A game with a windfall for a knowing few

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.