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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

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.

plouffy 8y ago
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.
- OscarCunningham 8y ago
  > 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.
  - plouffy 8y ago
    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" [1] http://parismuseescollections.paris.fr/fr/musee-carnavalet/oeuvres/dix-neuvieme-loterie-de-l-hotel-de-ville-de-paris-etablie-par-arrets-du#infos-principales http://parismuseescollections.paris.fr/fr/musee-carnavalet/o...
    - OscarCunningham 8y ago
      Thanks for doing the research! 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.
plouffy 8y ago
> (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).
caf 8y ago
This thesis ( https://deepblue.lib.umich.edu/bitstream/handle/2027.42/63676/rkruckeb_1.pdf?sequence=1 https://deepblue.lib.umich.edu/bitstream/handle/2027.42/6367... ) on page 111 has some of the details. 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.

plouffy 8y ago

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.

OscarCunningham 8y ago
> 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.
- plouffy 8y ago
  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" [1] http://parismuseescollections.paris.fr/fr/musee-carnavalet/oeuvres/dix-neuvieme-loterie-de-l-hotel-de-ville-de-paris-etablie-par-arrets-du#infos-principales http://parismuseescollections.paris.fr/fr/musee-carnavalet/o...
  - OscarCunningham 8y ago
    Thanks for doing the research! 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.

plouffy 8y ago

> (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).

caf 8y ago

This thesis ( https://deepblue.lib.umich.edu/bitstream/handle/2027.42/63676/rkruckeb_1.pdf?sequence=1 https://deepblue.lib.umich.edu/bitstream/handle/2027.42/6367... ) on page 111 has some of the details. 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.