SUNDERLAND — Billy’s Beer and Wine sold exactly $47 worth of lottery tickets the day before Marjorie Selbee arrived, just another sleepy day for the liquor store in this tiny Western Massachusetts town.
But from the moment the 70-something woman from Michigan entered the store early July 12, Billy’s wasn’t sleepy anymore. Over the next three days, Selbee bought $307,000 worth of $2 tickets for a relatively obscure game called Cash WinFall, tying up the machine that spits out the pink tickets for hours at a time.
Down the road at Jerry’s Place, a coffee shop in South Deerfield, Selbee’s husband, Gerald, was also spending $307,000 on Cash WinFall. Together, the couple bought more than 300,000 tickets for a game whose biggest prize — about $2 million — has been claimed exactly once in the game’s seven-year history.
But the Selbees, who run a gambling company called GS Investment Strategies, know a secret about the Massachusetts State Lottery: For a few days about every three months, Cash WinFall may be the most reliably lucrative lottery game in the country. Because of a quirk in the rules, when the jackpot reaches roughly $2 million and no one wins, payoffs for smaller prizes swell dramatically, which statisticians say practically assures a profit to anyone who buys at least $100,000 worth of tickets.
During these brief periods — “rolldown weeks’’ in gambling parlance — a tiny group of savvy bettors, among them highly trained computer scientists from MIT and Northeastern University, virtually take over the game. Just three groups, including the Selbees, claimed 1,105 of the 1,605 winning Cash WinFall tickets statewide after the rolldown week in May, according to lottery records.
They also appear to have purchased about half the tickets, based on reports from the stores that the top gamblers frequent most.
“Cash WinFall isn’t being played as a game of chance. Some smart people have figured out how to get rich while everyone else funds their winnings,’’ said Mohan Srivastava, an MIT-educated statistician who gained fame in gambling circles when he found a flaw in a Canadian scratch ticket game that allowed him to pick the winners more than 90 percent of the time.
It is hard to say precisely how much each gambler has won because they have a year to claim prizes and the lottery does not track winning tickets of less than $600. But the Selbees have already claimed nearly $1 million in prize money this year, entirely in tickets valued at $802 to $24,821. Their final haul will undoubtedly be considerably larger.
Srivastava calculated that a gambler who bought 200,000 Cash WinFall tickets during four rolldown weeks in a year would win enough to cover the $1.6 million investment and earn a profit of $240,000 to $1.4 million — without ever winning the jackpot.
Srivistava’s calculations suggest that the top five groups and individuals playing Cash WinFall collectively win back the cost of their tickets plus $1 million to $6 million in profits each year from about 12 days of gambling. On the other 350-plus days of the year, less-sophisticated Cash WinFall players generally lose money, their losses building up the multimillion dollar pool that is ultimately paid out during the rolldowns.
The high-stakes players’ dominance of Cash WinFall is putting an uncomfortable spotlight on the state lottery, which has known about the phenomenon for years but only recently started to police the game under new state Treasurer Steven Grossman.
Cash WinFall is so lucrative to stores that sell the tickets — which get a commission equal to 5 percent of the sales — that some are tempted to break the rules to accommodate the high rollers’ needs. A Globe reporter saw Marjorie Selbee behind the counter at Billy’s, apparently operating the Cash WinFall machine in violation of a lottery rule that store employees alone can work the ticket dispenser.
Within days, the lottery suspended ticket-selling privileges at Billy’s, Jerry’s, and five other stores after agency inspectors discovered violations, such as printing out Cash WinFall tickets for bettors who were not there.
However, lottery officials stressed that stores did not tamper with the machines that generate the tickets or otherwise aid the gamblers. “It is very important to note that their actions in no way compromised the operation or integrity of the game,’’ said lottery officials in a statement. More broadly, some question why the state would sponsor a game that is vulnerable to betting tactics that funnel most of the prize money to just a few.
“It’s a private lottery for skilled people,’’ said Secretary of State William Galvin, who has been scrutinizing lottery games since he ran for treasurer 20 years ago. “The question is why?’’
But lottery officials say the game is successful, generating a respectable $11.8 million in profits in 2011 even though the agency sometimes pays out more money than it takes in during the rolldown weeks. Lottery officials say they more than offset the cost of rolldown weeks over the rest of the year.
“It’s a niche game for a different audience,’’ explained Paul Sternburg, the lottery’s executive director. “You want to bring in as many players as possible. Some people chase a huge jackpot. Others are looking at odds.’’
One thing is certain, however: The players who invest big money in Cash WinFall do not want to talk about it, refusing to discuss the game or explain the secret of their success.
Mark Fettig of Tennessee, one of the top 10 winners during the May rolldown week, urged the Globe not to write a story at all, saying “it would be immoral’’ to attract more people to Cash WinFall and potentially dilute the winnings of current players.
Yuran Lu, a 28-year-old MIT graduate who majored in electrical engineering, computer science, and math, seems far removed from the blue-collar image of a lottery player. This year’s second-leading Cash WinFall winner — his Random Strategies Investments has cashed in more than 500 winning tickets worth a total of $765,168 so far — Lu was on a five-week vacation in Europe during the rolldown week in July, so he said other members of his group had to buy tickets for him.
