A lot of the probability you learn in high school came about because people wanted to understand certain games of chance.
The thing described here is a good example. It sounds like there were some underpriced bonds that were also lottery coupons, and Voltaire scooped them up.
The history of people trying to beat games of chance with math is incredibly interesting.
Take Ed Thorp. He actually built a machine to measure how fast the ball was going round a roulette table, out of the very first transistors on the market. Yes, back when computers were stored in a house. If you look at the odds though, the house advantage is only slight in most casino games. A small tilt can favour the player.
Ed and a load of MIT people also went on to break Blackjack through a hole in the implementation. Turns out if you don't reshuffle often, the odds change and you can devise a system for winning.
Yet another group of MIT kids did the lottery thing again.
The rules of the lottery are a bit sparse, but it sounds like a guaranteed pool.
The lottery worked like this:
(1) If you have Hotel de Ville bonds you can participate (if not for the lottery, these were almost free since no one thought they would actually get paid).
(2) The pot of the lottery is 500,000 (money from government) + money from selling tickets.
(3) An individual can only buy 1 ticket.
(4) Each ticket is not worth the same. An individual can buy one ticket at a cost of 1/1000 of the debt you wish to be repaid on. So if you have 1,000£ of debt, you can buy 1 ticket for 1£.
(5) You get paid 0.85 * 1000 * cost of your ticket.
(6) All tickets sold are put in a wheel of "fortune" [1]. A ticket is picked, the value of the winning is subtracted from the pool. And this process continues until the pool is "in debt" (however, the last ticket is redeemed in full, so in essence it's very likely that the government would have to pay in more than 500,000). This debt does not carry forward into the next pool
So looks like Voltaire, and his mates (with help of the notaries that were asked to sell the tickets) were able to buy all the tickets available (and were even able to buy the tickets discounted!) ensuring that they would collect on >500,000 government guarantee.
This is still very confusing to me. The total amount that the bettors could gain was 500,000 (or just over). This must have been much less than the total value of the bonds, since otherwise the bonds would not have been worthless. So it's not possible for Voltaire and his friends to have made more money than they originally lost by being owners of bonds that became worthless. How did this make Voltaire rich?
(Also, the discount that the syndicate got on the tickets should be irrelevant. That money is going into the pool so they're getting it back either way.)
EDIT: Aha! Maybe the way it worked it that there was actually another rule.
(7) There are only a limited number of tickets available. Many fewer than 1000 times the number of bondholders.
Then Voltaire and his friends can profit by buying up all the tickets, since they don't hold all the bonds. Even though 500,000 was a negligible fraction of the total value of the bonds, it was a huge multiple of the value of the bonds held by Voltaire and his friends.
I don't think so. The pool value is 500,000 + sold tickets. So there's no reason for the organisers to limit the number of sold tickets. Since, as the number of tickets sold increase, the pool value increases. As the pool value increases, the number of bonds that gets paid off increases, so less debt for Hotel de ville (bondholders would be paying other bondholders).
I think the key is that no one thought Hotel de Ville bonds would get repaid, so their value would be approximately zero (or around about there). So Voltaire could buy all the bonds for cheap. Therefore, rather than there being a limit of the number of tickets available, he controls the number of tickets bought, since him (and his buddies) are the only bondholders and can buy tickets.
> So there's no reason for the organisers to limit the number of sold tickets.
But maybe they stupidly did so anyway? (Perhaps because they only knew how to draw randomly from the number of tickets that could physically fit into a large tumbler.)
> I think the key is that no one thought Hotel de Ville bonds would get repaid, so there value would be approximately zero (or around about there). So Voltaire could buy all the bonds for cheap.
That would also make sense, but it seems implausible to me that Voltaire would be able to buy up the bonds cheaply after the lottery had already been announced.
The article mentions records of the results, but unfortunately all I could find is the announcement of the 19th draw (I think the results of the 18th draw are below, but they don't show names) [1]. Looks like you were right and the number of tickets were limited to 20,000 "LE PUBLIC est averti que les Billets de la dix-neuvième Loterie de la Ville, toujours fixés au nombre/ de Vingt mille, depuis & compris le numéro 20001 jusques & compris le numéro 40000, commenceront d'être distribués le Samedi 19 Juin 1762"
This version of the story is also more in the spirit of the original article. It's not just that the government was more solvent than people thought; Voltaire is making money by cleverly exploiting a technicality in the lottery system.
