6 ms·

A game with a windfall for a knowing few

200 points by eas 15y ago

ph0rque 15y ago
Neatly summarized by this comic: http://www.smbc-comics.com/index.php?db=comics&id=2320#comic http://www.smbc-comics.com/index.php?db=comics&id=2320#c...
jacques_chester 15y ago
State-owned lotteries transfer wealth from one group of people to another group without any coercion. I don't see why private individuals can't participate in the transfers also. More generally, this is an example of how simple changes (the rolldown) can have surprising consequences. TBQH I'm surprised the lottery operators aren't just keeping the surplus funds rather than doing a "roll down".
- justincormack 15y ago
  They usually have to publish a payout rate, it is a common requirement for most forms of pure chance gambling. If people dont win you need some form of rollup. However if you keep it purely on the single big win it does not lead to schemes like this.
  - jacques_chester 15y ago
    Is the published payout rate based on calculated odds or on the historical payouts made?
  - alanfalcon 15y ago
    Plus when you fund larger and larger jackpots (by keeping the rollup purely on the single big win) you get more and more people buying more and more tickets. I think Massachusetts would be likely to earn more money by being able to advertise a much, much larger jackpot and losing these "rollup day" "gamblers" (when your mathematical theoretical return is so far above 100%, I hesitate to call it gambling) but apparently they have some incentive to keep things the way they are (do lottery officials have relatives or buddies who are among those gaming the system?) because they've let this go on so long.
    - fvryan 15y ago
      This is just one of many games in MA. There are other Major Jackpot games with huge payouts.
- JoachimSchipper 15y ago
  Apparently, this particular lottery was created to pay out a bigger percentage of revenue than other lotteries. That is not entirely a bad idea: if people are going to gamble, it's better that they don't lose too much money. This particular scheme pays out most of the money to a select few, though, which defeats the point.
  - jacques_chester 15y ago
    > This particular scheme pays out most of the money to a select few, though, which defeats the point. Does it? To me the only point of a lottery is for the operator to make a predictable profit; that predictability is why governments like them so much. Who wins the jackpot is pretty close to irrelevant.
    - derleth 15y ago
      Wait for the political fallout when the people funding the jackpots realize all their money is going to out-of-staters and they have no chance of winning anything, ever. (Yes, I'm pretty sure that's how this will be reported in local media.)
      - mhb 15y ago
        The Boston Globe isn't local?
        derleth 15y ago
        Good question. When I say 'local', I mean the Deming Headlight and the Havre Daily News. You know, all the papers nobody outside a hundred mile radius of the town cares about. The Boston Globe is up there with the LA Times and the Washington Post and so on and so forth, in the national, if not global, ranks.
  - joezydeco 15y ago
    It makes a lot more sense to just run the Lottery as a raffle (pick one serial number from all tickets sold, or have a fixed amount of sellable tickets), but you can see how states are more enticed by the idea of open-ended ticket sales. Illinois actually has true raffles a few times a year and they have always sold out before the drawing date.
- markmarknewyork 15y ago
  According to the calculation by Hao Li in 2006 (should be at MSU that time) (see Hao Li's article at http://www.jofamericanscience.org/journals/am-sci/0201/06-lihao-0106.pdf http://www.jofamericanscience.org/journals/am-sci/0201/06-li...): By knowing the total tickets Ntt each time, Pjh can be estimated easily: Pjh=1-(1-P6) Ntt Lottery P6 is the probability of matching 6 numbers. In the case of the WINFall lottery, P6=1/13,983,816. The total tickets Ntt each time can be estimated by its samples and their probabilities. The WINFall lottery has 4 samples, matching 6 numbers N6, matching 5 N5, matching 4 N4 and matching 3 N3 respectively. N3 is the largest sample of the WINFall lottery. As far as we have four samples in hand: N6 N5 N4 and N3, we use N3 to calculate the total tickets. Because the more sample are there, the small differences we have (Statistics Accuracy). The Ntt is: Ntt=N3/P3 P3 is the probability of matching 3 numbers. In the case of lottery WINFall, P3=1/57. To win is really practical. However, government should make more money than buyers even following the abave rule.
