
A game with a windfall for a knowing few - eas
http://www.boston.com/news/local/massachusetts/articles/2011/07/31/a_lottery_game_with_a_windfall_for_a_knowing_few/?p1
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ph0rque
Neatly summarized by this comic: [http://www.smbc-
comics.com/index.php?db=comics&id=2320#c...](http://www.smbc-
comics.com/index.php?db=comics&id=2320#comic)

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bumbledraven
_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>). 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>, 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.

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nonymousse
Which company has this as a hiring problem?

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bumbledraven
Past tense. They don't have that hiring problem posted any more, but it was
for mathematicians/software developers in the R&D group. If you're asking
because you have an approximate solution, let me know (email address in
profile) and I can put you in touch with people there who would be very
interested to see what you've come up with.

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jacques_chester
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".

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JoachimSchipper
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
> 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
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
The Boston Globe isn't local?

~~~
derleth
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.

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patio11
The subtext: "Bad private investor syndicates exploiting math to steal money
from poor people. That is the government's job."

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beezee
Group buy anyone?

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

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

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michael_dorfman
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.

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veyron
Didn't voltaire do this centuries ago?

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hugh3
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
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.

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meatsock
"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.

