Voltaire and a mathematician found the one flaw that let a penny lottery ticket win the same jackpot as an expensive one

the problem

A government lottery gave every ticket equal odds no matter what it cost

background

what everyone would do

Buy lottery tickets the normal way, spending roughly what you expect to win back on average — the only strategy that makes sense in a lottery correctly priced so that no ticket, cheap or expensive, is worth more than what was paid for it.

what they saw

The French government had designed the lottery to help retire its own small-denomination municipal bonds, and every bond, regardless of its face value, got exactly one lottery ticket with exactly the same odds of winning the same fixed jackpot. That meant a ticket attached to a tiny, cheap bond had precisely the same shot at the prize as a ticket attached to an enormous one — so buying up the cheapest bonds in bulk bought the same winning odds per ticket as buying expensive ones, for a fraction of the price. The lottery wasn't really mispricing risk; it was mispricing which bonds deserved which odds, and nothing stopped an outsider from noticing and exploiting exactly that gap.

the move

La Condamine assembled a syndicate, with Voltaire helping recruit investors and arranging for tickets to be distributed under different names to avoid drawing attention, and the group systematically bought up the smallest available municipal bonds to acquire as many equally-weighted lottery tickets as their money could reach. The strategy won repeatedly across roughly seven months of drawings in 1729.

why it works

By systematically buying up the smallest, cheapest bonds available rather than a random assortment, La Condamine and his syndicate maximized the number of equally-weighted lottery entries they could acquire for a given amount of money, effectively buying the jackpot's odds at a wholesale discount nobody had designed the system to prevent. Because nothing in the lottery's actual rules distinguished a ticket bought this way from any other, the strategy required no fraud or rule-breaking at all — when the French finance minister eventually took them to court, the case failed precisely because they had done nothing the rules technically forbade.

the payoff

Voltaire's own indiscretion — reportedly writing mocking notes referencing La Condamine on some winning tickets — helped expose the scheme, and France's finance minister took the syndicate to court in an attempt to claw back the winnings. The case failed: the group had broken no actual rule of the lottery, and they kept their winnings, estimated at roughly half a million livres for Voltaire alone. The lottery itself was shut down in 1730, and the finance minister who brought the failed case was dismissed.

where it breaks

It only works while the flaw stays undetected or unfixed — the moment the issuer notices the same handful of cheap units keep winning disproportionately, they can close the loophole by repricing or restructuring the odds, which is exactly what happened here once Voltaire's own indiscretion drew attention to the scheme. And it requires enough capital and coordination to buy up a meaningful share of the underpriced units before anyone else notices the same gap — a flaw obvious to one sharp observer rarely stays a secret, or a monopoly, for long.

what came after

Voltaire used his winnings to help fund a literary and philosophical career largely free of financial pressure for the rest of his life, while La Condamine redirected his own fortune toward scientific expeditions, including his celebrated 1735 voyage to Peru to measure the shape of the Earth — making the lottery scheme, purely by accident of what its winners went on to do with the money, one of the more consequential mathematical arbitrages in history.

references

1. [1]Charles-Marie de La CondamineMacTutor History of Mathematics, University of St Andrews, 2021mathshistory.st-andrews.ac.uk
2. [2]How Voltaire Made a Fortune Rigging the LotteryToday I Found Out, 2013todayifoundout.com

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