Update. I have another post on tonight’s Powerball drawing with updated calculations. It just might surprise you.
With the next Powerball estimated jackpot at 1.3 billion dollars, I decided to figure out whether it was worth buying a ticket. I did this calculation a few years back, but since then Powerball has changed the odds^{1} in an attempt to get bigger jackpots. Looks like it’s worked.
Some notes:
- The jackpot is not $1.3 billion unless you choose to get the payout of 30 payments over 29 years. Otherwise the estimated immediate cash payout is “only” $806 million.
- If you don’t consider taxes, it’s a good bet to buy a Powerball ticket for this drawing. After all, an expected value of $3.08 is greater than the $2.00 “investment.”^{2}
- Taxes are not insignificant. The top federal tax bracket is 39.6%.^{3} The top Oregon bracket is 9.9%.^{4}
- I oversimplified the tax calculations, applying the top appropriate bracket over the entire amount for each line, instead of doing multiple calculations. I think this could only possibly be significant for the second line, maybe resulting in an error in the expected value of a penny or two. So, not significant.
- I don’t attempt to account for multiple winners. I don’t have enough data.^{5}
So, is “sucker bet” fair? Wikipedia defines a sucker bet as “A sucker bet is a gambling wager in which the expected return is significantly lower than the wager(s).” I guess it’s up to you whether $1.77 is significantly less than $2.00.
See you in the Powerball line. ;-)
- That’s right — they made it harder to win. ↩
- It’s hard for me to call a lottery purchase an investment. So, scare quotes. ;-) ↩
- Should you be lucky enough to win, it will be important to note that the lottery will withhold only 25% for your federal taxes. I guess the IRS expects you to be smart enough to not spend the other 14.6% before the taxes are due. Don’t make them wrong. ↩
- Unless you’re also in Oregon, your state income taxes are likely lower. ↩
- I guess one benefit of the lottery making it harder to win is that it has also decreased the odds of simultaneous winners. There is something you can do to decrease the odds of sharing a winning ticket with someone else — stop using your favorite numbers, especially if they are based on calendar dates. You’re only using a subset of the available numbers and so is everyone else doing what you’re doing. Let the computer choose random numbers for you with a quick pick. ↩