5 ms·

Can anyone explain the strategy like I'm 5? I'm confused by his answer.

bsaul 7y ago
Even weirder is the statement that the State that organized the lottery made more money thanks to them buying massive amount of tickets ( or maybe it was the publicity around the first newspaper article that triggered more interest, and so more participant in general ?)
- Piskvorrr 7y ago
  I understand the opposite: the State didn't lose any money, (but didn't make any money from these people winning, either); it made money from lottery as usual, but not from these people. (There's an implication that more people in general bought tickets, didn't win, and so the organizer made money from those - but it's not entirely clear.)
  - thaumasiotes 7y ago
    The state makes money from every ticket purchased. The lottery simply pays out a fixed percentage of ticket revenue. More ticket sales means more money to the state, regardless of whether those tickets, when purchased, had an expected positive or negative return.
    - pliny 7y ago
      If the ticket has an expected positive return for the buyer, then the state must be losing money.
      - progval 7y ago
        It has an expected positive return only on the days there was a Rolldown. Money came from people who played on days there wasn't one.
      - 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)
      - thaumasiotes 7y ago
        You're not thinking about this the right way. The ticket doesn't have a positive expected return as a structural feature of the lottery. It has a positive expected return conditional on the total number of tickets sold being less than a fixed value.
      - steventhedev 7y ago
        For that particular round of the game, yes. Overall? No, unless the game is very badly designed. The whole situation arises from rolling over the losses between rounds, which "sweetens" the pot for intelligent players. It's also a good way to inflate your numbers if you know that your game might get cut next year (e.g. it might be better to show turnover of 100mm and payouts of 90mm than turnover of 10mm and payouts of 8mm).
        thaumasiotes 7y ago
        > It's also a good way to inflate your numbers if you know that your game might get cut next year (e.g. it might be better to show turnover of 100mm and payouts of 90mm than turnover of 10mm and payouts of 8mm). ...wouldn't that be better under all possible circumstances? Would you rather have $10 million or $2 million?
        steventhedev 7y ago
        whooops! 100mm with 99mm payout vs 10mm and 8.5mm payout then...
      - chrismcb 7y ago
        The prize pool losses the money, not the state. This was a mechanism to keep the overall prize pool from getting too large. Of one person won the main prize, then they would get a car majority of the prize pool. Otherwise the prize pool was essentially distribute among all the players. Yes technically if enough people played, they could have spent more than the prize pool, but, if enough people played, then the chance that one person won goes up as well.
      - Piskvorrr 7y ago
        The ticket only has an expected positive value return under certain limited circumstances, not all the time (i.e. when jackpot has not been won for a time). State is not losing money in total - just moving around the distribution of prizes, but the sum total remains constant. If anyone would be losing money here, it would be a hypothetical winner of the jackpot - but as the jackpot is only redistributed when there is no such winner for some time...
      - diminoten 7y ago
        No, because the payout for the state (the amount they planned on losing) was always the same. The amount was "lost" regardless, it just depended on if it went to one big winning ticket or hundreds/thousands of smaller winning tickets.
      - eridius 7y ago
        For this to be true, every additional winning ticket purchased must result in a net loss to the state. But it doesn't, every additional winning ticket purchased is money going to the state. The losers in this case are the other people with winning tickets, because their payouts become smaller¹. ¹Well, given one assumption about how the game is run. The other assumption is that the 3- and 4-number winning tickets have a fixed payout calibrated such that this doesn't fully exhaust the pot, and in this case the "loser" for each additional winning ticket is whoever wins the full pot next time as the pot will be lower than it would otherwise have been.
        zaroth 7y ago
        I think in this case the winnings were fixed and the surge in sales in Rolldown days would cause the pot to be drawn down much more, meaning a longer delay before the next Rolldown day. So Rolldowns probably became less frequent, but otherwise the lottery made their money and everyone took home exactly the winnings they would have in that particular game.
    - deleted 7y ago
      [deleted]
  - M2Ys4U 7y ago
    Are state lottery ticket purchases taxed? That'd also bring in a chunk of change.
- jarfil 7y ago
  That is correct: since these were not usual players who abstained from playing, but rather casual players who bought extra tickets just on rolldown, while the State got a cut from every ticket sale, they were effectively pouring extra money into the lottery, increasing the State's income. Even if they re-invested their previous winnings, that would be twice (or more) that the State would get its cut from the same money, still increasing its income.
