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I feel like mathematically, you must be right. One of the sides must be calculating their expected value wrong. For example I can offer to pay a $3 jackpot (sp

by zawerf 7y ago

I feel like mathematically, you must be right. One of the sides must be calculating their expected value wrong. For example I can offer to pay a $3 jackpot (split across winners) for a $1 game for guessing heads or tails. If more than 3 people play the game, I make money. For each player, the naive way to calculate expected return is $3 * 0.5 + $0 * 0.5 - $1 = $0.5. So the players also think they are making money. But once you account for jackpot splitting, that "expected value" isn't positive anymore. To calculate this correctly, the player (who has less information) need some way to model the distribution of the number of other players.

thaumasiotes 7y ago
> mathematically, you must be right. One of the sides must be calculating their expected value wrong. He isn't right. The state doesn't work with expected values in any way. Money comes in via ticket sales, some of it goes into the state budget, the rest goes out as lottery payouts. There is no element of chance in any of that. As you point out here and I point out elsewhere, the expected value of a ticket for the purchaser depends on the total number of tickets sold, which has been mostly elided from the discussion. In fact, it's mostly irrelevant as to this past event; at the actual ticket volumes, returns really were positive on the days in question.
- pliny 7y ago
  The way the game is presented in the article is that the low payout numbers are fixed (so a 3 match on a given rolldown game pays out $50 regardless of how many winners there are). This is consistent with the state lotteries I know. In this scenario every ticket sold causes the state to lose money, on average.
  - chrismcb 7y ago
    No. Every ticket sold causes the prize pool to lose money. The amount the state makes increases.
- zawerf 7y ago
  It's a zero sum game. If one side is positive, the other side must be negative. If jackpot isn't paid out, state gets (ticket_sales), players in total gets (-ticket_sales). If jackpot is paid out, state gets (ticket_sales - jackpot), players gets (jackpot - ticket_sales). The winning players get ((jackpot - winning_ticket_sales) / num_winners) each, the rest gets (losing_ticket_sales). Either way the expected value for an individual player is always the opposite sign of the expected value of the state. The interpretation that people might be using is that: when the tickets sold is low, it's positive expected value for the players. When sales cross the jackpot, it's positive expected value for the state. But then it becomes negative value for the player! There's no point in time where both sides are winning. (And of course that interpretation is pretty meaningless because you don't want to calculate the expected return based on the current number of tickets sold. You want the forecast of the eventual number of tickets sold. The state never really loses, even at the start because they have a pretty good idea of what this number will be in the end)
  - kd5bjo 7y ago
    It’s a zero-sum game, but there are 3 parties: the state general fund, the prize pool, and the players. By regulation, a fixed percentage of each ticket sale goes to the state general fund and the rest goes to the prize pool. Also by regulation, all the money that goes into the prize pool must eventually be paid out to players. The unpaid prize pool getting too big can cause problems for the operator: there may be accusations by the regulator that it’ll never be paid out, or it could be stolen or mismanaged leaving the operator insolvent because they no longer have the funds they are required to give to players. A rolldown event is the operator choosing to increase the payout schedule to an expected win for the purpose of reducing their liability of unpaid prizes; tickets having a positive expected value is the entire point.
    - zaroth 7y ago
      Swarming the rolldown day would just have the effect of diminishing the prize pool faster, and therefore a longer delay before the next rolldown day.
  - toyg 7y ago
soneil 7y ago
The simple correction is that the pot doesn't live in your pocket. And the lottery don't offer a fixed jackpot, they offer the contents of the pot. So a realistic correction of this, would be that for each $1 game, 50 cents goes in the pot, 50 cents goes in your pocket. If 3 people play and all 3 win, their payout is 50 cents. Obviously 50/50 odds lead to a disappointing game for the players - a bigger pot needs lower odds - but either way, the house never loses.

by zawerf 7y ago

thaumasiotes 7y ago

> mathematically, you must be right. One of the sides must be calculating their expected value wrong. He isn't right. The state doesn't work with expected values in any way. Money comes in via ticket sales, some of it goes into the state budget, the rest goes out as lottery payouts. There is no element of chance in any of that. As you point out here and I point out elsewhere, the expected value of a ticket for the purchaser depends on the total number of tickets sold, which has been mostly elided from the discussion. In fact, it's mostly irrelevant as to this past event; at the actual ticket volumes, returns really were positive on the days in question.

pliny 7y ago
The way the game is presented in the article is that the low payout numbers are fixed (so a 3 match on a given rolldown game pays out $50 regardless of how many winners there are). This is consistent with the state lotteries I know. In this scenario every ticket sold causes the state to lose money, on average.
- chrismcb 7y ago
  No. Every ticket sold causes the prize pool to lose money. The amount the state makes increases.
zawerf 7y ago
It's a zero sum game. If one side is positive, the other side must be negative. If jackpot isn't paid out, state gets (ticket_sales), players in total gets (-ticket_sales). If jackpot is paid out, state gets (ticket_sales - jackpot), players gets (jackpot - ticket_sales). The winning players get ((jackpot - winning_ticket_sales) / num_winners) each, the rest gets (losing_ticket_sales). Either way the expected value for an individual player is always the opposite sign of the expected value of the state. The interpretation that people might be using is that: when the tickets sold is low, it's positive expected value for the players. When sales cross the jackpot, it's positive expected value for the state. But then it becomes negative value for the player! There's no point in time where both sides are winning. (And of course that interpretation is pretty meaningless because you don't want to calculate the expected return based on the current number of tickets sold. You want the forecast of the eventual number of tickets sold. The state never really loses, even at the start because they have a pretty good idea of what this number will be in the end)
- kd5bjo 7y ago
  It’s a zero-sum game, but there are 3 parties: the state general fund, the prize pool, and the players. By regulation, a fixed percentage of each ticket sale goes to the state general fund and the rest goes to the prize pool. Also by regulation, all the money that goes into the prize pool must eventually be paid out to players. The unpaid prize pool getting too big can cause problems for the operator: there may be accusations by the regulator that it’ll never be paid out, or it could be stolen or mismanaged leaving the operator insolvent because they no longer have the funds they are required to give to players. A rolldown event is the operator choosing to increase the payout schedule to an expected win for the purpose of reducing their liability of unpaid prizes; tickets having a positive expected value is the entire point.
  - zaroth 7y ago
    Swarming the rolldown day would just have the effect of diminishing the prize pool faster, and therefore a longer delay before the next rolldown day.
- toyg 7y ago

soneil 7y ago

The simple correction is that the pot doesn't live in your pocket. And the lottery don't offer a fixed jackpot, they offer the contents of the pot. So a realistic correction of this, would be that for each $1 game, 50 cents goes in the pot, 50 cents goes in your pocket. If 3 people play and all 3 win, their payout is 50 cents. Obviously 50/50 odds lead to a disappointing game for the players - a bigger pot needs lower odds - but either way, the house never loses.