The gap between a bond’s price and its lottery value
The scheme depended on a mismatch: eligibility was tied to holding government bonds, but those bonds could be bought cheaply. If the lottery assigned chances according to the bonds’ stated value rather than what buyers had actually paid for them, a participant could acquire more qualifying entries for less money than the rules’ designers may have anticipated.
That is the loophole Voltaire and a mathematician recognized. Their advantage was not a lucky guess about which number would win; it was the ability to turn a relatively small outlay into a large number of chances. The lottery’s rules made the bonds a gateway to participation, and the bond market’s low prices made that gateway unusually affordable.
Why the rules produced a windfall
A lottery meant to attract buyers could therefore reward people who understood both parts of the arrangement: how the bonds qualified them and how cheaply those bonds could be obtained. The state’s apparent shortcut—using bond ownership to determine access—created an incentive that was easy to miss if officials focused on the bonds’ formal value instead of their market price.
Voltaire reportedly collected roughly half a million francs. The episode shows how a public scheme can be exploited without anyone predicting the draw: when eligibility is based on one measure of an asset and its cost on another, the difference can become the real prize.
