Jerry and Marge Selbee: $27 million in tickets, the $2 million roll-down, and the lottery ticket that was worth more than it cost

Three minutes

Gerald Selbee has a degree in mathematics from Western Michigan University and spent seventeen years running a convenience store in Evart, Michigan, population about 1,900, with his wife Marjorie. They sold the store in 2000. In 2003 he walked back into it and picked up a brochure for a new Michigan Lottery game called Winfall: a $1 ticket, six numbers from 49, a jackpot that had to be at least $2 million. The brochure also described the game’s gimmick. If the jackpot climbed past $5 million without a winner, the next drawing was a “roll-down”: unless someone matched all six, the jackpot was split among the people who had matched five, four or three. He told 60 Minutes it took him three minutes to see what that meant, and that his first thought was that a million other people must have seen it too.

If I played $1,100 mathematically I’d have one 4-number winner, that’s 1,000 bucks. I divided 1,100 by six instead of 57 because I did a mental quick dirty and I come up with 18. So I knew I’d have either 18 or 19 3-number winners and that’s 50 bucks each … So I got $1,100 invested and I’ve got a $1,900 return.Jerry Selbee to Jon Wertheim, 60 Minutes (2019), on the first Winfall roll-down he worked out

He tested it with his own money before telling his wife. Jason Fagone’s account has the first serious bet at $3,400 of tickets returning $6,300, then $8,000 returning $15,700; 60 Minutes rounds the first to $3,600. Then he told Marge, formed a company called GS Investment Strategies, and sold shares to family and friends at $500 each. By the spring of 2005 the club had 25 members, among them three state troopers, a factory plant manager and a bank vice-president, and had played twelve roll-downs. That May the Michigan Lottery closed Winfall, citing poor sales. A member of the club who had lived in Massachusetts emailed Jerry: that state had just launched a game called Cash WinFall. Could they play that?

He looked at it for ten minutes. A Cash WinFall ticket cost $2 instead of $1, the numbers ran 1 to 46 instead of 1 to 49, and the roll-down fired at $2 million instead of $5 million. Otherwise it was the same game. In August 2005 he drove 700 miles east.

The roll-down

Massachusetts launched Cash WinFall in September 2004 to replace Mass Millions, a game that had lost its players by going a whole year without a jackpot winner. The new game was built in-house on the Michigan model and designed to pay out 60 cents of every dollar, with drawings on Monday and Thursday nights, a minimum jackpot of $500,000, and four smaller prizes. The Inspector General’s letter gives the odds the Lottery published and the standard prizes, and then the prizes actually paid in one typical roll-down.

The roll-down formula, fixed by the Lottery in 2004: 26% of the capped jackpot to the match-fives, 47% to the match-fours, 27% to the match-threes, each tier’s share divided equally among its winning tickets and added to the standard prize. On 8 February 2010 the jackpot pool was about $2.4 million, so $633,383 ÷ 35 + $4,000 = $22,096 (calculation for this article confirms the letter’s figures to the dollar).

Read the two prize columns against the odds and the whole story is already there. At the standard prizes a $2 ticket is worth about 40 cents in cash and another 29 cents in free tickets, 37% of its price even counting a share of the minimum jackpot. On a roll-down night the same ticket, at the same odds, carries $2.14 in expected cash, $2.43 with the free tickets at face value. The Inspector General put it in one sentence: “In every roll-down drawing in the game’s history, for every $1 wagered, there was $1.15 (or usually more) sitting in the Cash WinFall prize pool.” The only question was who would collect it, and the answer is whoever could buy enough tickets for the averages to arrive.

The first three rows are the letter’s; the letter calls the result “a cash profit of 12.8 percent”, which its own table does not support ($425,640 ÷ $400,000 = 1.064), and “almost 25 percent” once the free tickets are spent on the next roll-down ($425,640 ÷ $341,434 = 1.247, which it does). The standard deviation and the 21.7% margin with free tickets at face value are calculations for this article, treating each tier’s count as Poisson. At that spread, a 200,000-ticket play that does get its roll-down still ends with less cash than it started with about 29% of the time.

