João Freitas

The following is a story about how an accountant beat the math behind the lottery in several countries. It’s a lesson in game theory.

On Wednesday night, a Californian won the $1.08B Powerball lottery, one of the largest prizes in history. But it’s not the most improbable victory. We’re republishing this story from August 2018 about an economist who perfected the lottery:

Just after 11 PM on February 15, 1992, a janky ball machine at the Virginia State Lottery HQ spit out 6 winning numbers on live television: 8… 11… 13… 15… 19… 20.

In the coming days, officials would find out that one “person” had secured not only the $27,036,142 jackpot, but 6 second prizes, 132 third prizes, and 135k minor prizes collectively worth another $900k.

What unfolded next was the strangest, most improbable lottery tale in history — one involving thousands of international investors, dozens of complex computer systems, and a mathematical savant who’d masterminded the entire operation from the other side of the world.

This is the story of the man who “gamed” the lottery by buying every possible combination.

In the late 1960s, a young Romanian economist named Stefan Mandel was struggling to get by.

At the time, Romania was under oppressive Communist rule, a period marred by poverty, job and food shortages, and “profound misery.” Mandel’s salary of 360 lei (US $10) a month was not enough to make ends meet, and, as he later told Planet Money, he needed a way to “get some serious money, quickly.”

Many Romanians in Mandel’s predicament had, out of necessity, turned to lives of crime. But Mandel, a self-described “philosopher-mathematician,” saw another way out: The lottery.

stefan mandel

stefan mandel

Top: Stefan Mandel spent more than a decade reading mathematical theories before winning his first lottery in the 1960s; Bottom: Mandel’s lottery feats made headlines in his hometown Romanian newspaper (Via Busra; Illustrations: The Hustle)

Let’s take a step back here: What kind of idiot banks on winning the lottery? You’re literally more likely to win an Olympic gold medal, have identical quintuplets, or get crushed by a vending machine.

Well, Mandel wasn’t just any guy — he was a natural with numbers who spent every spare minute analyzing theoretical probability papers written by the 13th-century mathematician Leonardo Fibonacci. And, after years of research, he wrote a “number-picking algorithm” based on a method he dubbed “combinatorial condensation.”

“I’m a weekend mathematician, an accountant without too much education,” he later told a Romanian magazine. “But mathematics properly applied can guarantee a fortune.”

Here’s how it worked.

If a player picked 6 numbers in a 49-ball lottery, his odds of winning were 1 in 13,983,816. If he selected 15 numbers (which required purchasing 5,005 games — one for each possible combination), his odds of winning increased to 1 in 2,794. Mandel claimed that his algorithm could reduce these 5,005 combinations to just 569.

If the 6 winning numbers fell among his 15 picks, he’d be guaranteed to win at least a 2nd prize and hundreds of smaller prizes — and he’d have a 1 in 10 chance of winning the grand prize.

Mandel banded together with 4 friends, each of whom bought 228 tickets per draw.

Miraculously (and with a lot of luck), he won the first prize of 72,783 lei (about US $2k, or $16.8k adjusted for inflation). After expenses, he walked away with  enough to bribe foreign ministry officials and flee Romania for a new life — and a bigger jackpot.

Turning lottery wins into a business

After 4 years of roaming around Europe, Mandel settled in Australia and he set out to game the lottery in a different way.

In the typical lottery, a set of numbers within a certain range (say, 1-50) are randomly selected;  if yours match in any order, you win the jackpot. The chances of winning are based on the number of possible combinations of these numbers, often in the millions.

But Mandel caught on to something: In certain lottos, the jackpot would climb to an amount more than 3x the cost of buying every combination.

For example, let’s say a lottery required 6 picks of numbers between 1 and 40. This would yield 3,838,380 possible number combinations (calculator here). Now, let’s say that same lottery had a $10m jackpot. In theory, Mandel could buy a ticket for every single combination at $1 each and be guaranteed a win — and, after taxes, a decent profit.

