickets. They just figured out the right time and the right volume for buying tickets.
I don't know how the lottery works, but I imagine he also got a bit lucky. Apparently there wasn't enough people who caught on to the trick to significantly put a dent in his game. He was also lucky that the game wasn't popular enough to prevent triggering the roll-downs. Playing just 7 times a year even over the course of 7 years isn't a great sample size to account for long term variance. I wonder if there was a chance he could have lost money on some plays.
The original Mass gaming commission report is floating around out there, if anyone is looking for additional reading on this subject,
though it is of limited interest, outside of a select few MIT students and a couple from Michigan.
I wish lotteries handed out many $1M prizes instead of giving $250M to one person. People understand what to do with $1M (I think) but most people are ruined by $250M.
Everywhere, people say they prefer lotteries where there are more prizes with smaller wins, instead of one winner with huge jackpot. But also everywhere, their actual bahaviour is that when there is one big jackpot, they bet more.
And those who arrange lotteries do know their business.
That actually sounds like a good idea. Though there is the old saying "the lottery is just a tax on the poor".
My aunt actually won 2 million back in 2007. She had just divorced my uncle (so I guess she is my ex-aunt) and bought a ticket and used the birthdays of me and a few others as the numbers. She was smart in that she chose to set up a trust fund with yearly pay outs instead of a lump sum. She told her sister that she was going to give her a million, but then after realizing that the tax was going to be around a million, she then changed her mind.
She then bought a not too fancy house on the beach for probably too much money (this was in 2007 after all). Then bought a non running yacht for $40k and a new car. Her first pay out check for the year was spent in a matter of weeks and she still had monthly payments on the new toys so she couldn't quit work either. Then she realized that the house payments were for 30 years, yet her pay out plan was only for 25 years and it would not be easy to make payments those last 5 years without more refinancing (she is still trying to figure that one out).
She got scammed many times on house repairs. When she first moved in, for what ever reason she said she needed to get the windows replaced. She paid a local contractor $9k to replace the windows. He showed up with a trailer full of windows and unloaded them all (and I guess that is when she paid him). He said he'd be back later in the week to do the install. Months went by with no contact so she found another local laborer to install them. But he quickly realized that all the windows were the wrong size and basically just junk left over from other jobs.
The $40k yacht never ran. Spent several years paying people to work on it, no telling how much. Then she finally sold it for $20k.
Then a couple of years ago, a hurricane hit the coast. Her house stood, but windows were blown out and the house got completely soaked inside. It was gutted and rebuilt for $80k. Right before this happened, she had actually fallen in a parking lot of a pet supply store after tripping over a piece of rebar that was left over from a curb demolition. She caught herself with both hands but it tore both shoulder cuffs. I don't think lawyers even got involved. The store cut her a check for $80k. It was that $80k that she used to repair the house with. The insurance still hasn't paid her back yet. Something about they wanted every contractor preapproved or something and they reject every receipt or invoice that she sends in (still an ongoing issue).
I actually watched a video on CNBC's YouTube recently about the lottery and one thing they mentioned is that they've made the odds of winning worse to let bigger jackpots build up, so they're actually going in the opposite direction of what you'd like.
The reason they don't do that is marketing; more people play for big jackpot. I think even saying there might 250 $1 million winners this week isn't as big of an enticement.
I understand how numbers work, so I don't usually play the lottery. But I do play when the jackpot cracks $1B. Not because I expect to win, but for the thrill of playing.
That thrill is only there when the jackpot is at $1B.
When I read this kind of stories about US lotteries (and there seem to be several of this kind of stories going around), I always wonder how on earth it is possible for so many cases of failed lottery rule design to exist in the first place, and for those clear failures to persist for so long.
Did no one notice that the lottery always lost huge sums of money during the Rolldown draws, while it gained money on normal draws (as it should always be the case)? No one noticed that certain convenience stores suddenly sold hundreds of thousands worth of tickets in these draws, while most other stores sold a normal amount?
Irish Lottery, 1992, brute force - you could purchase all ~2M combinations for < IR£1M . The company played dirty when they realised what was happening, then later changed the game when they'd finished the forehead slapping:
https://en.wikipedia.org/wiki/National_Lottery_%28Ireland%29...
