In the 1990s, Stefan Mandel won the lottery again and again. He achieved this using incredibly simple mathematics. However, the logistics required to execute his approach were extraordinarily complex. Here is how it unfolded.
The odds of winning the jackpot with a single ticket depend on the total number of possible combinations and the specific rules of the game. Take EuroMillions as an example. This lottery asks you to choose five main numbers from fifty, plus two “stars” from twelve. The total number of combinations for the main numbers is 50 choose 5, which equals 2,118,760. The total number of combinations for the stars is 12 choose 2, which equals 66.
To calculate the chances of hitting the jackpot, you then multiply the two totals: 2,118,760 multiplied by 66, which comes to about 139,838,160. In other words, the approximate odds of winning the EuroMillions jackpot with a single ticket are about 1 in 139 million.
You’ll notice, however, that if you could buy more and more of these combinations, you would eventually reach a point where your odds were 139,838,160 in 139,838,160. Put another way, the math is straightforward (the concept is known as “full coverage”). The problem lies in logistics. In the 1990s, the Romanian-born Australian economist and mathematician Stefan Mandel faced that very challenge. According to The Hustle, he noticed that in some lotteries, the jackpot sometimes exceeded three times the cost of purchasing every possible combination.
Determining All Possible Combinations
To operate, Mandel first looked for lotteries that offered exceptionally large payouts. He would then determine the total number of possible number combinations in the target lottery. Remember that the formula for a combination is n! / (r!(n−r)!), where n is the total number of elements and r is the number of elements to choose. In a lottery that requires picking 6 numbers from 49, for example, n = 49 and r = 6. Using the combination formula, we get: 49! / (6! 43!) = (49 × 48 × 47 × 46 × 45 × 44) / (6 × 5 × 4 × 3 × 2 × 1) = 13,983,816. Thus, there are 13,983,816 possible combinations.
Mandel then formed groups of people or established companies to pool funds in order to buy every possible combination. This often required mobilizing a large number of investors ahead of time. His team would then print millions of tickets (something some lotteries permitted at the time), each representing a different combination. This entailed coordinating printing according to the specific rules of each lottery and the time constraints.
That wasn’t all. Mandel and his team had to physically submit all the tickets to authorized outlets before ticket sales closed. Again, this demanded intricate logistics and precise coordination. And finally, once the winning numbers were drawn, Mandel and his team had to check every ticket to determine how many of the combinations had won prizes.
Fourteen Jackpots
In the end, while Stefan Mandel came under investigation by the FBI and CIA, no wrongdoing was ever found. All told, he and his team won no fewer than fourteen lotteries across several countries, including Australia and the United States, netting millions of dollars. He later retired to a beachfront home on the tropical islands of Vanuatu.
Naturally, Mandel’s successes also prompted authorities to adjust lottery rules in many places to prevent mass-ticket purchases and to ensure fair play. Today, his exact method is therefore impossible to reproduce.
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