Who They Were

Jerry Selbee was a retired Kellogg's plant manager from Evart, Michigan with a bachelor's degree in mathematics. He and his wife Marge had run a convenience store for 17 years. In 2003, Jerry noticed a brochure for Michigan WinFall at a gas station. He read the rules, did the math in his head in about five minutes, and realized the game had a structural flaw that made it profitable during specific weeks.

The Game: WinFall and Its Rolldown Feature

Michigan WinFall and Massachusetts Cash WinFall were standard pick-6 lottery games with one unusual feature: a rolldown. When the jackpot reached $5 million without a winner, instead of growing further, the entire jackpot was redistributed to lower prize tiers.

The Exact Calculation Jerry Did

How the Operation Scaled

Jerry's first investment was $3,600. He won $6,300 - a $2,700 profit. He and Marge repeated this every rolldown week. They formed GS Investment Strategies LLC and brought in 32 shareholders. At their peak, they invested $720,000 in a single rolldown week, purchasing over 312,000 tickets.

The operation was entirely manual. Jerry and Marge spent 10-12 hours filling out betting slips by hand before each rolldown. When Michigan shut down WinFall in 2005, they discovered Massachusetts had launched Cash WinFall. They began making regular trips to Massachusetts, continuing for another six years.

The Investigation

Both Michigan and Massachusetts lottery officials investigated the Selbees. The Massachusetts Inspector General launched a formal investigation in 2011 after the Boston Globe published an exposé. The investigation concluded in 2012. The official finding: the Selbees had not broken any laws. They had simply identified a mathematical feature of the game and exploited it legally. The game was shut down in January 2012, but the Selbees kept every dollar.

The Discovery

In early 2005, James Harvey - an MIT student living in Random Hall dormitory - was looking for a senior thesis topic. He came across Massachusetts Cash WinFall and began analyzing its prize structure. Within days, he had independently reached the same conclusion as Jerry Selbee: during rolldown weeks, each $2 ticket had an expected value greater than $2. Harvey visited the Massachusetts Lottery headquarters in Braintree and met with a lottery official who confirmed his analysis.

The first pool was 50 students contributing $20 each ($1,000 total). They bought 500 tickets for the February 7, 2005 rolldown. One ticket matched 4 numbers, paying $2,364. Harvey's analysis showed that buying $600,000 in tickets during a rolldown would generate a 15-20% return on investment - guaranteed.

How the Syndicate Operated

The MIT group grew from a dormitory pool into a sophisticated operation. They used spreadsheets to track purchases and winnings, divided ticket-buying duties among members, and purchased from retailers across Massachusetts. By 2010, the group was investing $300,000-$600,000 per rolldown event. They competed directly with the Selbees' GS Investment Strategies and at least two other syndicates.

By 2010, the three major syndicates combined were claiming 70-80% of all prizes during rolldown weeks. The Massachusetts Inspector General's 2012 report confirmed that lottery officials had known about the high-volume betting since at least 2005 but had taken no action.

Who He Was

Stefan Mandel was born in Romania in 1934. A self-taught mathematician and economist, he developed his lottery strategy out of desperation - living under communist rule on a monthly salary of $88, he needed money to emigrate. He spent years developing "combinatorial condensation" - an algorithm that reduced the combinations needed to guarantee a win. His first Romanian win in 1964 gave him enough to bribe officials and emigrate, first to Israel, then to Australia.

The Method: Combinatorial Condensation

Mandel's core insight: if you buy every possible combination of numbers in a lottery, you are guaranteed to win the jackpot. The question is whether the jackpot is large enough to profit after ticket costs, operational expenses, and taxes. His rule: only proceed when jackpot exceeds 3x the total cost of all combinations.

The Virginia Operation (February 15, 1992)

Mandel formed "The International Lotto Fund" in Melbourne, Australia, raising $5 million from 2,500 investors. He sent a team to Richmond, Virginia in the three days before the draw. The team fanned out across grocery stores and convenience stores, filling out hand-written betting slips. They purchased approximately 5 million of the 7,059,052 possible combinations before time ran out - and won the $27 million jackpot.

The Virginia Lottery initially questioned whether to pay out, but ultimately awarded the full $27 million. After paying investors, taxes, and operational costs, Mandel's net profit was estimated at several million dollars. After 1992, multiple countries and US states changed rules to prevent combinatorial coverage. Mandel retired to Vanuatu in the South Pacific.