beezee 15y ago
Group buy anyone?
Gatsky 15y ago
How come there aren't any lottery start-ups?
- michael_dorfman 15y ago
  Because it is a state-run monopoly in most jurisdictions, and in the remaining ones would likely require a legal staff substantially larger than the programming staff.
- jacques_chester 15y ago
  There's lots of them. Most of them are ... not quite legal.
- peregrine 15y ago
  While not legally gambling look at penny auctions. They are essentially a raffle and a ripe for governmemnt control.
- cdr 15y ago
  There are a few start-ups I know of that sell lottery technology/services to states, but afaik it's mostly dominated by big players and hard to break into.
- VladRussian 15y ago
  to disrupt the industry run by government and the mob?
- chopsueyar 15y ago
  I believe they were mentioned in the article. These people are buying tickets under companies, not individuals.
meatsock 15y ago
"As a result, sophisticated players do not actually want the jackpot to be paid out - unless it is going to them." if they were truly sophisticated they would enjoy it just the same whoever it went to.
hugh3 15y ago
And thanks, boston.com, for spoiling it for everybody. No doubt the loophole will be closed now that it's out in the open.
- jimminy 15y ago
  It's been written about before. I read about it in '08 or '09, and over the years have tried to find an article on it but those always come back with articles on scratch-off flaws.
veyron 15y ago
Didn't voltaire do this centuries ago?
bumbledraven 15y ago
Mark Kon, a professor of math and statistics at Boston University, calculated that a bettor buying even $10,000 worth of tickets would run a significant risk of losing more than they won during the July rolldown week. A $2 Cash WinFall ticket allows you to pick a set of 6 distinct integers from the set {1..46}. The lottery commission then picks six distinct integers at random from the set {1..46}, effectively by drawing numbered balls without replacement from an urn. The payouts for May 9, 2011 were $24821 for a match-5 (a ticket that has 5 numbers in common with the set chosen by the lottery), $824 for a match-4, and $26 for a match-3 (http://goo.gl/gSTsF http://goo.gl/gSTsF). It's easy to show that buying a ticket on that day had a positive expected value. [Edit to show expected value calculation: According to http://www.masslottery.com/games/lottery/cash-winfall.html http://www.masslottery.com/games/lottery/cash-winfall.html, the probability of a match-5 is 1/39028.41, the probability of match-4 is 1/800.58, and the probability of a match-3 is 1/47.40. Then the expected value of a $2 ticket on May 9, 2011 was $24821/39028.41 + $824/800.58 + $26/47.40 = $2.21.] $10,000 will buy 2,000 [Edit: oops, actually 5,000. Also fixed in what follows] Cash WinFall tickets. When you can only buy a few tickets in a lottery like this, the distribution of the numbers on your tickets greatly affects your chances of coming out ahead. For instance, if you buy 5,000 copies of the ticket {1,2,3,4,5,6}, your chances of coming out ahead are much worse than if you buy 5,000 tickets with a bunch of different numbers, although of course your expected winnings are the same in each case, provided no one hits the jackpot. It's actually an open problem to create a set of 5,000 Cash WinFall tickets that maximize your chances of coming out ahead. Indeed, a Boston-area employer (that's still hiring!) posted a hiring problem based on this for several years.
- mhb 15y ago
  $10,000 buys 5000 tickets, but I'd be interested in seeing how the positive expected value is easily shown.
- deleted 15y ago
  [deleted]
- mhb 15y ago
  Right. I was actually interested in seeing how the probabilities were calculated which doesn't seem as easy.
deleted 15y ago
[deleted]
deleted 15y ago
[deleted]
deleted 15y ago
[deleted]
deleted 15y ago
[deleted]
joeycfan 15y ago
I don't see the problem here. These people had the brains to figure this out, the bucks to bet on it and the balls to try it out. Life itself is 'A game with a windfall for a knowing few'
patio11 15y ago
The subtext: "Bad private investor syndicates exploiting math to steal money from poor people. That is the government's job."
deleted 15y ago
[deleted]
markmarknewyork 15y ago
About the calculation of this WinFall game, visit: http://www.jofamericanscience.org/journals/am-sci/0201/06-lihao-0106.pdf http://www.jofamericanscience.org/journals/am-sci/0201/06-li...

