Even within a university as famously quirky as the Massachusetts Institute of Technology, Random Hall has a reputation for being a little quirky. According to a campus legend, the students who first lived there in 1968 wanted to call the dormitory “Random House” until the publisher of the same name sent them a letter to object. The individual floors also have names. One is called “Destiny”, a result of the sale of the naming rights on eBay by its insolvent residents; the winner was a man who wanted to name her after his daughter, for 36 dollars.
In 2005, another plan took shape in the corridors of Random Hall. James Harvey was about to complete his maths studies and needed a project for his final semester. In search of a topic, he began to take an interest in lotteries.
He began analyzing well-known lottery games such as Powerball and MegaMillions, but was soon fascinated by Cash WinFall, a game that was introduced in 2004 and exists only in the state of Massachusetts. The rules were simple. Players chose six numbers for each two-dollar ticket. If all six numbers in the draw matched, they won a jackpot of at least half a million dollars. If they hit some, but not all, numbers, they won a smaller sum. The lottery designed the game in such a way that out of each of each of the $2.00 was paid out as a prize, while the rest was used for local good causes.
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In many ways, WinFall was like all other lottery games. However, it had an important difference: Normally, when no one wins the jackpot in a lottery, the prize rolls over to the next draw. If there is no winning ticket next time, it rolls over again until someone finally has all the numbers right. The problem with rollovers is that winners – who are a good advertisement for a lottery – can be rare. And if for a while no smiling faces and huge cheques appear in the newspapers, people might stop playing.
The Massachusetts Lottery faced this very challenge in 2003, when its Mass Millions game was without a winner for a whole year. They decided that WinFall would avoid this unpleasant situation by sadicating the jackpot. If the prize money went up to 2 million dollars without a winner, the jackpot was “shut down” and instead divided among players who had three, four, or five numbers.
Before each draw, the lottery published its estimate for the jackpot, which was based on ticket sales from the previous draws. When the estimated jackpot reached $2 million, players knew that the money would be paid out if no one had six numbers. People soon realized that the odds of winning in a roll-down week were much better than at other times, which meant that ticket sales were always rising sharply before these draws.
When he studied the game, Harvey realized that it was easier to make money at WinFall than with other lotteries. In fact, the expected profit was sometimes positive: when a roll-down took place, at least 2.30 dollars in prize money were waiting for every 2.00 dollar bill sold.
In February 2005, Harvey and some of his MIT fellows formed a betting group. About 50 people took part in the first series of lots – and raised a total of 1,000 dollars – and tripled their money when their numbers came up. Over the next few years, playing the lottery became a full-time job for Harvey. In 2010, he and another team member founded the company. They called it Random Strategies Investments, LLC, after their old MIT accommodations.
Other syndicates also joined the action. A team consisted of biomedical researchers from Boston University. Another group was led by Gerald Selbee, a retired shopkeeper and former maths student who had previously succeeded with a similar game elsewhere. In 2003, Selbee noticed a loophole in a Michigan lottery game that included rolldowns. With a 32-strong tipping community, Selbee bought lots en masse for two years and won jackpots before the lottery was discontinued in 2005. When Selbee’s typing community heard about WinFall, they turned their attention to Massachusetts. There was a good reason for the influx of such betting teams: Cash WinFall had become the most profitable lottery in the United States.
In the summer of 2010, the WinFall jackpot again approached the payout limit. After a prize of 1.59 million dollars was not collected on August 12, the lottery estimated that the jackpot for the next draw would be 1.68 million dollars. Since a roll-down was certainly only two or three draws away, the betting syndicates began to prepare. By the end of the month, they planned to have thousands of dollars more in profits.
But the roll-down didn’t come two or even three draws later. He arrived the following week, on August 16. For some reason, there had been a huge increase in ticket sales, enough to push the total prize money to more than 2 million dollars. This flood of sales triggered an early roll-down.