There is a story similar to the dollar coin gig to earn reward miles. A long time ago when plastic gift cards were first a thing, stores didn't have a way to update the balance. The scheme would be to buy a $100 gift card from Walmart using your credit card (getting the miles). You would then use the gift card to buy a $0.35 pack of gum. Since the store couldn't update the balance, they would give you cash as change. You could then just deposit the change to your bank and pay off the credit card. Rinse, repeat.
So for $0.35, you could get $100 in equivalent reward miles. Now stores have changed, they can now update balances on the card and therefore won't issue cash as change.
Look up Joan Ginther - ex-Stanford statistician and she won scratchcard lotteries multiple times (I seem to recall by arbing non-uniform geographical distribution of winning cards). Unfortunately I can't find a technically satisfying article and don't have ability to find one right now...
Remember that you can look at a lot of data on the US like this and come up with seemingly shocking figures, simply because of the huge population of the USA and their higher than average disposable income. I bet if you looked at other things like total amount spent on other optional/nonessential items - chewing gum or fabric softener, for example - you'd end up with a dollar value in excess of what many governments spend :-)
It's very common for people who win small prizes to 'reinvest' their winnings though. Someone who spends $5 and wins $25 might then just buy $25 of tickets with that win. If they're playing online that money never really exists - it's just an account balance in a database going up and down.
I highly recommend the book; it is a popular mathematics book, written by a real mathematician, discussing some real mathematics, with an engaging style.
I love that this guy, who is probably, what, 80? 81? pulled off this huge math heist after probably a lifetime spent doing math running a convenience store.
I bet it feels great to have that sense of, like, ease with himself in old age, having made a mark on the world in a way that hurt no one and helped a lot of people.
It might make a little more sense with the numbers. WinFall was a typical lottery game where you choose 6 of 46 numbers[1]. As with most lottery games, there is a jackpot payout but there are also payouts for matching 3, 4, and 5 of the numbers. The odds breakdown goes like this[2]:
Result | Odds
-------------
6 of 6 | 1 in 9,366,819
5 of 6 | 1 in 39028.41
4 of 6 | 1 in 800.58
3 of 6 | 1 in 47.40
2 of 6 | 1 in 6.83
The issue with WinFall is that when the jackpot increased past $5MM, the expected value of the non-jackpot winnings becomes favorable to the player. I.e. a 5-of-6 matching ticket might normally yield $4,000 but may yield >$20,000 for a "Roll-down" game. So if you go out and buy 200,000 tickets for the roll-down game (assuming all tickets are different and numbers are selected at random), you should expect to have 5 5-of-6 tickets, 250 4-of-6 tickets, 4,219 3-of-6 tickets, and 29,283 2-of-6 tickets. The combined winnings of all of those tickets makes it profitable.
If nobody wins the big jackpot ("guess all the numbers") for some time, parts of it are given to the smaller winners ("guess a few of the numbers"). In this case, which happened once in a while, it became more likely that you'll win more than you have bet. Usually this means you'll win some $50; they have bet many, many times, and won $50 times many.
Doesn't work any more, rules have changed so this way of winning was removed.
The jackpot grows off of people losing money. Once people have lost enough money ($5M), the chances of winning the money with a single ticket are raised, however you can no longer win the whole $5M with a single ticket - the money is now distributed over a larger pool of tickets.
After that it becomes a good bet, because you can bet smaller amounts, but still win more than you put in initially - you're profiting off of people who lost money before you.
Even weirder is the statement that the State that organized the lottery made more money thanks to them buying massive amount of tickets ( or maybe it was the publicity around the first newspaper article that triggered more interest, and so more participant in general ?)
* Expected value of the lottery tickets is normally negative. (You pay $1, you expect on average to get back less than $1).
* At a certain point, if the jackpot grows too large, the game switches to a new "windfall" mode where the expected value is actually _positive_ to bleed off the jackpot. (You pay $1, you expect on average to get back more than $1).
* The couple and the MIT students only played during the positive expected value times.
Overall the game still makes money for the state, it's just it has two distinct regimes, and the people playing during negative-EV essentially bankroll both the state and the positive-EV players.
I was wondering how both these syndicates and the state we winning. I think I understand now.
Lotteries are zero sum games so no extra money is being created. All ticket purchases either go to the state or the winners. So if the players have a positive return how can the state also be winning?
The players have a positive return only for the rollover round. The players have a negative return for all other rounds, where the state makes its money, and the syndicates don't play.
So the people who lost are all the suckers who played in non-rollover rounds.