- Double_a_92 7y ago
  The money was "stolen" from the person that would have won the jackpot. The maximum jackpot was just smaller, it didn't make a difference to the lottery who actually won that money. They could say that the jackpot will be split among everyone that has exactly one number right in the next round, and still make profit.
Piskvorrr 7y ago
If nobody wins the big jackpot ("guess all the numbers") for some time, parts of it are given to the smaller winners ("guess a few of the numbers"). In this case, which happened once in a while, it became more likely that you'll win more than you have bet. Usually this means you'll win some $50; they have bet many, many times, and won $50 times many. Doesn't work any more, rules have changed so this way of winning was removed.
- tylerhou 7y ago
  But which set of tickets do you buy?
  - Piskvorrr 7y ago
    From the article, it seems that it doesn't matter, they're random. (Or were random, apparently it's over now, doesn't matter.) To make up an example: Let's say that betting $1 in some way has a 4% chance of winning, and the payout is 20x bet, so if you win on one ticket, you get $20. So, you buy a lot of tickets (say 1000), and you pay $1000. Most of them don't win anything, but 4% of them win $20; $1000 x 4% x 20 = $800; you have won some, but you have $200 less than you started with. Not a good deal. However, if nobody wins the jackpot, it is distributed amongst smaller payouts, which changes the equation: still 4% chance, but payout is now $30. Again, you pay $1000, buy 1000 tickets, most don't win anything, but the 4% that do, you get $1000 x 4% x 30 = $1200. You have $200 more than you started with. Profit! Of course, this will only work if you buy many tickets; buying one or two, you're unlikely to win anything at all. The actual numbers were different in these cases, but the general principle is the same.
    - amelius 7y ago
      That requires a lot of faith in the fairness of the particular lottery.
      - loblollyboy 7y ago
        A. Any lotto requires faith. B. Selbee didnt put all his money in initially. C. The parent comment is just explaining a concept w a hypothetical example
emerongi 7y ago
The jackpot grows off of people losing money. Once people have lost enough money ($5M), the chances of winning the money with a single ticket are raised, however you can no longer win the whole $5M with a single ticket - the money is now distributed over a larger pool of tickets. After that it becomes a good bet, because you can bet smaller amounts, but still win more than you put in initially - you're profiting off of people who lost money before you.
- chrismcb 7y ago
  Someone can always win the whole 5M. It is just that if the prize for large enough and no one win, then the amount of the small prizes increased. It was a way to keep the total payout low.
martin_b 7y ago
There is a great lecture about it from The Royal Institution https://www.youtube.com/watch?v=kZTKuMBJP7Y https://www.youtube.com/watch?v=kZTKuMBJP7Y
kickopotomus 7y ago
It might make a little more sense with the numbers. WinFall was a typical lottery game where you choose 6 of 46 numbers[1]. As with most lottery games, there is a jackpot payout but there are also payouts for matching 3, 4, and 5 of the numbers. The odds breakdown goes like this[2]: Result | Odds ------------- 6 of 6 | 1 in 9,366,819 5 of 6 | 1 in 39028.41 4 of 6 | 1 in 800.58 3 of 6 | 1 in 47.40 2 of 6 | 1 in 6.83 The issue with WinFall is that when the jackpot increased past $5MM, the expected value of the non-jackpot winnings becomes favorable to the player. I.e. a 5-of-6 matching ticket might normally yield $4,000 but may yield >$20,000 for a "Roll-down" game. So if you go out and buy 200,000 tickets for the roll-down game (assuming all tickets are different and numbers are selected at random), you should expect to have 5 5-of-6 tickets, 250 4-of-6 tickets, 4,219 3-of-6 tickets, and 29,283 2-of-6 tickets. The combined winnings of all of those tickets makes it profitable. [1]: https://www.mass.gov/files/documents/2016/08/vv/lottery-cash-winfall-letter-july-2012.pdf https://www.mass.gov/files/documents/2016/08/vv/lottery-cash... [2]: https://en.wikipedia.org/wiki/Lottery_mathematics https://en.wikipedia.org/wiki/Lottery_mathematics
- em-bee 7y ago
  so in each game the money that is not won is collected in the pool until the pool is bigger than the overall cost for all tickets? and in other games this doesn't work because they are 'winner-takes-all'?
- treydey 7y ago
  This is what I was looking for! Thanks.
losvedir 7y ago
* Expected value of the lottery tickets is normally negative. (You pay $1, you expect on average to get back less than $1). * At a certain point, if the jackpot grows too large, the game switches to a new "windfall" mode where the expected value is actually _positive_ to bleed off the jackpot. (You pay $1, you expect on average to get back more than $1). * The couple and the MIT students only played during the positive expected value times. Overall the game still makes money for the state, it's just it has two distinct regimes, and the people playing during negative-EV essentially bankroll both the state and the positive-EV players.

