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.

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.

“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.

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.

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.

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.

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.

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.