A Lottery for People Who Are Good at Math

[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".

[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.

[mjtokelly]

A more elaborate explanation can be found here:

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

[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. :-)

[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

[barbie17]

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

[ojbyrne]

From the article, listing risks:

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

[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.

[vlad]

Actually. Most lotteries become good bets when the jackpots get large enough.

Lotteries never become a good bet. However, if one wanted to waste their money, picking a number that doesn't resemble a birthday or something someone else would choose would be a good idea. On the other hand, if you won the lottery from a $2 entry, $500K would be just as good as $15m since it was all random anyway.

[fallentimes]

Why would you avoid 12345 and geometric progressions?

[zach]

And concentrate on numbers over 31 -- many "lucky numbers" are birthdates.