The lottery officials were as surprised as anyone else: they had never sold so many lots when the estimated jackpot was so low. When WinFall was introduced, lottery officials had investigated the possibility that someone might intentionally roll the draw by buying up a large number of lots. The lottery was aware that ticket sales depended on the estimated jackpot – and on potential payouts – and didn’t want to be caught underestimating the prize money.
They calculated that a player who used the automatic lottery machines in the shops, who were spending tickets with any numbers, would be able to make 100 bets per minute. If the jackpot were less than 1.7 million dollars, the player would have to buy more than 500,000 notes to get it over the 2 million dollar limit. Since this would take well over 80 hours, the lottery did not believe that anyone would be able to type the sum above $2 million, unless the jackpot was already over $1.7 million.
The MIT group thought differently. When James Harvey started working on the lottery in 2005, he made a trip to the town of Braintree, where the lottery offices were located. He wanted to get a copy of the guidelines for the game, which specify exactly how the prize money is distributed. At that time, no one could help him. But in 2008, the lottery finally sent him the guidelines. The information was a boost for the MIT group, which had previously relied on its own calculations.
Looking at past draws, the group found that the estimate for the next win was almost always below the crucial value of 2 million dollars if the jackpot was not above 1.6 million dollars. Pushing the draw over the limit on August 16 was the result of extensive planning. In addition to waiting for a reasonable jackpot size – one that was close but less than 1.6 million dollars – the MIT group had to fill in about 700,000 tips, all by hand. “It took us about a year to adjust to it,” Harvey said later. The effort was worth it: it is estimated that they earned around 700,000 dollars this week.
Unfortunately, the gains didn’t last long. Within a year, the Boston Globe published a story about the loophole in WinFall and the betting syndicates that had benefited from it. In the summer of 2011, Gregory Sullivan, the Massachusetts inspector general, produced a detailed report on the matter. Sullivan pointed out that the actions of MIT Group and others were entirely legal, and he concluded that “no one’s chances of winning were affected by betting in large quantities.” Nevertheless, it was clear that some people made a lot of money with WinFall, and the game was gradually taken out of circulation.
Even if WinFall had not been removed, the Boston University syndicate would have told the inspector general that the game would not have been profitable for the betting agencies. More people bought tickets during the roll-down weeks, so the prices were divided into ever smaller pieces. While the risk of losing money increased, potential profits shrank. In such a competitive environment, it was crucial to gain an advantage over other teams. The MIT group did this by understanding the game better than many of its competitors: they knew the probabilities and payouts, and knew exactly how big their advantage was.
However, success in betting is not limited only by competition. There is also the not entirely unimportant question of logistics. Gerald Selbee pointed out that a group that wanted to maximize their profits during a roll-down week had to buy 312,000 bet slips, but the process of buying so many notes was not always easy. The ticket machines would jam in wet weather and run slowly when the ink became scarce. Once, a power outage got in the way of the MIT Group’s preparations. And some businesses refused to serve teams.
There was also the question of how to store and organize all the tickets purchased. The syndicates had to store millions of loss certificates in boxes to show them to tax auditors. It was also a headache to find the winning tickets. Same-year-old claims to have won around 8 million dollars since he started working on lotteries in 2003. But after a draw, he and his wife had to work 10 hours a day and examine their collection of notes to identify the winning notes.
Syndicates have long used the tactic of buying large combinations of numbers – a method known as a “brute force attack” – to beat lotteries. Simple brute force approaches do not require many calculations to perform them. The only real obstacle is buying enough lots. It is more a question of manpower than mathematics, and this reduces the exclusivity of methods. While clever roulette players only have to outwit the casino, lottery syndicates often have to compete with other teams trying to win the same jackpot.
Despite the constant competition, some typing communities have managed to make repeated – and legal – profits. Some of them are even so reliably successful that they even have investors and file tax returns. What was once sporadic efforts to beat the system has grown into an entire industry.