The bonds had already been defaulted on, so they were valueless apart from their ability to be converted into lottery tickets. They went around and bought up most of the defaulted bonds cheaply, which they were able to do because most of the bondholders apparently didn't trust the municipal government or their lottery and were not keen to throw further good money after bad, even though the math indicated it was a winning investment.
Then they just entered the lottery as many times as they could each drawing. The total payout was the total of the purchased tickets plus the 500,000 livres overlay provided by the Government, so their expected value was strongly positive each drawing.
So I don't think there was really a flaw in the lottery at all. The Government expected to lose 500,000 livres each drawing, the only people leaving value on the floor here were the bondholders who sold their defaulted bonds to Voltaire, La Condamine and their mates rather than enter the lotteries themselves.
> (Also, the discount that the syndicate got on the tickets should be irrelevant. That money is going into the pool so they're getting it back either way.)
Voltaire doesn't want to stump up all the money up-front (while he's confident that he will win, he may not have the capital required to purchase all the tickets he wants). So his agreement with the notaries allows him to purchase more tickets than he might have been if he wasn't allowed to get the discount (think of it as leverage).
There is an interesting part in Casanova's autobiography where he is in Paris, and he is trying to sell a Lottery implementation to the governement. If I remember correctly he even meets a minister of Louis XV, but the project never really starts.
Casanova was essentially a conman always looking for new scheme to make money : he started his careers pretending having the knife of St. Peter used to cut Christ's ears, and used it as a divination tool to find buried treasure. And he later used numerology.
That gives you some ideas of who was interested in Lotteries in the XVIIIth century.
> he started his careers pretending having the knife of St. Peter which used to cut Christ's ears
Are you sure you are not confusing "the knife used to cut Christ's ears" with "the sword used to cut the ear of one of the men who came to arrest Jesus"? Because I never heard the former, and I'm under the impression that I whould have.
You are correct my memory is a bit fuzzy, and your interpretation is probably correct.
Edit : after further checking, he was pretending having the knife of st. Peter, used to cut off the high priest servant's ear in the garden of Gethsemane to prevent the arrest of Jesus. (Which makes more sense..)
10 Then Simon Peter having a sword drew it, and smote the high priest's servant, and cut off his right ear. The servant's name was Malchus.
11 Then said Jesus unto Peter, Put up thy sword into the sheath: the cup which my Father hath given me, shall I not drink it?
Historically, actually having a relic of a saint is very poorly correlated with claiming to have a relic of a saint, even when people aren't explicitly trying to con people.
We really have almost zero proof that most of the 'real' relics are legitimate. Many value the meaning more than the actual item, especially when considering the perspective of the church.
[…] France had nearly gone bankrupt. The bankers were to blame, having devised financial instruments that magicked debt away, only for it to return multiplied once it was discovered that the collateral wasn’t there. […]
In the book How Not to Be Wrong: The Power of Mathematical Thinking Paperback, Jordan Ellenberg discusses this as an example of a poorly-designed lottery where people with enough mathematical sophistication and enough financial resources could game the system:
It always surprises me when Voltaire is called a philosopher. I was also surprised when Epic Rap Battles of History picked him for their lineup of 3 western philosophers. What philosophy has he written?
My impression is that Voltaire is mostly known for him political pamphlets, propaganda, poetry, and of course his financial investments, including gaming the lottery.
During the Enlightenment, the term Les philosophes (https://en.wikipedia.org/wiki/Philosophes) basically refers to all public intellectuals who were proponents of rationalism, classical liberalism, and who engaged in political criticism, even many were not scholars on metaphysics themselves. To this day, because of their great historical influences to political philosophy in general, they are often simply called "philosophers".
The Stanford Encyclopedia of Philosophy has a good summary,
> At the center of his work was a new conception of philosophy and the philosopher that in several crucial respects influenced the modern concept of each. Yet in other ways Voltaire was not a philosopher at all in the modern sense of the term.
There's a similar modern story of a Romanian man who gamed the modern lottery by buying all possible combinations. I wonder is he was inspired by Voltaire.
The thing described here is a good example. It sounds like there were some underpriced bonds that were also lottery coupons, and Voltaire scooped them up.
The history of people trying to beat games of chance with math is incredibly interesting.
Take Ed Thorp. He actually built a machine to measure how fast the ball was going round a roulette table, out of the very first transistors on the market. Yes, back when computers were stored in a house. If you look at the odds though, the house advantage is only slight in most casino games. A small tilt can favour the player.
Ed and a load of MIT people also went on to break Blackjack through a hole in the implementation. Turns out if you don't reshuffle often, the odds change and you can devise a system for winning.
Yet another group of MIT kids did the lottery thing again.