Powerball jackpot at $400 million: A mathematical reason to buy ticket

Wednesday night’s Powerball jackpot is at $400 million. Do you still need an excuse to buy a ticket? We have one!

But first let’s make it clear: You should probably never play the lottery. With odds like 1 in 175 million, a $2 Powerball ticket is just plain dumb.

Now, with that out of the way, you can justify your expenditure with math, specifically the statistical concept of “expected value,” or the expected payoff from some event.

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To figure out the expected value when it comes to the lottery, tally up each prize’s winnings (including small prizes*) multiplied by its odds.

Usually, the expected value is less than the cost of the ticket, that dumb $2. But there’s a magic number for the Powerball jackpot. When the Powerball jackpot crosses the $287-million threshold, the “expected” value is equal to $2, the same as the cost of your ticket.

That doesn’t mean that it’s easier to win.

No, your odds are always the same godawful 1 in 175 million.

But with a jackpot of $400 million, that expected value is $2.64. So there’s your mathematical excuse for buying that dumb ticket. Someone’s gonna win (eventually).

(*Note: Payouts in California are slightly different and determined by the number of lottery tickets sold.)

[Updated at 9:03 a.m. on Feb. 19: Alert reader Brian Wathen pointed out that the expected value of a lottery ticket will decrease if there’s more than one winner. For a full explanation check out Jeremy Elson’s article on the subject.]

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