Even weirder is the statement that the State that organized the lottery made more money thanks to them buying massive amount of tickets ( or maybe it was the publicity around the first newspaper article that triggered more interest, and so more participant in general ?)

Piskvorrr 7y ago
I understand the opposite: the State didn't lose any money, (but didn't make any money from these people winning, either); it made money from lottery as usual, but not from these people. (There's an implication that more people in general bought tickets, didn't win, and so the organizer made money from those - but it's not entirely clear.)
- thaumasiotes 7y ago
  The state makes money from every ticket purchased. The lottery simply pays out a fixed percentage of ticket revenue. More ticket sales means more money to the state, regardless of whether those tickets, when purchased, had an expected positive or negative return.
  - pliny 7y ago
    If the ticket has an expected positive return for the buyer, then the state must be losing money.
    - progval 7y ago
      It has an expected positive return only on the days there was a Rolldown. Money came from people who played on days there wasn't one.
    - 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)
    - thaumasiotes 7y ago
      You're not thinking about this the right way. The ticket doesn't have a positive expected return as a structural feature of the lottery. It has a positive expected return conditional on the total number of tickets sold being less than a fixed value.
    - steventhedev 7y ago
      For that particular round of the game, yes. Overall? No, unless the game is very badly designed. The whole situation arises from rolling over the losses between rounds, which "sweetens" the pot for intelligent players. It's also a good way to inflate your numbers if you know that your game might get cut next year (e.g. it might be better to show turnover of 100mm and payouts of 90mm than turnover of 10mm and payouts of 8mm).
      - thaumasiotes 7y ago
        > It's also a good way to inflate your numbers if you know that your game might get cut next year (e.g. it might be better to show turnover of 100mm and payouts of 90mm than turnover of 10mm and payouts of 8mm). ...wouldn't that be better under all possible circumstances? Would you rather have $10 million or $2 million?
        steventhedev 7y ago
        whooops! 100mm with 99mm payout vs 10mm and 8.5mm payout then...
    - chrismcb 7y ago
      The prize pool losses the money, not the state. This was a mechanism to keep the overall prize pool from getting too large. Of one person won the main prize, then they would get a car majority of the prize pool. Otherwise the prize pool was essentially distribute among all the players. Yes technically if enough people played, they could have spent more than the prize pool, but, if enough people played, then the chance that one person won goes up as well.
    - Piskvorrr 7y ago
      The ticket only has an expected positive value return under certain limited circumstances, not all the time (i.e. when jackpot has not been won for a time). State is not losing money in total - just moving around the distribution of prizes, but the sum total remains constant. If anyone would be losing money here, it would be a hypothetical winner of the jackpot - but as the jackpot is only redistributed when there is no such winner for some time...
    - diminoten 7y ago
      No, because the payout for the state (the amount they planned on losing) was always the same. The amount was "lost" regardless, it just depended on if it went to one big winning ticket or hundreds/thousands of smaller winning tickets.
    - eridius 7y ago
      For this to be true, every additional winning ticket purchased must result in a net loss to the state. But it doesn't, every additional winning ticket purchased is money going to the state. The losers in this case are the other people with winning tickets, because their payouts become smaller¹. ¹Well, given one assumption about how the game is run. The other assumption is that the 3- and 4-number winning tickets have a fixed payout calibrated such that this doesn't fully exhaust the pot, and in this case the "loser" for each additional winning ticket is whoever wins the full pot next time as the pot will be lower than it would otherwise have been.
      - zaroth 7y ago
        I think in this case the winnings were fixed and the surge in sales in Rolldown days would cause the pot to be drawn down much more, meaning a longer delay before the next Rolldown day. So Rolldowns probably became less frequent, but otherwise the lottery made their money and everyone took home exactly the winnings they would have in that particular game.
  - deleted 7y ago
    [deleted]
- M2Ys4U 7y ago
  Are state lottery ticket purchases taxed? That'd also bring in a chunk of change.
jarfil 7y ago
That is correct: since these were not usual players who abstained from playing, but rather casual players who bought extra tickets just on rolldown, while the State got a cut from every ticket sale, they were effectively pouring extra money into the lottery, increasing the State's income. Even if they re-invested their previous winnings, that would be twice (or more) that the State would get its cut from the same money, still increasing its income.
Double_a_92 7y ago
The money was "stolen" from the person that would have won the jackpot. The maximum jackpot was just smaller, it didn't make a difference to the lottery who actually won that money. They could say that the jackpot will be split among everyone that has exactly one number right in the next round, and still make profit.

