A retired Kellogg's worker with a knack for mathematics raked in more than \$10 million (\$13.8M) profit by gaming an obscure state lottery with his wife, family and friends.

Jerry and Marge Selbee made national headlines in 2011 after a Boston Globe article exposed how small groups of high-stakes gamblers were making massive profits every three months by buying hundreds of thousands of dollars worth of lottery tickets.

Cash WinFall, a Massachusetts State Lottery game modelled after one in the Selbee's home state of Michigan, where they first started their scheme, had a unique gimmick — when the jackpot reached \$2 million (\$2.7M), if no one picked all six numbers, the payout would "roll down" to lower-tier prizes.

Because the probability of matching all six numbers was so low, the jackpot was rarely claimed — it only happened 10 times in 769 games. Mr Selbee did the sums and quickly realised that on "roll-down weeks", the price of a \$2 ticket was, statistically, worth more than \$2.

The trick was buying enough of them. "I just multiplied it out," the 79-year-old told The Huffington Post this week. "And then I said, 'Hell, you got a positive return here.'"

After the Michigan State Lottery's Winfall game was shut down without warning in 2005, one member of Mr Selbee's gambling syndicate, GS Investment Strategies LLC, spotted the Massachusetts version and suggested they give it a go instead.

The couple soon developed a routine, driving more than 1100km in the week before a roll-down to Springfield, Massachusetts, where they would split up to spend 12-hour days printing pink lottery tickets at two small retailers, party store Billy's Beverages and diner Jerry's Place — in some cases up to \$614,000 (\$848,056) worth, or more than 300,000 tickets each.

According to The Boston Globe's calculations, anyone who bought more than \$100,000 (\$138,120) worth of Cash WinFall tickets in a roll-down week was practically guaranteed a profit.

"Cash WinFall isn't being played as a game of chance," MIT-educated statistician Mohan Srivastava told the paper at the time. "Some smart people have figured out how to get rich while everyone else funds their winnings."

Two other gambling syndicates had figured it out as well — one led by a group of MIT students, and another by a biomedical researcher at Boston University. After a roll-down week in May 2011, the three groups collected 1105 out of the 1605 of the winning Cash WinFall tickets.

"It's a niche game for a different audience,'' the lottery's executive director Paul Sternburg said at the time. "You want to bring in as many players as possible. Some people chase a huge jackpot. Others are looking at odds.''

The news caused a massive scandal and sparked an investigation by state authorities.

The Massachusetts Inspector General's report, released the following year, concluded that while the state lottery made mistakes and some regulations were broken by the groups, the high-volume betting "did not adversely affect other players' odds of having a winning ticket".

The report also found the high volume betting was "allowed and encouraged because it provided a financial benefit to the state". "Cash WinFall was a financial success for the Lottery," it concluded.

"It generated about \$US300 million in ticket sales, with nearly \$US120 million of that going to Lottery operations and the pool of funds distributed to cities and towns.

"The high-volume bettors were a financial boon to the Lottery, collectively buying roughly \$2 million in tickets for a typical roll-down drawing — 40 per cent of which the Lottery would keep to redistribute to cities and towns."

The report highlighted that the entire point of the game was to attract a "huge influx" of betting by distributing a windfall to betters whenever the jackpot reached \$2 million, so the emergence of individuals and groups buying large volumes of tickets was "legal and financially advantageous".

"As long as the Lottery announced to the public an impending \$2 million jackpot that would likely trigger a roll-down, an ordinary bettor buying a single ticket or any number of tickets was not disadvantaged by high-volume betting," it said.

"In short, no one's odds of having a winning ticket were affected by high-volume betting. Small bettors enjoyed the same odds as high-volume bettors. When the jackpot hit the roll-down threshold, Cash WinFall became a good bet for everyone, not just the big-time bettors."

The Inspector General reviewed 44 roll-downs and found only one instance during which the Lottery failed to forecast the jackpot would reach \$2 million before the next drawing, to "the detriment of ordinary bettors".

In that case, the rival MIT betting group "forced" a roll-down by buying 700,000 lottery tickets costing \$1.4 million (\$1.9M). The report said the unique structure of the game created "unprecedented enforcement challenges for the Lottery".

"The activity of Cash WinFall's high-volume bettors understandably attracted a lot of attention when it was described in the Boston Globe last year," it said. "The stories gave broad circulation to something the Lottery had known for years: Cash WinFall was different than the Lottery's other games.

"A small number of people had figured out how to profit from Cash WinFall because they realised that when the jackpot reached \$2 million, each \$2 ticket was, statistically speaking, worth more than it cost.

"They also knew that the more tickets one had, the more likely it was that one's actual results would reflect the statistical probabilities. Anyone who put these two facts together would see an obvious way to make money: sit on the sidelines while other players build the jackpot up close to \$2 million, and then jump in."

The Selbees played their last game of Cash WinFall in January 2012.

In nine years of playing the lottery — 12 times in Michigan and 43 times in Massachusetts — they had grossed nearly \$27 million (\$37.2M) and made \$7.75 million (\$10.7M) in before-tax profit, distributed among the 20 or so members of GS Investment Strategies.

"If you figured it out and you could do this, would you do it?" Mr Selbee told The Huffington Post. "I'm just asking. Would you?"