Mandel maintained that “any high school math student could calculate the combinations.” But this method came with some major logistical setbacks. How would he get the capital? And how could he possibly fill out hundreds of thousands of tickets, number by number?

Mandel’s system was simple — but incredibly complex from a logistical standpoint (The Hustle)

Over a period of years, Mandel convinced hundreds of investors to pool their money together and create a “lotto syndicate.” He then developed a full-fledged automation system: A room full of printers and computers running on an algorithm that pre-populated tickets with every combination.

Computers revolutionized Mandel’s process. Before, he’d been limited to writing out millions of combinations by hand, where a single mistake could ruin 8 months’ worth of work; now, he could outsource the work to a machine.

Throughout the 1980s, Mandel’s syndicate would wait until a jackpot was 3x bigger than the cost of covering all possible combinations, then “move to buy” thousands of tickets. They managed to win 12 lotteries (and rake in 400k smaller prizes) across Australia, including a $1.1m haul in 1986.

“Everyone said to me: You can not, you will not succeed! ” Mandel told a Romanian newspaper at the time. “Now, the voices that have long [cast me as] a dreamer have been silenced.”

But Mandel’s system soon attracted negative attention.

His repeated wins prompted Australian lottery authorities to change the law, disallowing a single person from covering every possible combination.

So, he set his sights on much bigger feat — one that would make international headlines and boggle the minds of lottery officials around the world.

Virginia or bust

Mandel began by identifying lotteries where the jackpot had risen to at least 3x the cost of buying all possible combinations.

Ultimately, he printed out tickets for 6 US lotteries, including Massachusetts ($37m jackpot to 9m combinations), Arizona ($11m to 5.1m), and Virginia.

Virginia’s lottery offered several advantages. It was fairly new, and allowed buyers to purchase tickets in unlimited quantities and print them at home. But most importantly, its numbers only ranged from 1 to 44 (other states went as high as 54). This meant that with 6 picks, there were “only” 7,059,052 possible combinations, compared to the usual 25m+.

Top: A 1992 headline from the New York Times; Bottom: a 1992 Virginia lottery ticket (via NYT Archives)

Mandel set up an agency with a major insurance company. Under the shell corporation Pacific Financial Resources, he established a trust called the International Lotto Fund (ILF) and convinced 2,560 people to buy a 10-year whole life insurance policy, with a $4k annual premium. Mandel then used this money, legally, to buy each person a stake in the lottery.

In a Melbourne warehouse, he set up 30 computers and 12 laser printers, and hired 16 full-time employees to print millions of tickets pre-populated with every combination — a process that took 3 months. He then shipped the one-tonne of paper weight to a point-person in the US at a cost of $60k.

With the tickets secured in Virginia, Mandel had to wait until the jackpot hit a number that would make financial sense after taxes, overhead, and paying off investors.

A state lottery prize typically begins in the low millions and increases every time a drawing goes by with no winner. (When you see those insane $758m jackpots, it means nobody has won in quite some time.) Mandel had to anticipate when to strike, and had to hope for the best that there wouldn’t be multiple winners to dilute the pot and ruin his margins.

On February 12, 1992, the Virginia Lottery jackpot hit $15.5m. Mandel’s team on the ground was given a simple directive: Go.

And nobody — not even Mandel — could’ve anticipated the madness that would ensue.

As Mandel knew, the “buy all combinations” method of winning the lottery was more of a logistical than a financial challenge. The hard part was yet to come.

Tickets could be legally printed at home, but they still had to be taken to an authorized lotto retailer in the US, paid for (at $1 each), and processed. Waltzing into a gas station with 1.4m tickets and a truckload of cash wasn’t an option.

Mandel hired the accounting firm Lowe Lippmann to transfer $9m in investor funds to Crestar Bank in Boston, where it was cut into $10k cashier’s checks. He then lined up advance deals with Virginia-based retail chains to buy the tickets in bulk. All he needed was a point-person on the ground to orchestrate the mayhem.

