To get the expected after-tax jackpot payout, you would then multiply that number by the probability of winning the jackpot, which is 1 divided by 292,201,338. What’s the end result? A whopping expected payout of $1.12…on a ticket that cost you $2. Once you add in the expected payouts from all the other potential Powerball prizes, that number increases to $1.32. And again, that assumes you live in a state with no income taxes.
So right now, given the advertised cash payout and the number of people playing, it does not make financial sense to purchase a Powerball ticket. That said, we’re not all that far off from a jackpot that might justify the purchase of a ticket. If the lump sum cash payout (not the annuity value) increases to $1.4 billion, and the number of tickets sold hovers around 500 million, the total expected payout of a $2 Powerball ticket will be $2.01, making the purchase of a ticket a rational decision in pure mathematical terms.