200 points by eas 15y ago

Neatly summarized by this comic: http://www.smbc-comics.com/index.php?db=comics&id=2320#comic http://www.smbc-comics.com/index.php?db=comics&id=2320#c...

jacques_chester 15y ago

State-owned lotteries transfer wealth from one group of people to another group without any coercion. I don't see why private individuals can't participate in the transfers also. More generally, this is an example of how simple changes (the rolldown) can have surprising consequences. TBQH I'm surprised the lottery operators aren't just keeping the surplus funds rather than doing a "roll down".

justincormack 15y ago
They usually have to publish a payout rate, it is a common requirement for most forms of pure chance gambling. If people dont win you need some form of rollup. However if you keep it purely on the single big win it does not lead to schemes like this.
- jacques_chester 15y ago
  Is the published payout rate based on calculated odds or on the historical payouts made?
- alanfalcon 15y ago
  Plus when you fund larger and larger jackpots (by keeping the rollup purely on the single big win) you get more and more people buying more and more tickets. I think Massachusetts would be likely to earn more money by being able to advertise a much, much larger jackpot and losing these "rollup day" "gamblers" (when your mathematical theoretical return is so far above 100%, I hesitate to call it gambling) but apparently they have some incentive to keep things the way they are (do lottery officials have relatives or buddies who are among those gaming the system?) because they've let this go on so long.
  - fvryan 15y ago
    This is just one of many games in MA. There are other Major Jackpot games with huge payouts.
JoachimSchipper 15y ago
Apparently, this particular lottery was created to pay out a bigger percentage of revenue than other lotteries. That is not entirely a bad idea: if people are going to gamble, it's better that they don't lose too much money. This particular scheme pays out most of the money to a select few, though, which defeats the point.
- jacques_chester 15y ago
  > This particular scheme pays out most of the money to a select few, though, which defeats the point. Does it? To me the only point of a lottery is for the operator to make a predictable profit; that predictability is why governments like them so much. Who wins the jackpot is pretty close to irrelevant.
  - derleth 15y ago
    Wait for the political fallout when the people funding the jackpots realize all their money is going to out-of-staters and they have no chance of winning anything, ever. (Yes, I'm pretty sure that's how this will be reported in local media.)
    - mhb 15y ago
      The Boston Globe isn't local?
      - derleth 15y ago
        Good question. When I say 'local', I mean the Deming Headlight and the Havre Daily News. You know, all the papers nobody outside a hundred mile radius of the town cares about. The Boston Globe is up there with the LA Times and the Washington Post and so on and so forth, in the national, if not global, ranks.
- joezydeco 15y ago
  It makes a lot more sense to just run the Lottery as a raffle (pick one serial number from all tickets sold, or have a fixed amount of sellable tickets), but you can see how states are more enticed by the idea of open-ended ticket sales. Illinois actually has true raffles a few times a year and they have always sold out before the drawing date.
markmarknewyork 15y ago
According to the calculation by Hao Li in 2006 (should be at MSU that time) (see Hao Li's article at http://www.jofamericanscience.org/journals/am-sci/0201/06-lihao-0106.pdf http://www.jofamericanscience.org/journals/am-sci/0201/06-li...): By knowing the total tickets Ntt each time, Pjh can be estimated easily: Pjh=1-(1-P6) Ntt Lottery P6 is the probability of matching 6 numbers. In the case of the WINFall lottery, P6=1/13,983,816. The total tickets Ntt each time can be estimated by its samples and their probabilities. The WINFall lottery has 4 samples, matching 6 numbers N6, matching 5 N5, matching 4 N4 and matching 3 N3 respectively. N3 is the largest sample of the WINFall lottery. As far as we have four samples in hand: N6 N5 N4 and N3, we use N3 to calculate the total tickets. Because the more sample are there, the small differences we have (Statistics Accuracy). The Ntt is: Ntt=N3/P3 P3 is the probability of matching 3 numbers. In the case of lottery WINFall, P3=1/57. To win is really practical. However, government should make more money than buyers even following the abave rule.

beezee 15y ago

Group buy anyone?

