

A Lottery for People Who Are Good at Math - mjtokelly
http://freakonomics.blogs.nytimes.com/2009/01/27/a-lottery-for-people-who-are-good-at-math/

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aamar
I can confirm that this was exploited by a number of students in the
Cambridge, MA area, who -- in order to reduce individual risk and consolidate
the work involved -- pooled their money and reinvested the pool monthly. One
pool I know about (~8 people) reached ~$250k.

Seems like quick cash, but it turned into a lot of work: printing 150k tickets
in a way that they looked hand-filled out, pulling the winning cards, cashing
them in, and plenty besides. Once enough groups got wind, the margins dwindled
over the course of a few months to "not worth it".

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chris11
This has happened before. In November 1997, the New York State Lottery ran a
promotion where all the prizes were doubled every Wednesday. Players had
nearly a 20% edge over the house.
<http://catlin.casinocitytimes.com/articles/1226.html>

MAA: Math Horizons ran an article on it February 2007.

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mjtokelly
A more elaborate explanation can be found here:

<http://www.milliondollarideaguy.com/blog/?p=185>

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ralph
There was a syndicate at work when the UK lottery started. I persuaded them,
well some of them, the rest went along with it without comprehending, that
it's better to buy N tickets in one game than one ticket in each of N games.
Further, we used a set of 210 tickets that guaranteed a `match 3 of 6', i.e.
GBP10 win. (Tickets are GBP1 each.) So the syndicate saved instead of playing
and once we had enough we queued and bought the tickets, causing a few
grumbles from the Sainsbury's customers behind me in the queue.

We had just one ticket win anything. It matched 5 of 6, and our 6th was one
away from the `bonus' ball. So we won about GBP3,500. If we'd have got the
bonus, it would have been 100-ish times more!

I tried to convince my fellows that we were lucky, but, instead of saving
gradually for the next play, they put some of their winnings back in so they
could play the 210 tickets again the following week. They won GBP10.

Actually, 211 tickets were played, because quality checks showed one has been
miss-filled but naturally we didn't want to drop the erroneous one. :-)

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aposteriori
Let's not forget that it's only the _expected_ return, i.e., the return as the
number of trials goes to infinity. But, you don't have infinite money to
spend, so there's a good chance you'll go broke before you win (depending on
the variance). Another way of looking at it, it's a random walk with a bottom
barrier --- once it hits zero, you're out of the game.

~~~
gravitycop
_you don't have infinite money to spend, so there's a good chance you'll go
broke before you win_

I.e. risk-of-ruin: <http://en.wikipedia.org/wiki/Ruin_theory>

~~~
aposteriori
Thanks, wasn't aware of this name.

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barbie17
Now that it's known, it will be arbitraged away. The guy who discovered this
should have kept it a secret ;).

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ojbyrne
From the article, listing risks:

4\. Too many people try to take advantage of this scenario

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dnaquin
Actually. Most lotteries become good bets when the jackpots get large enough.
Assuming you don't split a pot with someone else, of course.

Avoid 12345, geometric progressions, etc.

~~~
tokenadult
_Assuming you don't split a pot with someone else, of course._

That's an assumption you can't make in a parimutuel lottery, which is the
usual lottery design. Mathematician Ian Stewart, author of many good books on
mathematics, gives one example of a lottery in Britain that had more than
seventy winners.

~~~
dnaquin
Absolutely. But even then, it's a good bet at some point.

That's the exact example I'm thinking of when I say avoid 12345, geometric
progressions, etc. I believe that example was a simple pattern.

