In January 2005, James M. Harvey was about to start his final semester at the Massachusetts Institute of Technology. Looking for an interesting independent study project for his last term, he considered a project evaluating the Lottery games Powerball and MegaMillions to determine which was more advantageous from the player’s perspective. While researching Powerball and MegaMillions, he also reviewed other Lottery games for comparison. That was when he began looking at Cash WinFall and noticed its unique “roll-down” feature.
In an interview, Mr. Harvey said that it took him only a few days to determine that it was possible to make a profit playing Cash WinFall. He did research, ran calculations and talked to friends in his MIT dorm, Random Hall.
Among other things, Mr. Harvey went to Lottery headquarters in Braintree and asked for the agency’s administrative bulletins for Cash WinFall. Although no one could locate the administrative bulletins, he was able to meet with a Lottery official who was very familiar with the technical aspects of the game. That conversation bolstered Mr. Harvey’s own analysis: during a roll-down, each ticket is worth more than it costs.
Back at Random Hall, Mr. Harvey embarked on two projects: drumming up interest in a party to watch the Feb. 6 Super Bowl and organizing a betting pool to play the next Cash WinFall roll-down, which he expected to occur the next day – Feb. 7. He didn’t generate much enthusiasm for watching the New England Patriots play for the championship, but his analysis of Cash WinFall had broader appeal. About 50 people each put $20 into Mr. Harvey’s lottery pool for the Feb. 7, 2005 roll-down.
Mr. Harvey and members of the MIT group bought 500 tickets at nearby retailers. One of those tickets matched four of the six winning numbers, paying $2,364. Together with some three out of six matches, Mr. Harvey’s group had turned $1,000 into about 3,000.
When Mr. Harvey and a fellow MIT alumnus, Yuran Lu, incorporated their betting enterprise in 2010, they named it Random Strategies Investments LLC in honor of the dorm where the Cash WinFall plan was launched.
According to Mr. Harvey, word circulated on the MIT campus about Cash WinFall and others formed similar betting pools that semester, as many as six. Other than Mr. Harvey’s, none of the MIT groups seems to have lasted very long or grown very large.
The $3,000 in winnings from the Feb. 7, 2005 roll-down drawing remained invested in the pool for future roll-downs. Upon graduation, some members of the MIT group invested additional money in the pool. Mr. Harvey and his colleagues ramped up their ticket purchases as quickly as funds allowed, to the point where they could buy 300,000 tickets for each roll-down drawing.
Mr. Harvey said his calculations determined that in general buying about 300,000 tickets was the best strategy. However, he varied the number of tickets purchased for particular roll-downs based on several factors: the amount required to push the jackpot up to $2 million, estimates of how much other groups would bet, and even weather forecasts. As long as the sets of numbers were chosen so that winning combinations were well distributed across the range of possible outcomes – and as long as no one hit the jackpot – Mr. Harvey could be virtually certain he and his investors would make a profit.
Even when the MIT group had enough money to purchase 300,000 tickets for a drawing, its ticket buying was limited by other factors. One constraint was simply getting enough ticket slips filled out. Mr. Harvey developed a computer program that would generate sets of numbers that would provide an optimal distribution across the range of possible drawing results. Under Lottery rules, betting slips can’t be computer generated so the group had to fill out betting slips by hand – oval by oval – to match each set of numbers generated by Mr. Harvey’s computer program. Simply filling out the betting slips was time-consuming. However, the betting slips could be reused so that once the slips had been created, Mr. Harvey and his friends did not have to repeat that part of the operation.
Another constraint was locating stores that would handle large volume purchases. Many retail outlets balked at processing tickets on the scale that the MIT group and other high-volume bettors were seeking. Handling 10,000 tickets, including scanning in the slip with the requested numbers, could easily take several hours. Many store managers objected to having a staff member monopolized for long stretches. Although retail stores make a 5 percent commission on Lottery sales, tying up a clerk for hours at the lottery terminal could interfere with other store operations.