A native of China who moved to northern Maine as a child, Lu had a “distinguished career even by MIT standards,’’ according to the campus newspaper, with an academic record that included math, computing, and engineering contest victories while his whimsically named “Kamikaze Puppy’’ placed second in a robot competition. Lu also developed a taste for high-tech pranks, The Tech reported: He once collected more than 600 student passwords to the MIT computer system and sent them to the administration just to show them how easy it was.
The Selbees, by contrast, formerly ran a corner store in Evart, Mich., one of the few states that has offered a game similar to Cash WinFall. That game was discontinued in 2004, the same year the Selbees formed their gambling company.
The next year, the couple began making treks to Massachusetts to play Cash WinFall, according to lottery records. The couple would not speak to a reporter who visited the stores July 12 when Marjorie Selbee was upset to learn that her Cash WinFall earnings were public information.
Lu initially agreed to talk about his gambling company, formed with MIT friends last year, but he subsequently did not return phone calls. However, available information suggests he approached Cash WinFall like a research project, asking the lottery for information about the other big players last year and using a social media website in December to ask questions about how “to determine the optimal time to buy a lottery ticket.’’
And winning at Cash WinFall, it turns out, is all about timing. On one level, the game is simple: If the numbers on six randomly selected balls match the six on your ticket, you win the jackpot. The game also doles out lesser prizes for matching five balls down to as few as two (free ticket).
Since its creation in 2004, the game has not exactly caught the gambling public’s imagination: Only one person has ever won the 1-in-9.36 million odds jackpot (one of the big-money players), and sales are stagnant, accounting for only about 1 percent of lottery revenues.
But Lu, like the Selbees and a few others, focused on a feature of the game that is extremely rare in the United States, according to gambling authorities contacted by the Globe. The jackpot grows gradually over time from a low of $500,000 to a limit of $2 million to $2.5 million; when the limit is reached and no one claims the big prize, the top prize money is poured into the smaller prizes — or “rolled down’’ — raising the odds of a significant payout.
During normal weeks, picking five out of six numbers correctly will generate a $4,000 prize, but the prize rises to $20,000 to $40,000 during rolldowns, depending on how many winning tickets are cashed. Fewer winning tickets translates to larger payouts: During Cash WinFall’s first year, the prize for picking five numbers correctly once exceeded $100,000. Likewise, the prize for picking four of six numbers swells from $150 to $800 or even $1,000, while the prize for picking three numbers jumps from $5 to $26 or more.
As a result, sophisticated players do not actually want the jackpot to be paid out — unless it is going to them. The odds of winning the lower prizes are so good, that they can gradually win a fortune just by betting hundreds of thousands of dollars every rolldown week.
Two math experts contacted by the Globe stressed that it is crucial for bettors to buy enough tickets so that they minimize the risk that, by random chance, they purchased mainly losing tickets.
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.
Only once in the history of Cash WinFall did Kon’s calculations not apply. During a rolldown in 2008, Wenxu Tong, who earned a doctorate at Northeastern and now works in California, won the nearly $2.5 million jackpot, leaving no jackpot to spread among the lesser prizes.
Today, he is the general partner in a company called Tong’s Fortunelot Limited Partnership, which has cashed in the third-most winning tickets this year. A lottery agent who sells tickets to the group said Tong’s Fortunelot invested $200,000 at his store in May and won $280,000.
Of course, the other big winners are the stores that sell these huge blocs of tickets: Marjorie Selbee’s three-day Cash WinFall buying binge earned Paul Mardas, the owner of Billy’s in Sunderland, a commission of about $18,000. Yet Mardas repeatedly said “I don’t know’’ when asked about Selbee and her company, even though Selbee, declining to identify herself, sat next to him.
The owner of Jerry’s in South Deerfield, which received a similar commission for selling tickets to Selbee’s husband, also declined to talk, saying only that he had met Gerald Selbee once or twice.
“It’s all above board,’’ said Jerry Dagrosa, who turned off the Cash WinFall machine when a reporter entered, even though Gerald Selbee was waiting to place tens of thousands of dollars in bets.
On the eve of the July rolldown, lottery officials sent a letter to stores that sell large volumes of Cash WinFall tickets warning that they cannot bend betting rules to accommodate big spenders. But state inspectors still found violations at seven of the 13 stores that sell the most tickets, including clerks who processed tickets for bettors who were not present, stores that let the customer operate the Cash WinFall machine, and stores that opened during off hours solely to allow customers to buy tickets.
The lottery temporarily suspended those seven from selling tickets, and all will be barred from selling more than $5,000 worth of Cash WinFall tickets a day in the future. Of the seven stores, only Billy’s and Jerry’s remain under suspension.
Lottery officials say they have no reason to apologize for Cash WinFall, created under former treasurer Timothy Cahill after a lottery player survey showed people wanted a game that had better odds of winning.
But lottery officials left uncertain the future of Cash WinFall, which saw a sales decline of nearly 10 percent in 2011. “This is generating income for us,’’ said lottery director Sternburg, “but we’re always looking to freshen up our portfolio.’’
Matt Carroll of the Globe staff contributed to this report. Andrea Estes can be reached at email@example.com. Scott Allen can be reached at firstname.lastname@example.org.