Who She Was

Joan Ginther holds a PhD in Statistics from Stanford University. She grew up in Bishop, Texas (population ~3,000) but lived in Las Vegas, Nevada. Between 1993 and 2010 she won four separate Texas Lottery prizes totaling $20.4 million. Mathematicians calculated the odds of four such wins at 1 in 18 septillion - a number so large it is considered functionally impossible by chance alone. She has never publicly explained her method.

The Suspicious Patterns

The Leading Theory: Scratch-Off Distribution Analysis

Texas Lottery publishes data on remaining prizes for every active scratch-off game. A statistician with the right skills could theoretically track which stores had received shipments of tickets from print runs with unclaimed top prizes. By calculating the expected value of tickets at specific locations - based on remaining prizes, tickets sold, and print run data - it may be possible to identify stores where the probability of a winning ticket is significantly higher than average.

This theory is unproven. Ginther has never confirmed or denied it. The Texas Lottery investigated all four wins and found no evidence of fraud. All wins were paid in full. She remains the most statistically improbable lottery winner in recorded history.

The Discovery

In June 2003, Mohan Srivastava - a geological statistician in Toronto - received some scratch-off lottery tickets as a small gift. One was an Ontario Lottery tic-tac-toe game. He won $3. While waiting for files to download at his office, he started thinking about how lottery commissions design scratch-off games and control the distribution of winners.

Srivastava noticed that the visible numbers printed around the scratch-off area of the tic-tac-toe game were not truly random. They were generated by an algorithm that, as a side effect, created a detectable pattern. He developed what became known as the "singleton method" - a way to predict whether a ticket was a winner before scratching it, using only the visible numbers.

The Singleton Method - Exactly How It Worked

Why the Flaw Existed

Lottery scratch-off games must be designed so that a precise percentage of tickets are winners - say, 1 in 3 tickets wins something. The algorithm that generates the visible numbers and the hidden numbers uses the same underlying random seed. To ensure the correct win ratio, the algorithm inadvertently created a correlation between the visible numbers and the hidden outcome. Singletons clustered on winning tickets because the algorithm needed to "use up" certain numbers to create a winning combination underneath.

What He Did With the Discovery

Srivastava tested his method on 20 tickets, predicting 19 outcomes correctly before scratching. He estimated the flaw could generate about $600 per day in profit if exploited full-time. He decided not to exploit it. Instead, he mailed a letter to the Ontario Lottery and Gaming Corporation explaining the flaw and including a sequence of 20 unscratched tickets with his predictions written on the outside of each envelope.

The OLG pulled the tic-tac-toe game within days. A subsequent investigation found similar algorithmic flaws in other scratch-off games across multiple US states. The discovery triggered an industry-wide redesign of scratch-off ticket algorithms. Srivastava received no financial reward for reporting the flaw.

The Setup

Stefan Klincewicz was a Cork-based accountant and mathematician who spotted a structural flaw in the Irish National Lottery in the early 1990s. The Irish Lotto required players to pick 6 numbers from 1-36, creating 1,947,792 possible combinations. At IR£0.50 per ticket, buying every combination would cost IR£973,896 - less than IR£1 million. The jackpot at the time was IR£1.7 million, making full coverage mathematically profitable.

Klincewicz assembled a syndicate of 28 people and raised approximately IR£975,000. The plan was to purchase every possible combination before the May 30, 1992 bank holiday draw - a draw chosen specifically because the jackpot had rolled over multiple times and was unusually large.

The Operation

On Friday May 29, 1992, agents monitoring the Irish National Lottery spotted unusual purchasing activity. People were visiting out-of-the-way newsagents and post offices across Ireland, buying lottery tickets in bulk - some spending up to IR£70,000 in a single transaction. The syndicate had deployed teams across the country to purchase tickets simultaneously.

Time ran out before they could complete full coverage. The syndicate managed to purchase approximately 1,655,000 of the 1,947,792 combinations - about 85%. They won the jackpot. They also won multiple smaller prizes. After costs, the net profit was approximately IR£310,000. The Irish National Lottery subsequently changed its rules to prevent bulk purchasing.

The Wins

Richard Lustig of Orlando, Florida won seven Florida Lottery prizes between 1993 and 2010, totaling $1,052,205. His wins included a $10,000 scratch-off, a $13,696 prize, a $73,658 prize, an $842,152 jackpot, and several smaller prizes. He wrote a book called "Learn How to Increase Your Chances of Winning the Lottery" and became a media fixture, appearing on numerous TV shows to explain his method.

His Claimed Method

What Statisticians Say