Admit it, we all like to take chances, and gamble sometimes - and governments around the world have always been aware of this. The first recorded lottery slips, from the time of the 2th century BC Han Dynasty, were found in China, and they were reportedly used to finance the Great Wall. However, sometimes governments miscalculate - and that's when fortune-seeking economists come to the picture. How can the system be defeated? And who invented how to beat the system? Read below.
How lottery works
Lottery games - and essentially, every game of chance - work from the phenomenon that humans can't always reasonably estimate their chances of winning or losing - they overestimate low chances and underestimate high chances. Exploiting this, lottery organizers have long started to create games where people have to purchase a ticket which has a certain chance of winning, but the maximum payout is lower than the total income from ticket purchases.
The most basic form of this would be a raffle (a.k.a. tombola); let's say that the ticket price is P and the number of tickets sold is N, making the chances of winning P/N. In this case, the organizer has to keep the payout sum below P*N - and he has to do this in a convincing way which makes people more engaged, and fascinated with the game.
Advanced lottery schemes
Such an example would be a lottery, where players have to pick X numbers correctly out of Y - note that while the chances of every number are equal, the interaction provides an illusion of control. (Meanwhile, your chances remain the same; X choose Y., that is X!/(X-Y)!Y!)
In this case, calculating the payouts optimal for the organizer would be more difficult; he'd have to consider scenarios where not only perfect slips, but others with 1,2 etc. mistakes also have payouts. While it's still not a horribly difficult task to do, you can complicate the recipe with special payoffs, lucky numbers, double pay days... the list goes on and on, and sometimes, even organizers themselves miscalculate. And that is where economists come in.
It all began with the French...
The first documented case of a tricky individual taking the jackpot of a lottery goes back as early as 1729, and to no other than the French philosopher Voltaire and his friend, the statistician Charles Marie de la Condamine (the Frenchman who later first proved that the earth is not completely round).
Their game of choice was the French Royal Lottery, started in the same year, with the goal of financing France's ever-growing public debt - the duo's plan however quickly saw those plans demolished.
The lottery tickets were essentially a compensation fund for the owners of French government bonds - in 1727, the French state cut the interest rate of all currently purchased state equities, and consequently investors started avoiding French bonds like fire.
To correct the situation, the Deputy Finance Minister of the time, Le Pelletier-Desforts had the idea of issuing lottery tickets to be backed up with bonds; every bond owner could purchase slips at a maximum sum of 1/1000 their bond wealth. The two types of tickets, for 1000 livre and 10000 livre bonds consequently cost 1 and 10 livres; however, their chances of winning were the same, and this is what Voltaire and Condamine exploited.
The plan that almost failed
The two friends managed to purchase enough 1000 livre bonds to successfully "corner the market" of lottery tickets; however, there was only a small number of notaries and an observant notary could have quickly guessed what was going on. To avoid this, Voltaire both invited a notary to his plot and purchased the tickets over an extended period of time; since tickets were drawn every month, but tickets were identical to one another even between months, he could go on purchasing the amounts necessary without anyone noticing, and go on winning every month.
However, the whole endeavour almost failed due to Voltaire's pride. At the time, it was customary to
sign the handed in tickets with good luck phrases; Voltaire wrote things like “Here’s to the good idea of M.L.C. [Marie De La Condamine]!” and “Long live M. Pelletier-Desforts!”. In time, Desforts got suspicious and discovered the syndicate, but by this time, Voltaire and Condamine were approximately 1,000,000 livres richer - when the Minister took them to court, the royal council role in Voltaire's favor, and Desforts lost his job. Even the lottery itself had to be closed, paving the way further towards bankruptcy and the eventual Revolution.
But if readers thing that such calculation fallacies are a thing of the past, I've got good news - they are wrong. Back in 1992, a group of Australians did the same thing with the Virginia lottery, gaining a hefty sum of 25 million dollars in the process - the rules were immediately changed, with the Virginia governor saying afterwards that "I would certainly loved to have had that one little ticket that they hadn't bought [...] and that little ticket was the winning number, I could say I told y'all."
An even more recent example is that of the Massachusetts lottery game called Cash Winfall, which was successfully exploited by a combined group of maths, science professors and MIT undergrads, gaining them a profit of 8 million dollars; the scheme was only discovered in 2010, when a Boston Globe article brought the scheme to light. Since then, Cash Winfall's rules have been changed to limit the maximum amount of ticket purchases per seller - but the chances themselves remained the same.
Who knows? Could you be the next statistician turned lottery winner?