September 11, 2013

# Lottery calculations

Even so often, one of the NZ lottery jackpots gets to be unusually large and we see an increasing stream of search engine hits from people looking for ways to win.

Via @mapcaptenor, here’s an analysis of the USA’s Powerball lottery, with the conclusion

The one sentence takeaway: no matter how big the jackpot gets, you should only buy Powerball tickets for their entertainment value.

In fact, an economics argument can get you this conclusion much more easily. All the facts you have about the lottery are available to pretty much anyone in the country, as is the opportunity to buy tickets. Unless you think you are one of the top handful of smartest investors in New Zealand, you should assume that other people will draw the same conclusion as you about whether it’s worth buying tickets. If you think it’s worth buying, so will quite a lot of other people, and collectively you’ll buy up enough tickets to ensure that the expected benefit falls to nearly zero.

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 »

• Stephen McNeill

Which reminds me of the old saying: Your chances of winning Lotto are only marginally improved by buying a ticket. Sigh!

• megan pledger

Andrew Gelman pointed to an interesting article about a statistician, Mohan Srivastava, working out how to beat an Ontario “scratchie” lotterie.
http://andrewgelman.com/2011/02/06/statistician_cr/
and
http://www.wired.com/magazine/2011/01/ff_lottery/all/1

The statistician worked out though that it was more cost effective to earn the income from his job than to work full-time beating the lottery.

• Nick Iversen

The economic argument falls down when you consider real life humans (or monkeys) rather than rational economic ones.

A bizarre example: http://www.pnas.org/content/early/2013/09/04/1308718110

This is a study of economic decisions made by thirsty monkeys.

• Thomas Lumley

Nick,

No, the argument doesn’t fall down, because it is sufficient to have just a few people in the country who assess the problem as a rational investment opportunity. There’s no need for most people to do so.