The one time it's mathematically advantageous to play Powerball

Adding up the expected values for all those prizes absenting the jackpot comes to $0.24 (for each prize: Prize x probability+prize x probability + etc.). So the jackpot’s contribution to the total expected value of a Powerball ticket can drop $.024. Since a ticket costs $2, we only need the jackpot’s portion of the ticket’s expected value to be $1.76 in order to have a a ticket that’s worth what it costs—and a break-even system.

So since we know we need the expected value of the jackpot’s portion a Powerball ticket’s worth ($1.76), we can find out how big the jackpot needs to be, just like we did in the simple version. By dividing the $1.76 by the probability of hitting it big, adjusting for taxes, adjusting for jackpot splitting, you get… $1.02 billion. But this is just the cash payout, which is usually three-fifths of the jackpot.

If the billboards and newscasters ever announce a $1.7 billion Powerball, the math’s likely to be in your favor.

Now, that’s figure is with a very conservative 200 million tickets sold. If the jackpot actually gets this big, far more tickets could be sold, making the likelihood of a split higher and driving the value of a ticket down—so you’d have to again wait for an increase in jackpot size raise the expected value of a ticket. But then, of course, more people would play, and the single-winner probability would drop again. It’s a vicious cycle.