Is Powerball a Mug’s Game?

It all depends on when you play—and what value you put on a dollar.

By Jordan Ellenberg

Illustration by Robert Neubecker

Were you stupid not to play?

I don’t have to ask myself; I played. My father and his Ph.D. in statistics put me in for a 20 percent share of his four tickets. But I got enough razzing from friends and neighbors that I thought it was worth explaining why, from a mathematician’s point of view, last Saturday’s drawing wasn’t necessarily dumb.

The question to ask is: What is the expected value of a lottery ticket? If the expected value is more than a dollar, and the ticket costs a dollar, you should buy a ticket. If the expected value is less than a dollar, you should keep your money.

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