For this task, Mandel turned to an esteemed associate by the name of Anithalee Alex.

Stefan mandel

Stefan mandel

Anithalee Alex, an ex-paratrooper and failed oil man, was Mandel’s unlikely man on the ground in Virginia (Illustration by The Hustle; image via ‘How’d They Do That?’, 1992)

Perennially outfitted in a gold rolex and a safari suit, Alex was a sweet talker who could “make the world seem like a bed of roses.” An ex-paratrooper turned Rolls Royce salesman turned oil prospector, he could often be seen gallivanting around his small town of Teutopolis, Illinois, in a t-shirt that read: “Please Lord, let me prove to you that winning the lottery won’t spoil me.”

When his old pal, Mandel, rang, Alex was fresh out of bankruptcy court, with $400k in debt and 16 maxed-out credit cards. He was ready for action — any action.

The job was harrowing: He was to coordinate the drop-off, payment, and processing of 1.4m lottery tickets at hundreds of stores all over Virginia.

The jackpot hit $15.5m on a Wednesday; the next draw would be on Saturday. This meant that he and his team had just 72 hours to pull it off.

A logistical nightmare

On February 12, 1992 — 3 days before the draw — Alex checked into a Holiday Inn in Norfolk, Virginia and set up a “command center” at the Koger Center, a nearby business park.

In the 88-acre “maze of buildings,” Alex met with a team of 35 couriers hired by Mandel (most of whom were certified accountants) and distributed cellophane-wrapped bundles of 10k tickets with stacks of $10k cashier’s checks.

“Think of it like an office pool,” he reportedly told the CPAs, “except a larger office pool.”

For 2 straight days, the couriers methodically descended on 125 gas stations and supermarkets. At Farm Fresh, Miller Mart, and Tinee Giant locations throughout the region, flummoxed store clerks were asked to buy and process 1.4m algorithmically-generated lotto tickets.

Stefan Mandel

Stefan Mandel

Mandel sat back in the shadows in Australia while his team orchestrated his Virginia plan (Via The Sydney Morning Herald, 1992)

“We thought they were nuts,” Rick Miller, a local gas station proprietor, later admitted. “But if someone comes up and says they want to buy 700k lottery tickets, we’re not going to chase them away.”

A representative at Farm Fresh, who sold a portion of tickets to Mandel’s team, had a more spirited take: “For someone to try to do this ticket-by-ticket is a very chancy proposition,” he said. “But that’s what lotto’s all about.”

By Saturday evening, the team was nearing completion. Then, disaster struck.

One of the chains who’d sold tickets in bulk got overwhelmed and quit in the final hours, leaving 140k tickets (700k combinations) on the table. When the deadline for entry arrived, around 1.24m of Mandel’s 1.4m tickets (6.4m of 7m combinations) had been processed. Mandel’s “fool proof” plan, which relied on securing every single possibility, was in jeopardy.

Like a regular lottery, winning the jackpot would ultimately come down to luck.

“The most incredible thing in the world”

Mandel knew that without 100% of the combinations secured, his strategy was reduced to a multi-million dollar game of chance.

He was aware of other ill-fated attempts to game a US lottery by bulk-buying tickets: In 1990, a Sacramento retiree bought 30k tickets with a diaper bag full of cash and walked away empty-handed; months later, a computer engineer known as “The Phantom” purchased 80k combinations at a Jacksonville, Florida bar and only won minor prizes.

Even if Mandel were to win, there was the possibility of multiple winners — a scenario that could significantly dilute the jackpot.

At 11:20 PM on February 15th, the numbers were drawn on live television. In a nearby warehouse, Alex and his team waited with baited breath.

Then, a victorious shout: They’d won.

