Lottery restricts high-level players

Grossman also said that Cash WinFall, which has seen declining sales since it was introduced in 2004, will be phased out next spring as part of the normal rotation of games.

“We want to do everything we can to make sure the integrity of the lottery is not questioned in any way, shape, or form,’’ he said, adding that restricting sales at each store will level the playing field among players.

Grossman was reacting to a Sunday Globe story that said that sophisticated gamblers had found a quirk in Cash WinFall’s rules that virtually guarantees they will make a large profit if they buy more than $100,000 worth of tickets at certain times of the year when prizes are four to 10 times larger than normal.

Those times, called “rolldown weeks,’’ take place when the Cash WinFall jackpot grows to roughly $2 million and no ticket wins the jackpot by matching six randomly chosen numbers. The jackpot money is then distributed among the secondary prize-winning tickets, increasing the payoff. For instance, the payoff for matching five numbers rises from $4,000 to a range from $17,500 to as much as $134,767, depending on how many winning tickets are sold.

Several groups - two of them led by highly trained computer scientists from MIT and Northeastern University - formed gambling companies and began pouring hundreds of thousands of dollars into Cash WinFall, a phenomenon lottery officials first noticed in 2005.

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 during rolldowns, without ever winning the jackpot, according to Mohan Srivastava, a Canadian statistician who found a flaw in a Canadian instant game that allowed him to detect winning tickets without scratching them.