900 miles, 312,000 tickets

The Selbees wanted stores that did very little lottery business, because every ordinary customer interrupted the printing. They found two in the Pioneer Valley, Billy’s Beverage in Sunderland and Jerry’s Place in South Deerfield, whose owners joined GS Investment Strategies. On 29 August 2005 they played Cash WinFall for the first time: 60,000 tickets, $120,000, a 45% profit by Jerry’s account. They put the winnings back in and raised the stake every roll-down until they could place 312,000 bets a drawing, which Jerry considered the game’s statistical sweet spot, roughly a third of them paid with free tickets from the previous play. The routine, repeated six to nine times a year for six years: drive 700 miles, print tickets at both stores from 5 a.m. to half past midnight for three days, watch the drawing, then sort the tickets by hand in a room at a Red Roof Inn, ten hours a day for ten days, and drive the losers home to a barn in Evart in plastic tubs in case the IRS ever asked. They were audited at least twice by the IRS and three times by the Massachusetts Department of Revenue. Nobody ever asked to see the tubs. There were, by Jerry’s count, 18 million losing tickets in them.

They were not alone, and they did not know it at first. In January 2005 an MIT senior named James Harvey had been comparing Powerball and Mega Millions for an independent study project, found Cash WinFall while looking for a comparison, and took a few days to reach the same conclusion. He went to Lottery headquarters in Braintree and asked for the game’s administrative bulletins; nobody could find them, but an official who knew the game confirmed his reading. For the 7 February 2005 roll-down about fifty people in his dormitory, Random Hall, put in $20 each; the pool bought 500 tickets, one of them matched four numbers for $2,364, and $1,000 became about $3,000. Harvey and Yuran Lu later incorporated as Random Strategies Investments. Over seven years the group bet between $17 and $18 million and, on the Inspector General’s floor estimate of a 20% margin, cleared at least $3.5 million. A Boston University biomedical researcher, Ying Zhang, found the same thing the same year while trying to prove to friends that the lottery was a tax on the poor; he formed the Doctor Zhang Lottery Club, bet up to $500,000 a drawing, and quit his job in 2006. The Inspector General interviewed four groups. Between them they wagered more than $40 million; the Globe’s reading of the letter put their winnings at about $48 million.

Dr Zhang told the Inspector General he priced the jackpot risk at 12% against a 15% margin by 2007 and scaled back; Jerry Selbee put the margin at 17–21% before tax. The letter’s own count: the jackpot reached $2 million 45 times, and on one of them, 10 July 2008, a ticket matched all six and there was no roll-down. The MIT group, the Michigan group and Dr Zhang each lost hundreds of thousands of dollars that night; the winner was a successor of Dr Zhang’s own club. If a syndicate had 312,000 of 1.3 million tickets it also held about a quarter of the jackpot chance itself, which softens but does not remove the risk.

There was a second kind of variance that Jerry chose on purpose. The MIT group filled in betting slips by hand from a program that spread its number sets evenly across the possible outcomes; the Selbees used the terminal’s Quic Pic to save the two slowest steps, which meant duplicates and an uneven spread. With 312,000 tickets a group should expect eight match-fives. On one drawing the Selbees had three; on another, thirteen. A Poisson count with mean 8 lands at three or fewer 4.3% of the time and at thirteen or more 6.4% of the time (calculation for this article), so neither was a sign of anything wrong. The thirteen came on 10 July 2008, the one night in the game’s history when a jackpot was hit at the cap and the match-five paid its standard $4,000.

And the margin shrank as the groups grew, for the reason the table shows: the roll-down was a fixed pool, and every extra ticket in the drawing was another claim on it. In the game’s first year fewer than 950,000 tickets were sold for a roll-down and a match-five paid up to $83,604. By 2007 the Lottery was selling 1.2 to 1.4 million tickets for nearly every one, most of them to the syndicates, and the same prize paid $19,000 to $28,000. The last twist came in August 2010, when the MIT group spent a year filling in 400,000 extra slips so that it could buy 700,000 tickets in three and a half days, push a $1.6 million jackpot over the cap by itself, and trigger a roll-down the Lottery never announced. It held seven of every eight tickets in that drawing, cashed 18 of the 21 match-fives at $30,282 and 868 of the 1,002 match-fours, and made about $700,000 on $1.4 million. The Lottery’s own 2005 risk analysis had concluded that a forced roll-down would take 83 hours at a terminal and could not be done. The Selbees learned of it afterwards, from the other side of the state.

