Non-awful lottery story
Stuff has a story on today’s Big Wednesday lotto that doesn’t say anything obviously untrue or misleading. I’m sure this isn’t a first, but it is rare enough to be notable.
The story doesn’t say anything about the odds, but in a sense that’s not the point: you don’t play the lottery to win, you play it to imagine winning. To quote another statistician
The benefit to playing the lottery comes entirely between buying the ticket, and when the winner is revealed. During this interval, someone who has bought the ticket can entertain the idea that they might win, and pleasantly imagine how much better their life could be with the money, what they would do with it, etc. … If a $1 lottery ticket licenses even one hour of imagining a different life, I don’t see how people who spend $12 for two or three hours of such imagining at a movie theater, or $25 for ten hours at a bookstore, are in any position to talk.
Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »
I’ve always wondered what the statistical expectation is with the New Zealand lotteries. It’s information I think should be disclosed by law along the lines of:
… for every dollar you spend on a lottery ticket you can expect a return of 60 cents.
Of course it won’t happen when the government sees lotteries as a revenue earner.
12 years ago
But I don’t think that’s the relevant number — the expected return is only relevant if the expected winnings are the only benefit to playing, and either you are buying a substantial fraction of all the possible numbers or if your utility for money is perfectly linear.
Even if you assumed that these were good approximations (which I can’t see being reasonable), you can’t calculate the expected return accurately without knowing how many tickets will be sold and what the distribution of numbers is, because you need to be able to estimate how many winners will divide the jackpot.
What makes more sense is to publish (a) your chance of winning a small prize, and (b) your chance of winning the jackpot. These might be clearer if expressed in terms of how much you would have to spend, the way that doctors use Number Needed to Treat.
That is, for Big Wednesay, you need to spend something like $300 to have a 50:50 chance of getting at least $20 in prizes, and you need to spend $15 million to have a 50:50 chance of winning the jackpot.
12 years ago
Another thought on this…
“The story doesn’t say anything about the odds, but in a sense that’s not the point: you don’t play the lottery to win, you play it to imagine winning.”
Of course, if you’re really imaginative you can do that with out buying a ticket.
12 years ago
Yes. The linked post by Cosma Shalizi talks about that — I just didn’t quote the whole thing.
12 years ago
But if you’re really imaginative you can do that with the fantasies movies and books provide.
It should come down to how easy it is to imagine the fantasy.
I think I’d find it easy to fantsise what it’d be like to be rich, and so the marginal benefit of buying a lottery ticket is low.
I’d find it much harder to come up with a Batman fantasy as good as any of Nolan’s movies, however.
12 years ago
I once had the luxury of working in a Lotto outlet and can confirm that this is exactly how they explain ‘the product’ in training seminars.
It was some time ago, but I recall that the odds of winning each division were available to anyone who asked at the Lotto counter. Tucked away in a folder in a draw of course…
12 years ago