When it’s still not worth playing the lottery
Following up on the recording-breaking Powerball jackpoint in the US, there’s a story on Time.com headlined “The One Time It’s Mathematically Advantageous to Play Powerball.” They’re still wrong, but they have taken many more of the relevant factors into account than usual, and it’s definitely worth reading.
On top of the microscopic chance of getting the winning numbers, they also look at the likelihood that you will have to share the jackpoint, the benefit of the minor prizes, the US federal tax payable on the winnings, and the fact that the advertised payout is actually inflated by about 60% — it’s the total future payment for a 30-year annuity you can buy with the prize, not the value of the prize itself.
They come to the conclusion that a jackpot worth more than about $2.2 billion is worth buying tickets for, in the sense that it has positive expected cash return. The one thing they don’t take into account is the non-linear utility of money. Two billion dollars isn’t actually worth two billion times as much as one dollar, unless you’re the US government or something. If this sounds strange, all that it’s saying is that each extra dollar is worth more to you than it is to a billionaire.
The diminishing value of extra money means that playing the lottery basically can’t be worthwhile if you evaluate it in terms of winning. The only way playing the lottery can make sense is if you get enough enjoyment from thinking about winning to be worth the upfront cost.
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 »
The utility of money, if all that a person does with it is spend it on himself, is pretty much like you describe.
But a person doesn’t have to spend it on themselves. They can screw with politics – imagine what would happen if all the political parties had equal resources. Or screw with the stock market for fun. Or they could give every school in the country a $1,000,000 trust fund and still be rolling in it.
8 years ago