Stefan Mandel

Stefan Mandel

Mandel’s victory made international headlines (via assorted US and Australian newspapers, 1992)

“When the $27m ticket came up, everybody was 6 feet off the ground,” Alex later said. “It was the most incredible thing in the world.” Purchased at a Farm Fresh in Chesapeake, the ticket had been processed in the twilight hours. Alex’s diligence had paid off.

From his home in Australia, Mandel sent out a short message to his 2,524 investors: “One of our target lotteries did jackpot to our required level,” he wrote. “We entered and won.”

The $27,036,142 jackpot (and $900k in secondary prizes) was to be paid out in 20 annual installments of $1.03m. But Virginia’s lottery czars had other plans.

What would Thomas Jefferson say?

Although completely legal under both US and Virginia state law, the Australian group’s feat was interpreted as an effort to “cheat” the traditional system.

“We might remember Thomas Jefferson’s view of a lottery,” Virginia Lottery director Ken Thorson pled to the press. “It is an opportunity for the common man to spend a small sum for the possibility of a higher prize… We never anticipated a group trying to make such a large purchase.”

Mandel was subjected to an investigation involving 14 international agencies, including the CIA, FBI, IRS, National Crime Authority, and Australian Securities Commission.

Ken Thorson, director of the Virginia Lottery, emerged as Mandel’s arch nemesis after the big win (Illustration by The Hustle; image via ‘How’d They Do That?’, 1992)

In the end, neither Mandel nor the ILF was found guilty of any wrongdoing. “I will live to be 150,” he proclaimed.  “I am not the type of person who lays down and dies because some glorified clerk doesn’t know what he’s doing.”

Meanwhile, in his home country of Australia, he became something of a folk hero: An article in People magazine described him as a kangaroo hopping out of the US with a pouch full of cash — defiant, victorious, and full of life.

And what became of the mastermind?

When the dust settled, each person who’d bought into the lottery through Mandel’s life insurance policy — small business owners, machine operators, housekeepers, and doctors — made out with around $1.4k.

Some were not pleased with this outcome. “Stefan Mandel is not only irrelevant,” a disgruntled investor later quipped. “He’s toxic.”

Meanwhile, Mandel paid himself a one-time “consultant’s fee” of $1.7m, and purportedly sold the annuity on the 20-year payout to a US insurance company for a lump sum of $14m. After overhead fees ($5.5m for the tickets, and $500k in expenses), he was left with a princely sum.

Records show that he funneled this cash into the Pacific Basin Fund, a Hong Kong-based account managed by his brother-in-law. “What we calculated to be the reality has changed,” he wrote in a 1994 letter to investors. “It may not seem such a hot investment now.”

After that, his investor updates went cold.

Stefan Mandel

Stefan Mandel

An advertisement Stefan Mandel ran in Australian newspapers to find investors for his lottery schemes (The Age, 1986-7)

Just a few years later, in 1995, Mandel declared bankruptcy. He then spent the next decade running various investment schemes — one of which earned him a 10-month jail sentence in Israel for the “alleged non-publication of a prospectus in a cooperative society.” (Mandel’s attorney said his conviction was later overturned, and that Mandel never spent a single day in prison.)

Today, Mandel spends his days at a beach house on a remote tropical island in Vanuatu, a country off the coast of Australia. He lives a quiet life and reports being “retired” from the lottery.

Anithalee Alex, his one-time associate, also dropped off the grid, and keeps a low-profile life somewhere in Illinois. “You could not have written a script as good as this,” he reminisced, years later. “This is one time real life was better than fiction.”

Though we were able to piece together the logistics of Mandel’s 20-year lottery career, he’s never revealed the minute details of his algorithm. As he told an enquiring AP reporter in 1992, “That would be like Coca-Cola revealing their recipe.”

His legacy lives on in US legislation: All 44 states that run lotteries have enacted laws preventing the profitable replication of Mandel’s strategy. In effect, this secures him a title as the first and last man to ever successfully game the lottery by buying every possible combination.

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