The Powerball jackpot: what are the odds
The chance of winning Powerball on a usual Lotto draw is fairly easy to calculate: you need pick 6 numbers correctly out of 40, and the powerball number correctly out of 10. The number of possible combinations is 3,838,380×10=38,383,800, so your chance is 1 in 38,383,800. Buying 10 combinations twice a week, you’d get a perfect match a bit more than once every 37,000 years.
On Saturday, the prize was $38 million dollars. If tickets were $1 or less, the big prize would pay for buying all 38 million combinations — and the expected value of even smaller numbers of tickets would be more than they cost. However, tickets cost $1.20 per “line” ($0.60 for the six numbers, $0.60 for the Powerball), so you’d still lose money on average with each ticket you buy.
‘Must Win’ jackpots like the one on Wednesday are different. The $40 million prize has to go, so the expected prize value per “line” is $40 million divided by the number of lines sold. Unfortunately, we don’t know what that number is. For the last ‘Must Win’ jackpot there were 2.7 million tickets sold, but we don’t know how many lines that represents; the most popular ticket has 10.
It looks like the expected value of tickets for this draw might be positive. However ‘expected value’ is a technical term that’s a bit misleading in English: it’s the average (mean) of a lot of small losses and a few big wins. Almost everyone who buys tickets for Wednesday’s draw will miss out on the big prize — the ‘averages’ don’t start averaging out until you buy millions of tickets. Still, your chances are probably better than in usual weeks.
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 »
Best to buy your tickets at the last minute. If you buy a ticket a day before the draw there is about a 1 in 38,000 chance of dying before the draw.
Since this is 1000 times more likely than winning the jackpot you are far far more likely to be dead than a winner.
For better odds of being alive when you win buy the tickets at the last moment.
On the off-chance of being dead when you come to buy the ticket well at least you have saved yourself (or your estate) 20 bucks (or whatever a ticket costs).
8 years ago
This seems to make the assumption that your utility function for money doesn’t change when you die?
8 years ago