Where the edge came from

It is worth being exact about what the Selbees and the MIT group had found, because it is rarer than it sounds. They had not found a flaw in the randomness, like Eddie Tipton’s rootkit, or a flaw in the printing, like Mohan Srivastava’s scratch tickets. The draw was fair and every ticket had the same odds, which is what the Inspector General meant by “no one’s odds of having a winning ticket were affected”. What they had found was a prize structure in which the pool for one drawing was larger than the money bet on it. The surplus had a source: every $2 ticket bought while the jackpot was small put about 32 cents toward a jackpot that, 44 times out of 45, nobody won. The roll-down handed that accumulated money to whoever was holding tickets on the night. The small players’ money arrived first; the syndicates arrived when the price of a ticket fell below its value. As the Globe put it on 31 July 2011, casual players were unwittingly subsidising the big groups, and as the Inspector General put it a year later, the Lottery had known since 2005 and welcomed it, because 40 cents of every syndicate dollar went to the Commonwealth. Cash WinFall sold about $300 million of tickets and sent nearly $120 million to the state.

That is the difference between a lottery with a cap and a casino game, and it is the reason the question “is there a Cash WinFall at the tables?” has a short answer.

A dice round pays out of the stake it was played for, by a formula that returns 99 cents of every dollar on average, at every target, on every roll, with nothing carried from one round to the next. There is no pool that fills while other people play and empties on a night you can predict. A roll-down needs a jackpot that accumulates and a rule that releases it; a provably fair engine has neither, which is precisely why its edge can be published to the hundredth of a percent and never changes sign. Nobody can do to a dice table what the Selbees did to Cash WinFall. Nobody can have it done to them, either.

Dice figures from the verified formula: each $2 bet returns $3.96 with chance 49.995%, mean −$0.02 and standard deviation $1.9999, so 200,000 bets have mean −$4,000 and standard deviation ≈ $894. The dice column is not an argument for the dice table; it is the honest shape of a game whose edge cannot flip. [How many bets before the edge shows](/LANG/blog/how-many-bets-before-the-edge-shows-priced-the-40000-rolls-that-hide-a-1-percent-house-edge/) prices the same comparison for a single player.

Aftermath

Andrea Estes of the Globe’s Spotlight team got a tip in June 2011, found Sunderland on the Lottery’s list of frequent winners, walked into Billy’s Beverage on 12 July and found Marge and the owner printing tickets with nobody else in the store. The story ran on 31 July 2011 under the headline “A game with a windfall for a knowing few”. Within two days Treasurer Steven Grossman capped any store’s Cash WinFall sales at $5,000 a day and announced the game would be phased out; in October the limit became $2,500 per terminal per drawing with free-ticket redemptions counted against it, and that was the end of the syndicates. Seven stores were suspended, Billy’s and Jerry’s for 26 days, for letting customers run the terminals and for their owners’ membership of the club, rules the Lottery wrote down for the first time six days after the suspensions. The last drawing was on 26 January 2012.

The Inspector General’s letter of 27 July 2012 found no collusion, no leaked information and no illegality, and said the Lottery had been “institutionally surprised” only once, by the MIT forced roll-down, after which it fixed its jackpot estimates. It also found the Lottery had known about the syndicates since 2005, had bent its own rules to serve them, had put second terminals into both Selbee stores in 2011, and had answered a compliance officer’s 2010 report with one reply: “How do I become a member of the club when I retire?” Grossman apologised in public for a game that “allowed syndicates to gain special opportunities that others did not have”. The Selbees’ last play was in January 2012. Fagone’s tally from their books is nearly $27 million grossed over nine years in two states and $7.75 million net before taxes, shared among the shareholders of GS Investment Strategies; 60 Minutes rounds it to $26 million and “nearly $8 million”. Paramount made a film of it in 2022.

The lesson is not that lotteries can be beaten. Cash WinFall could be beaten because a committee in 2004 wrote a cap into a game to make it exciting, and the cap turned a few drawings a year into a bet with the sign reversed. Everything else in the story, the 900-mile drives, the Red Roof Inn, the two million ovals the MIT group filled in by hand, the three match-fives when eight were due, the night in July 2008 when the jackpot went to someone else, is what it costs to collect an edge of a few percent in a game built on variance. Jerry Selbee did not beat the odds. He read them, in three minutes, and then spent nine years doing the grind that the reading implied. “The only thing I found really remarkable,” he said, “is nobody else really seemed to grasp it.”