Christian points me to this amusing story by Jonah Lehrer about Mohan Srivastava, (perhaps the same person as R. Mohan Srivastava, coauthor of a book called Applied Geostatistics) who discovered a flaw in a scratch-off game in which he could figure out which tickets were likely to win based on partial information visible on the ticket. It appears that scratch-off lotteries elsewhere have similar flaws in their design.
The obvious question is, why doesn’t the lottery create the patterns on the tickets (including which “teaser” numbers to reveal) completely at random? It shouldn’t be hard to design this so that zero information is supplied from the outside. in which case Srivastava’s trick would be impossible.
So why not put down the numbers randomly? Lehrer quotes Srivastava as saying:
The tickets are clearly mass-produced, which means there must be some computer program that lays down the numbers. Of course, it would be really nice if the computer could just spit out random digits. But that’s not possible, since the lottery corporation needs to control the number of winning tickets. The game can’t be truly random. Instead, it has to generate the illusion of randomness while actually being carefully determined.
I’d phrase this slightly differently. We’re talking about $3 payoffs here, so, no, the corporation does not need to control the number of winning tickets. What they do need to control is the probability of a win, but that can be done using a completely random algorithm.
From reading the article, I think the real reason the winning tickets could be predicted is that the lottery tickets were designed to be misleadingly appealing. Lehrer writes:
Instead of just scratching off the latex and immediately discovering a loser, players have to spend time matching up the revealed numbers with the boards. Ticket designers fill the cards with near-misses (two-in-a-row matchups instead of the necessary three) and players spend tantalizing seconds looking for their win. No wonder players get hooked.
“Ticket designers fill the cards with near-misses . . .”: This doesn’t sound like they’re just slapping down random numbers. Instead, the system seems to be rigged in the fashion of old-time carnival games in order to manipulate one’s intuition that the probability of near-misses should be informative about the underlying probability of hits. (See here for some general discussion of the use of precursors to estimate the probability of extremely rare events.)
In this sense, the story is slightly more interesting than “Lottery designers made a mistake.” The mistake they made is directly connected to the manipulations they make in order to sucker people into spend more money.
P.S. Lehrer writes that Srivastava does consulting. This news story should get him all the business he needs for awhile!