Every decade or so some "lottery loophole" like this is discovered, exploited, publicized, and rules are updated to close it. I'm curious to see if another loophole resulting in a massive rework of the lottery system will ever present itself, or if the laws and rules have finally prevented that after the last few.
I really enjoyed this story! The best part is people like to think this loop hole is easy “profit”. No one pointed out the fact that they would go on 10 day benders buying/sorting/etc. to get the profit! Even this loop hole for easy profit was incredibly arduous in manual labor.
[+] [-] twic|6 years ago|reply
Incredibly, the MIT group bet between $17 and $18 million on Cash Winfall over a seven-year period, earning at least $3.5 million in profits. Almost the exact same rate of return as the Selbees.
A nice illustration of the fact that there is only one mathematics, and it's equally available to everyone!
[+] [-] bhl|6 years ago|reply
[+] [-] SilasX|6 years ago|reply
And yes, it is a risk, even if your mask is solid. There's always the risk that the lottery commission could say "oh, come on, the terms and conditions prohibit this kind of thing", leading to a protracted legal battle.
[+] [-] Hydraulix989|6 years ago|reply
[+] [-] jedberg|6 years ago|reply
It was only years later that someone finally ran the numbers and figured out the actual house advantage of the game [1], but no one cared because everyone who had a table was making money on it. Even with regular blackjack, the casinos always make way more than the statistical house advantage because people play poorly.
It was probably the same deal here. The State didn't care what they actual odds were, they just cared that they were making money on it.
[0] https://en.wikipedia.org/wiki/Blackjack_Switch
[1] https://wizardofodds.com/games/blackjack/switch/
[+] [-] qtplatypus|6 years ago|reply
[+] [-] gexla|6 years ago|reply
The title is misleading. There was no loop-hole. There was simply a structure of the game and the people in the article were able to exploit that structure. They were playing the same rules as everyone else. Buy tickets. They just figured out the right time and the right volume for buying tickets.
I don't know how the lottery works, but I imagine he also got a bit lucky. Apparently there wasn't enough people who caught on to the trick to significantly put a dent in his game. He was also lucky that the game wasn't popular enough to prevent triggering the roll-downs. Playing just 7 times a year even over the course of 7 years isn't a great sample size to account for long term variance. I wonder if there was a chance he could have lost money on some plays.
[+] [-] hnick|6 years ago|reply
[+] [-] js2|6 years ago|reply
https://news.ycombinator.com/item?id=16494280
On this submission:
http://highline.huffingtonpost.com/articles/en/lotto-winners...
[+] [-] joshstrange|6 years ago|reply
[+] [-] fragmede|6 years ago|reply
[+] [-] coldcode|6 years ago|reply
[+] [-] ptaipale|6 years ago|reply
And those who arrange lotteries do know their business.
[+] [-] esaym|6 years ago|reply
My aunt actually won 2 million back in 2007. She had just divorced my uncle (so I guess she is my ex-aunt) and bought a ticket and used the birthdays of me and a few others as the numbers. She was smart in that she chose to set up a trust fund with yearly pay outs instead of a lump sum. She told her sister that she was going to give her a million, but then after realizing that the tax was going to be around a million, she then changed her mind.
She then bought a not too fancy house on the beach for probably too much money (this was in 2007 after all). Then bought a non running yacht for $40k and a new car. Her first pay out check for the year was spent in a matter of weeks and she still had monthly payments on the new toys so she couldn't quit work either. Then she realized that the house payments were for 30 years, yet her pay out plan was only for 25 years and it would not be easy to make payments those last 5 years without more refinancing (she is still trying to figure that one out).
She got scammed many times on house repairs. When she first moved in, for what ever reason she said she needed to get the windows replaced. She paid a local contractor $9k to replace the windows. He showed up with a trailer full of windows and unloaded them all (and I guess that is when she paid him). He said he'd be back later in the week to do the install. Months went by with no contact so she found another local laborer to install them. But he quickly realized that all the windows were the wrong size and basically just junk left over from other jobs.
The $40k yacht never ran. Spent several years paying people to work on it, no telling how much. Then she finally sold it for $20k.
Then a couple of years ago, a hurricane hit the coast. Her house stood, but windows were blown out and the house got completely soaked inside. It was gutted and rebuilt for $80k. Right before this happened, she had actually fallen in a parking lot of a pet supply store after tripping over a piece of rebar that was left over from a curb demolition. She caught herself with both hands but it tore both shoulder cuffs. I don't think lawyers even got involved. The store cut her a check for $80k. It was that $80k that she used to repair the house with. The insurance still hasn't paid her back yet. Something about they wanted every contractor preapproved or something and they reject every receipt or invoice that she sends in (still an ongoing issue).