In addition, the MIT group, like other high-volume bettors, invariably had thousands of “free bets” to redeem from prior drawings. The store clerk is required to do twice as much work to process a free bet. First, the agent must scan the earlier ticket to redeem the free bet and then scan the betting slip. In addition, the store only gets a 1 percent commission – 2 cents – on a free bet redemption because it is considered a claimed prize, not a new sale. In Mr. Harvey’s words, “it was really a grind.”
Over time, Mr. Harvey said the group found a handful of retail Lottery agents – a Texaco station and a White Hen Pantry in Belmont, a convenience store in Back Bay across the Charles River from MIT, and a Mobil station in Amesbury – that would process the group’s large orders accurately. The MIT group used these four locations over and over again.
Other factors could also slow Random Strategies down. If the weather was humid, the ticket machines were more likely to jam. If a terminal was running low on ink, it could take several tries to redeem a winning ticket. Once, a power outage in the Belmont and Cambridge area interrupted the group’s pre-roll-down ticket buying.
Identifying the winning tickets was also time-consuming. Mr. Harvey wouldn’t describe his ticket-sorting operation in detail, saying his system was proprietary. He did reveal that he kept records showing the panels of six-number sets played in each drawing so that as soon as the numbers were announced he could quickly know how many winners the group held at each prize level. He also said he has storage boxes filled with millions of losing Cash WinFall tickets to present to auditors. Mr. Harvey said state and federal tax authorities have audited his group almost every year since they started playing Cash WinFall.
Tax compliance was also a headache for high-volume bettors. Every time Random Strategies turned in a batch of winning tickets, the Lottery generated a W-2G for every member of the group. Even small investors in the MIT group – for example, someone who won $800 over the course of a year – would get dozens of W-2Gs every year and have to spend hours accounting for their winnings on their tax returns. The hassle prompted some people to cash out and leave the investment pool, Mr. Harvey said. The tax hassle was one reason that the MIT group, which began with 40 to 50 people, dropped to a couple dozen participants in the years after graduation and ended with 10 members at the conclusion of Cash WinFall earlier this year.
For Mr. Harvey, operating the Cash WinFall investment pool was a nearly full-time occupation during the group’s seven-year participation in the game. It also involved substantial time commitments from two or three other members of the MIT group. Mr. Harvey did other engineering projects on the side when his schedule permitted, but refining the calculations, filling out betting slips, organizing ticket purchases, claiming prizes and keeping track of the group’s business records was time-consuming work.
It was also a lucrative enterprise. Mr. Harvey said the MIT group wagered between $17 million and $18 million on Cash WinFall. He declined to disclose what its profits were. The OIG estimated that the MIT group made at least $3.5 million before taxes, assuming that it had profits before taxes of a minimum of 20 percent during its seven-year participation in the game.
The rewards of his participation in Cash WinFall have not dramatically changed Mr. Harvey’s lifestyle. Mr. Harvey said that when he began playing Cash WinFall, his car was a 1995 Chevrolet Corsica which he had purchased for $500 at a government auction. As the MIT group became successful at Cash WinFall, he upgraded his ride to a high-mileage 1999 Nissan Altima.
Short version: * Massachusetts makes a lottery based on frequent small jackpots rather rare large ones. If the jackpot goes over 2 million, the partial match prizes pay out more to reset the jackpot to 500k. * Mathematicians determine that not only does this have positive expected value, but if you buy enough tickets then you are statistically guaranteed a profit as long as nobody else wins the jackpot (as opposed to huge national lotteries which sometimes have positive expected value, but you only get money if you win the whole thing). * It becomes some peoples' full-time job to play this lottery when it is profitable. * Lottery Commission knows it's the same people winning. They don't care because they get 40% of the money no matter who buys the tickets. Lottery Commission would only care if they got bad press that caused other people to stop playing the lottery. * Boston Globe publishes article and gives them bad press. * Lottery Commision kills the program, goes through full investigation, and writes report.
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On August 02 2012 18:52 Shikyo wrote: How on earth can you even win money in lottery if the company always takes their cut?
You'd need to get either a significant bonus for winning alot(need to mass buy tickets in this case I guess) or some specific combinations would have a higher chance to win(You need to play those and hope the masses don't play them in order to stay profitable).
