Probability and persistence

How Voltaire exploited a lottery loophole

I want to tell you a story about probability and persistence. Because while there are many ideas that work in theory, it sometimes takes a certain audacity to make them work in practice.

The story begins in 1729, with Voltaire returning to France after more than two years in exile. Despite his growing reputation as a writer and philosopher, he was struggling financially. But that would change after meeting mathematician Charles-Marie de La Condamine at a dinner.

As they spoke, the conversation turned to lotteries. To encourage citizens to buy bonds, the French government had recently launched a new lottery, with tickets tied to the value of the bonds a person held. This had sparked a flurry of interest; the monthly jackpot was 500,000 livres (around £5m in modern money).

The lottery was proving popular, but Condamine had also proved it had a flaw. He’d noticed that if someone bought enough tickets, it would be possible to engineer a lottery win. And crucially, it would be possible to ‘buy’ the prize money for much less than the value of the prize itself.

Voltaire once said, ‘No problem can withstand the assault of sustained thinking.’ In 1729, winning the French bond lottery was the problem of the day. And Condamine had hit upon a potential solution. All they needed was a way to buy enough tickets to net the top prizes.

Voltaire helped Condamine and his colleagues find investors, and with their mathematical approach, they’d end up winning for seven months in a row. Although the group weren’t breaking the law, eventually the government worked out what they were doing and closed the loophole. Still, the winnings were enough to leave the group extremely well off; it’s been estimated that Voltaire’s share was at least half a million livres.

Voltaire wouldn’t be the last to carry out a ‘brute force’ attack on a lottery. One of the most famous examples came in May 1992, with a wager that Stefan Klincewicz and his twenty-seven collaborators carried out. This time, the target was the Irish National Lottery. Like Condamine, they’d wondered how much it would cost to ‘buy’ the jackpot. They worked out they’d need around £1m to buy up every possible combination of lottery numbers; by definition, it would include the winning ticket. In most weeks, the jackpot wouldn’t be large enough to justify the outlay, but if there was a rollover – like the £1.7m jackpot in May 1992 – they could in theory buy their way to a win.

That was the theory. Turning it into reality required over a million ticket purchases – each filled out by hand – as well as a cat-and-mouse game with lottery officials who were trying to stop them. They also had to contend with bad luck; in the end they weren’t the only ones to win the jackpot that week. Still, when all the prizes were tallied up, they netted a £300,000 profit.

Just over a decade later, students at the appropriately named ‘Random Hall’ at MIT would attempt a similarly ambitious effort. They focused on the WinFall lottery; during a rollover week, there could be $2.30 up for grabs for every $2 sold.

I think there is a valuable lesson about the audacity of effort in stories like these. It’s a lesson about the curiosity to wonder whether the odds are really that stacked against the player. And the refusal to accept common assumptions about the possibility of success. And the ambition to see a mathematical opportunity and turn it into a reality, no matter how implausible that reality might seem to most.