Been a wild ride...
[+] [-] droidist2|6 years ago|reply
https://www.youtube.com/watch?v=wYxYSgg6JEI&t=4m30s
[+] [-] wvenable|6 years ago|reply
[+] [-] OscarCunningham|6 years ago|reply
[+] [-] jedberg|6 years ago|reply
That thrill is only there when the jackpot is at $1B.
[+] [-] c0nfused|6 years ago|reply
[+] [-] bayareanative|6 years ago|reply
[+] [-] Slartie|6 years ago|reply
Did no one notice that the lottery always lost huge sums of money during the Rolldown draws, while it gained money on normal draws (as it should always be the case)? No one noticed that certain convenience stores suddenly sold hundreds of thousands worth of tickets in these draws, while most other stores sold a normal amount?
[+] [-] Xunxi|6 years ago|reply
You can see the entire video here.
https://www.cbsnews.com/news/jerry-and-marge-selbee-how-a-re...
[+] [-] danielecook|6 years ago|reply
See also:
https://www.businessinsider.com/us-mint-ends-the-dollar-coin...
[+] [-] mrspuratic|6 years ago|reply
[+] [-] giarc|6 years ago|reply
So for $0.35, you could get $100 in equivalent reward miles. Now stores have changed, they can now update balances on the card and therefore won't issue cash as change.
[+] [-] yomly|6 years ago|reply
[+] [-] js2|6 years ago|reply
https://www.cjr.org/united_states_project/lottery-winners-fo...
Discussion:
https://news.ycombinator.com/item?id=15262440
[+] [-] onetimemanytime|6 years ago|reply
[+] [-] smcl|6 years ago|reply
[+] [-] onion2k|6 years ago|reply
[+] [-] chrshawkes|6 years ago|reply
[+] [-] ocfnash|6 years ago|reply
I highly recommend the book; it is a popular mathematics book, written by a real mathematician, discussing some real mathematics, with an engaging style.
[+] [-] notfed|6 years ago|reply
[+] [-] mattdeboard|6 years ago|reply
I love that this guy, who is probably, what, 80? 81? pulled off this huge math heist after probably a lifetime spent doing math running a convenience store.
I bet it feels great to have that sense of, like, ease with himself in old age, having made a mark on the world in a way that hurt no one and helped a lot of people.
He stuck the landing
[+] [-] gowld|6 years ago|reply
[+] [-] treydey|6 years ago|reply
[+] [-] kickopotomus|6 years ago|reply
[1]: https://www.mass.gov/files/documents/2016/08/vv/lottery-cash...
[2]: https://en.wikipedia.org/wiki/Lottery_mathematics
[+] [-] Piskvorrr|6 years ago|reply
Doesn't work any more, rules have changed so this way of winning was removed.
[+] [-] emerongi|6 years ago|reply
After that it becomes a good bet, because you can bet smaller amounts, but still win more than you put in initially - you're profiting off of people who lost money before you.
[+] [-] bsaul|6 years ago|reply
[+] [-] losvedir|6 years ago|reply
* At a certain point, if the jackpot grows too large, the game switches to a new "windfall" mode where the expected value is actually _positive_ to bleed off the jackpot. (You pay $1, you expect on average to get back more than $1).
* The couple and the MIT students only played during the positive expected value times.
Overall the game still makes money for the state, it's just it has two distinct regimes, and the people playing during negative-EV essentially bankroll both the state and the positive-EV players.
[+] [-] martin_b|6 years ago|reply
[+] [-] seventhtiger|6 years ago|reply
Lotteries are zero sum games so no extra money is being created. All ticket purchases either go to the state or the winners. So if the players have a positive return how can the state also be winning?
The players have a positive return only for the rollover round. The players have a negative return for all other rounds, where the state makes its money, and the syndicates don't play.
So the people who lost are all the suckers who played in non-rollover rounds.
[+] [-] fewrx|6 years ago|reply
[+] [-] elamje|6 years ago|reply
[+] [-] unknown|6 years ago|reply
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[+] [-] unixhero|6 years ago|reply
[+] [-] unknown|6 years ago|reply
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[+] [-] bamurphymac1|6 years ago|reply
[+] [-] RickJWagner|6 years ago|reply