Then again I'm not sure what the format here exactly was but lotteries should never be smart things to invest on if they're designed properly
The money comes from the people who feed the jackpot by playing the game on the non-rolldown weeks. I have absolutely no idea why anybody buys tickets for off weeks when the Lottery Commission clearly advertises that some weeks are much more profitable than others. I also agree that attempting to replicate these deeds yourself is unwise, but it does make a fascinating story.
could be wrong, but sounds like it's similar to counting cards in blackjack no?
edit:i'm meaning in respect to you have a higher chance of winning as time goes on (depending on the data) given cards dealt.
it seems very similar to me, who is a fellow math major. i don't know the equations for this but in a few classes we've gone over the card counting strategy and it seems (with repsect to the higher chance to win if no one else is winning) similar because in card counting, you have a higher chance to hit a higher "tier" card in blackjack depending upon the current count at the table.
On August 02 2012 17:30 Silidons wrote: could be wrong, but sounds like it's similar to counting cards in blackjack no?
Figuring out which lotteries are profitable is the easy part. If you read the report, the Commission would actually post on their website which ones are forecasted to "winfall." The report does list an incidence in which the Commission failed to notify of a profitable lottery, but this was a super-sneaky play by the MIT syndicate to dump lots of money into the jackpot to hit the winfall trigger suddenly.
The hard part is physically buying thousands of tickets, which seems to have taken all three groups a fair amount of time.
Anyway, I think this is super-awesome.
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On August 02 2012 17:51 Silidons wrote: i'm meaning in respect to you have a higher chance of winning as time goes on (depending on the data) given cards dealt.
it seems very similar to me, who is a fellow math major. i don't know the equations for this but in a few classes we've gone over the card counting strategy and it seems (with repsect to the higher chance to win if no one else is winning) similar because in card counting, you have a higher chance to hit a higher "tier" card in blackjack depending upon the current count at the table.
In this case, the "count" is just the lottery jackpot total, which increases by ~60% of the ticket value every time someone buys a ticket. The total only goes up and you only care about the binary condition of whether this number is over 2 million. After the jackpot goes over 2 million, the partial match payouts are buffed so that the jackpot will reset to exactly 500k for the next week's game. At this point the smart player stops playing and waits however many weeks it takes for the jackpot to go to 2 million next. It's like a roulette wheel that's weighted in your favor as Mizu said.
In blackjack counting you are looking for a dynamic measure of your odds of being dealt a high card. This number goes could go up or down each turn as cards are dealt.
On August 02 2012 17:30 Silidons wrote: could be wrong, but sounds like it's similar to counting cards in blackjack no?
There have been national lottos, in which the payout was greater than the cost of buying all the cards. There was actually some business company, who hired there people to go get employed at a gas station, just so they could get all the lottery tickets.
i'm meaning in respect to you have a higher chance of winning as time goes on (depending on the data) given cards dealt.
it seems very similar to me, who is a fellow math major. i don't know the equations for this but in a few classes we've gone over the card counting strategy and it seems (with repsect to the higher chance to win if no one else is winning) similar because in card counting, you have a higher chance to hit a higher "tier" card in blackjack depending upon the current count at the table.
Not exactly the same but there is a group in Australia known as 'Punter's Club' which use sophisticated mathematical modelling and computer programs to bet on various website for various things around the world. It is estimated that one individual has earnt $32mil AUD (approx same as USD) over the last three years.
This has been in the media in Aus recently due to betting pay-outs not being taxed and the government is wanting to claim a tax on his $32mil profit. Basically the group is run like a business.
"The court documents show that the club's turnover increased from $555 million in 2004 to $2.453 billion in 2006. It made a $66 million profit in 2006 and it is expected that these profits continued to grow in the years since." - The Age
On August 02 2012 17:51 Silidons wrote: i'm meaning in respect to you have a higher chance of winning as time goes on (depending on the data) given cards dealt.
it seems very similar to me, who is a fellow math major. i don't know the equations for this but in a few classes we've gone over the card counting strategy and it seems (with repsect to the higher chance to win if no one else is winning) similar because in card counting, you have a higher chance to hit a higher "tier" card in blackjack depending upon the current count at the table.