Gatsky 15y ago

How come there aren't any lottery start-ups?

michael_dorfman 15y ago
Because it is a state-run monopoly in most jurisdictions, and in the remaining ones would likely require a legal staff substantially larger than the programming staff.
jacques_chester 15y ago
There's lots of them. Most of them are ... not quite legal.
peregrine 15y ago
While not legally gambling look at penny auctions. They are essentially a raffle and a ripe for governmemnt control.
cdr 15y ago
There are a few start-ups I know of that sell lottery technology/services to states, but afaik it's mostly dominated by big players and hard to break into.
VladRussian 15y ago
to disrupt the industry run by government and the mob?
chopsueyar 15y ago
I believe they were mentioned in the article. These people are buying tickets under companies, not individuals.

meatsock 15y ago

"As a result, sophisticated players do not actually want the jackpot to be paid out - unless it is going to them." if they were truly sophisticated they would enjoy it just the same whoever it went to.

hugh3 15y ago

And thanks, boston.com, for spoiling it for everybody. No doubt the loophole will be closed now that it's out in the open.

jimminy 15y ago
It's been written about before. I read about it in '08 or '09, and over the years have tried to find an article on it but those always come back with articles on scratch-off flaws.

veyron 15y ago

Didn't voltaire do this centuries ago?

bumbledraven 15y ago

Mark Kon, a professor of math and statistics at Boston University, calculated that a bettor buying even $10,000 worth of tickets would run a significant risk of losing more than they won during the July rolldown week. A $2 Cash WinFall ticket allows you to pick a set of 6 distinct integers from the set {1..46}. The lottery commission then picks six distinct integers at random from the set {1..46}, effectively by drawing numbered balls without replacement from an urn. The payouts for May 9, 2011 were $24821 for a match-5 (a ticket that has 5 numbers in common with the set chosen by the lottery), $824 for a match-4, and $26 for a match-3 (http://goo.gl/gSTsF http://goo.gl/gSTsF). It's easy to show that buying a ticket on that day had a positive expected value. [Edit to show expected value calculation: According to http://www.masslottery.com/games/lottery/cash-winfall.html http://www.masslottery.com/games/lottery/cash-winfall.html, the probability of a match-5 is 1/39028.41, the probability of match-4 is 1/800.58, and the probability of a match-3 is 1/47.40. Then the expected value of a $2 ticket on May 9, 2011 was $24821/39028.41 + $824/800.58 + $26/47.40 = $2.21.] $10,000 will buy 2,000 [Edit: oops, actually 5,000. Also fixed in what follows] Cash WinFall tickets. When you can only buy a few tickets in a lottery like this, the distribution of the numbers on your tickets greatly affects your chances of coming out ahead. For instance, if you buy 5,000 copies of the ticket {1,2,3,4,5,6}, your chances of coming out ahead are much worse than if you buy 5,000 tickets with a bunch of different numbers, although of course your expected winnings are the same in each case, provided no one hits the jackpot. It's actually an open problem to create a set of 5,000 Cash WinFall tickets that maximize your chances of coming out ahead. Indeed, a Boston-area employer (that's still hiring!) posted a hiring problem based on this for several years.

mhb 15y ago
$10,000 buys 5000 tickets, but I'd be interested in seeing how the positive expected value is easily shown.
deleted 15y ago
[deleted]
mhb 15y ago
Right. I was actually interested in seeing how the probabilities were calculated which doesn't seem as easy.

deleted 15y ago

[deleted]

deleted 15y ago

[deleted]

deleted 15y ago

[deleted]

deleted 15y ago

[deleted]

joeycfan 15y ago

I don't see the problem here. These people had the brains to figure this out, the bucks to bet on it and the balls to try it out. Life itself is 'A game with a windfall for a knowing few'

patio11 15y ago

The subtext: "Bad private investor syndicates exploiting math to steal money from poor people. That is the government's job."

deleted 15y ago

[deleted]

markmarknewyork 15y ago

About the calculation of this WinFall game, visit: http://www.jofamericanscience.org/journals/am-sci/0201/06-lihao-0106.pdf http://www.jofamericanscience.org/journals/am-sci/0201/06-li...