Did you buy a ticket for the Mega Millions jackpot in Illinois, Kansas, or Maryland? If so, you may be in luck; those are the states where the winning tickets were sold. And the jackpot for this particular lottery is a world-record $640 million.
If you played, your chances of winning were of course not particularly good, as this amusing list attests. Among the events identified as being far more likely than buying a winning ticket: being struck by lightning, dating a supermodel, and the Mets winning the World Series. And yet, in this post from the political science blog The Monkey Cage, Joshua Tucker argues that buying a Mega Millions ticket would be a good investment, because the expected value of a $1 ticket is $1.83.
Of course, that holds true only you believe that your chances of winning are completely random and there’s no way to game the system. I don’t know what the case is for pick-6 game like Mega Millions, but, as Jonah Lehrer’s fascinating recent article in Wired reveals, it’s surprisingly easy to crack a scratch-off lottery game. As the article relates, a Toronto statistician named Mohan Srivastava discovered a trick that enabled him, with 90% accuracy, to pick the winning tickets of a scratch-off lottery game. What I love about the article is that it goes into Srivastava’s head and shows you how he used statistical reasoning to crack the code. His method involves examining how frequently a given number appears on a given ticket.
What’s disturbing is that, even after Srivastava brought his findings to the authorities, the flaw in the game continued to appear. Moreover, the article relates that there are reasons to believe that some people are gaming the system. For instance, evidence shows that break-even tickets are highly underredeemed and other types of tickets are highly overredeemed. In addition, some individuals have won a disproportionate number of lotteries, such as a lucky lady in Texas who has won over $1 million in that state’s lottery on four different occasions. (That the lucky winner is a former statistics professor does not exactly tend to alleviate one’s suspicions that something other amazing luck played a role in her good fortune). Srivastava also makes a compelling argument that organized criminals could be using lottery scrach-off games to launder money.
As I said, I have no idea whether Mega Millions can be gamed or not. But the evidence is clear that the scratch-off type games can be, and that authorities are frustratingly complacent about this problem. The takeaway here is that, if you’re thinking of playing these games, buyer beware. The odds are even more stacked against you than you may think, because your likelihood of winning is less than it would be if it were truly a game of pure chance.