In this case, the "count" is just the lottery jackpot total, which increases by ~60% of the ticket value every time someone buys a ticket. The total only goes up and you only care about the binary condition of whether this number is over 2 million. After the jackpot goes over 2 million, the partial match payouts are buffed so that the jackpot will reset to exactly 500k for the next week's game. At this point the smart player stops playing and waits however many weeks it takes for the jackpot to go to 2 million next. It's like a roulette wheel that's weighted in your favor as Mizu said.
In blackjack counting you are looking for a dynamic measure of your odds of being dealt a high card. This number goes could go up or down each turn as cards are dealt.
Yes, this is something that can happen with roll-downs. Basically when the jackpot has not been won several times in a row, the expected payoff of a ticket becomes positive. From there, it is in your own interest to pool money with friends and buy as many tickets as possible, since on average you will earn more money than you will lose.
However, it seldom happens with "regular" lotteries. In France, over the past 20 years, there were only 2 occurences of this happening.
So...if you want to beat the lottery...buy 300,000 tickets per draw? :S Whilst using a number based program. Interesting. Doesn't sound like he made much money though.
On August 02 2012 18:07 Pandemona wrote: So...if you want to beat the lottery...buy 300,000 tickets per draw? :S Whilst using a number based program. Interesting. Doesn't sound like he made much money though.
Please read the OP...
This is very specific to THIS lottery, because it the jackpot is very hard to win and there are lots of roll-downs.
You expected gain on a regular lottery ticket on a regular day is between $0.55 and $0.65 for a one-dollar ticket. Therefore, if you buy 300.000 tickets, you will lose between $105.000 and $135.000.
I hate seeing this kind of news, it always give the impression to some people that you can "beat" the lottery.
On August 02 2012 18:07 Pandemona wrote: So...if you want to beat the lottery...buy 300,000 tickets per draw? :S Whilst using a number based program. Interesting. Doesn't sound like he made much money though.
I don't think you need that many tickets to be profitable, rather that's maximum number of tickets that you want to invest given the number of other players in the game. Each ticket you put into the lottery lets you take more of the jackpot that other people contributed, but by itself it only adds ~60% of its value to the jackpot (rest goes to the state), and other people's tickets will win some of that jackpot too. It's a fairly straightforward math problem to compute the marginal value of each ticket, and assume that the other big groups are roughly doing the same thing, as both the Michigan and MIT groups seem to have settled on about the same value for optimal bid sizes.
The end of the Boston Globe article gives the following estimate on minimum number of tickets needed for profitability:
Mark Kon, a professor of math and statistics at Boston University, calculated that a bettor buying even $10,000 worth of tickets would run a significant risk of losing more than they won during the July rolldown week. But someone who invested $100,000 in Cash WinFall tickets had a 72 percent chance of winning. Bettors like the Selbees, who spent at least $500,000 on the game, had almost no risk of losing money, Kon said.
I think Prof. Kon is overestimating here by using a flawed statistical assumption. I believe he's incorrectly using the standard sqrt(p*(1-p)/N) as the variance for N tickets on a p probability of match-#, which is only correct on the assumption that tickets each give an independent and identical probability distribution of winning. The "independent" part is what I take issue with. The automated number picker is presumably to prevent duplicate tickets from being picked and spread numbers evenly across the match-3/match-4/match-5 prizes. Doing this does not change the expected value of one's winnings, but it does reduce the variance. As long as you get variance low enough to where you are hitting close to the expected value number of match 5's, that should be the mathematical profitability threshold criterion. I don't know exactly how many tickets that requires buying because I can't tell how much their computer programs actually reduce the variance. Spreading numbers evenly across the partial matches is an NP-hard vertex covering problem if solved exactly, so presumably it's just a heuristic. If you read the report, it notes that the Michigan group uses QuickPicks random numbers and thus doesn't have this advantage. But the idea is that you probably still need at least tens of thousands of tickets.
Playing statistics is across the lottery or sports is not really different from day trading. HFT uses super computers, where they send and receive information a fraction of a second faster than other Everyone else. By this they are able to "cheat the system." They have earned money every money every month.
On August 02 2012 17:58 lachy89 wrote: Not exactly the same but there is a group in Australia known as 'Punter's Club' which use sophisticated mathematical modelling and computer programs to bet on various website for various things around the world. It is estimated that one individual has earnt $32mil AUD (approx same as USD) over the last three years.