Piskvorrr 7y ago

If nobody wins the big jackpot ("guess all the numbers") for some time, parts of it are given to the smaller winners ("guess a few of the numbers"). In this case, which happened once in a while, it became more likely that you'll win more than you have bet. Usually this means you'll win some $50; they have bet many, many times, and won $50 times many. Doesn't work any more, rules have changed so this way of winning was removed.

tylerhou 7y ago
But which set of tickets do you buy?
- Piskvorrr 7y ago
  From the article, it seems that it doesn't matter, they're random. (Or were random, apparently it's over now, doesn't matter.) To make up an example: Let's say that betting $1 in some way has a 4% chance of winning, and the payout is 20x bet, so if you win on one ticket, you get $20. So, you buy a lot of tickets (say 1000), and you pay $1000. Most of them don't win anything, but 4% of them win $20; $1000 x 4% x 20 = $800; you have won some, but you have $200 less than you started with. Not a good deal. However, if nobody wins the jackpot, it is distributed amongst smaller payouts, which changes the equation: still 4% chance, but payout is now $30. Again, you pay $1000, buy 1000 tickets, most don't win anything, but the 4% that do, you get $1000 x 4% x 30 = $1200. You have $200 more than you started with. Profit! Of course, this will only work if you buy many tickets; buying one or two, you're unlikely to win anything at all. The actual numbers were different in these cases, but the general principle is the same.
  - amelius 7y ago
    That requires a lot of faith in the fairness of the particular lottery.
    - loblollyboy 7y ago
      A. Any lotto requires faith. B. Selbee didnt put all his money in initially. C. The parent comment is just explaining a concept w a hypothetical example

emerongi 7y ago

The jackpot grows off of people losing money. Once people have lost enough money ($5M), the chances of winning the money with a single ticket are raised, however you can no longer win the whole $5M with a single ticket - the money is now distributed over a larger pool of tickets. After that it becomes a good bet, because you can bet smaller amounts, but still win more than you put in initially - you're profiting off of people who lost money before you.

chrismcb 7y ago
Someone can always win the whole 5M. It is just that if the prize for large enough and no one win, then the amount of the small prizes increased. It was a way to keep the total payout low.

martin_b 7y ago

There is a great lecture about it from The Royal Institution https://www.youtube.com/watch?v=kZTKuMBJP7Y https://www.youtube.com/watch?v=kZTKuMBJP7Y

kickopotomus 7y ago

It might make a little more sense with the numbers. WinFall was a typical lottery game where you choose 6 of 46 numbers[1]. As with most lottery games, there is a jackpot payout but there are also payouts for matching 3, 4, and 5 of the numbers. The odds breakdown goes like this[2]: Result | Odds ------------- 6 of 6 | 1 in 9,366,819 5 of 6 | 1 in 39028.41 4 of 6 | 1 in 800.58 3 of 6 | 1 in 47.40 2 of 6 | 1 in 6.83 The issue with WinFall is that when the jackpot increased past $5MM, the expected value of the non-jackpot winnings becomes favorable to the player. I.e. a 5-of-6 matching ticket might normally yield $4,000 but may yield >$20,000 for a "Roll-down" game. So if you go out and buy 200,000 tickets for the roll-down game (assuming all tickets are different and numbers are selected at random), you should expect to have 5 5-of-6 tickets, 250 4-of-6 tickets, 4,219 3-of-6 tickets, and 29,283 2-of-6 tickets. The combined winnings of all of those tickets makes it profitable. [1]: https://www.mass.gov/files/documents/2016/08/vv/lottery-cash-winfall-letter-july-2012.pdf https://www.mass.gov/files/documents/2016/08/vv/lottery-cash... [2]: https://en.wikipedia.org/wiki/Lottery_mathematics https://en.wikipedia.org/wiki/Lottery_mathematics

em-bee 7y ago
so in each game the money that is not won is collected in the pool until the pool is bigger than the overall cost for all tickets? and in other games this doesn't work because they are 'winner-takes-all'?
treydey 7y ago
This is what I was looking for! Thanks.

losvedir 7y ago

* Expected value of the lottery tickets is normally negative. (You pay $1, you expect on average to get back less than $1). * At a certain point, if the jackpot grows too large, the game switches to a new "windfall" mode where the expected value is actually _positive_ to bleed off the jackpot. (You pay $1, you expect on average to get back more than $1). * The couple and the MIT students only played during the positive expected value times. Overall the game still makes money for the state, it's just it has two distinct regimes, and the people playing during negative-EV essentially bankroll both the state and the positive-EV players.