The one time it’s mathematically advantageous to play Powerball

The one time it’s mathematically advantageous to play Powerball

Wednesday’s Powerball jackpot is on its way to an estimated $1.4 billion, after nobody matched all six numbers in Saturday night’s drawing. The prize would be the biggest of all time, dwarfing the MegaMillions $656 million high-water mark of 2012. This is a big deal.

Unless you’re really, really smart and lucky—see Joan Ginther, among others—playing the lottery is a bad idea, financially speaking. Of course there’s the fun, thrilling aspect of playing, which is not to be discounted, even by a belt-and-suspenders-type publication like MONEY.

But there’s actually a case to be made that in some rare instances, it’s mathematically advantageous to roll the dice on some Powerball, or other lottery tickets. When a jackpot grows, it brings up the value of a ticket, which in Powerball’s case costs $2. That’s called the expected value, and it’s found by multiplying the payout by the probability of winning.

Here’s a simple example: In a basic lottery with just one prize, $1 tickets, and 100 people playing, any jackpot over $100 will mean that a ticket will be worth more than the $1 it costs. If you bought all the tickets for $100, you would win the jackpot and take home more than what you paid. So theoretically, at a certain size, a lottery ticket can actually be worth more than what you pay for it.

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