This has been in the media in Aus recently due to betting pay-outs not being taxed and the government is wanting to claim a tax on his $32mil profit. Basically the group is run like a business.
"The court documents show that the club's turnover increased from $555 million in 2004 to $2.453 billion in 2006. It made a $66 million profit in 2006 and it is expected that these profits continued to grow in the years since." - The Age
The strategy in the Australian example seems more simplistic. Basically, modeling the probabilities of a horse winning, and using that information to make bets. It's also quite ridiculous that the money you make from gambling is tax-exempt, but the ATO is trying to tax these guys just because they're making too much money from gambling.
On August 02 2012 18:07 Pandemona wrote: So...if you want to beat the lottery...buy 300,000 tickets per draw? :S Whilst using a number based program. Interesting. Doesn't sound like he made much money though.
Please read the OP...
This is very specific to THIS lottery, because it the jackpot is very hard to win and there are lots of roll-downs.
You expected gain on a regular lottery ticket on a regular day is between $0.55 and $0.65 for a one-dollar ticket. Therefore, if you buy 300.000 tickets, you will lose between $105.000 and $135.000.
I hate seeing this kind of news, it always give the impression to some people that you can "beat" the lottery.
I did read the OP... I don't know what kind of lottery this one was, but i was basing on it being the same as the ones i know off, EuroMillions - UK Lottery etc. x amount of numbers - match the numbers to win.
On the profit side, he was audited yearly and in total made a profit of $3.5million, doesn't that mean he beat the lottery? The only massive problems he occured, where getting the stores to print the tickets, keeping track of the tickets, and claming the prizes?
There is actually a pretty big difference if you ask me... Day trading is a null-sum game: all money is shared between the players, and the aggregate sum of wins and losses is strictly equal to 0 (assuming no transaction costs, which are negligible). So yes, provided you are able to gain more information more quickly and make arbitrage decision at a microsecond speed, you will earn money. In that sense, one can "beat" the market.
In a lottery game, as soon as you buy a ticket, between 35 and 45% of the value of this ticket goes directly in the organizer's pocket, while the remaining amount of money is injected into the jackpot. For this reason, the aggregate sum of wins and losses of players is hugely negative in a regular setting, which is why you cannot beat a lottery (except for very rare occasions I mentioned earlier where the amount of roll-downs makes your expected value positive).
In January 2005, James M. Harvey was about to start his final semester at the Massachusetts Institute of Technology. Looking for an interesting independent study project for his last term, he considered a project evaluating the Lottery games Powerball and MegaMillions to determine which was more advantageous from the player’s perspective. While researching Powerball and MegaMillions, he also reviewed other Lottery games for comparison. That was when he began looking at Cash WinFall and noticed its unique “roll-down” feature.
Lotteries like EuroMillion and National Lotto have limited roll-down, so the same method cannot be applied to these lotteries. Overall, playing the lottery is a terrible, terrible idea if you are expecting something else than the thrill of the draw and good fun and laugh with your friends: putting 5€ on a saving account each week will make me way more money than playing the lottery on average.
On August 02 2012 18:27 Ahelvin wrote: I hate seeing this kind of news, it always give the impression to some people that you can "beat" the lottery.
As the report states, it took these groups a ton of time to buy enough tickets to make this profitable. It became at least someone's full-time jobs. The Lottery Commission estimates in the article that the Random Hall syndicate made $3.5 million over 6.5 years as a group of 10-50 people. No idea what their winnings amounted to once split between themselves and normalized to a per-hour basis, but it's clearly not mega millions for everyone.
I didn't know that roll-downs were standard procedure in France. In the US almost all lotteries will just keep boosting the jackpot until it reaches huge numbers in hopes that even more suckers, err.. customers, will be drawn to the huge number and play the game. Yes, this was just a roll-down lottery and nothing else.
edit: Sorry, apparently I don't know how a European roll-down normally works (I've never bought tickets in any lottery and don't plan to). This lottery rolls down $2,000,000 -> $500,000 instead of just the excess over the jackpot cap.