The Math of Powerball

Ethan Siegel in Starts With A Bang:

This past week, the Powerball lottery jackpot went past $500,000,000, one of the largest sums in history, where the $564.1 million jackpot wound upbeing split by three winners. In order to win, you need to match five normallottery numbers — white balls numbered 1-through-59 — plus the Powerball: a red ball numbered 1-through-35. Each Powerball ticket costs $2, plus you have the option to pay an extra $1 to activate the power play, a multiplier that increases your payout for non-jackpot prizes.

Of course, if you win, you’ll conclude it will have been worth it, even if the payout was small, while if you lose, you’ll probably conclude that it wasn’tworth it. (Until the next drawing, of course, when you get another chance!)

But what does mathematics have to say about this? In particular:

• What are your odds of winning each individual combination?
• How much does each winning possibility pay out?
• Is it worth it to activate the power play option?
• And finally, how big does the jackpot have to be in order for playing the Powerball lottery to be “worth it”?

When you say worth it, by the way, it has a very specific meaning when it comes to mathematics. It means that the amount you can expect to win, on average, is greater than the amount you have to bet in order to play.

More here.