There is a lot of bad information out there about the Powerball (now $1.5B!).
Q: What are the odds of winning?
A: 1 in 292 million. Winning numbers from Powerball are chosen by picking 5 balls from the first 69 balls (numbered 1 to 69) and a 6th ball from a second set of 26 balls (numbered 1 to 26). Each ticket costs $2.
Q: Should I play the lottery?
A: Maybe. You have the same probability of winning (1 in 292 million) any time you play. What is different is the payout. If you must play, play when there is a big payout. You have more competitors when the jackpot is high, but winning is relatively rare and you are still more likely to walk away with more winnings when the jackpot is high (even if you have to share the jackpot with others). You can win $1M if you get the first 5 numbers right, but keep in mind that the $1M does not increase if the jackpot gets bigger.
Bottom line: if you never play the lottery, this is a good time to buy a ticket.
Q: I’ve read that I should buy tickets Pennsylvania. Is Pennsylvania lucky?
A: No. Each ticket is equally likely to win regardless of where it was sold. There are some tax implications based on where you live and where you purchased your tickets. Don’t buy a ticket in New York if you don’t live there or you will have to pay New York income tax if you win.
Q: Will someone win?
A: It depends on how many tickets were purchased. 440M tickets were purchased for the January 9 lottery. Assuming that all tickets are randomly generated and 500M tickets are purchased this time, there is a 82% chance that someone will win. We can break down that 82% further: 31% chance of a single winner, 26% chance of two winners, 15% of 3 winners and 9.4% chance of 4+ winners.
If 600M tickets are purchased, then there is a 87% someone will win.
If 700M tickets are purchased, then there is a 91% someone will win.
If 800M tickets are purchased, then there is a 93.5% someone will win.
If 900M tickets are purchased, then there is a 95% someone will win.
If 1B tickets are purchased, then there is a 97% someone will win.
So while it’s likely that someone will win, there is still a good chance the jackpot will roll over again.
Q: I read that 70% of winning tickets have been computer generated. Does this mean that I’m less likely to win if I pick my own numbers.
A: First of all, if 70% tickets sold are computer generated, then this a meaningless statement. Each ticket is equally likely to win, regardless of how the numbers were picked.
Q: Do you recommend picking the same numbers every time?
A: That doesn’t matter. Each combination of numbers is equally likely to win.
Q: An ABC News analysis of past Powerball winners suggests that 8, 54, 14, 39 and 13 have been drawn the most frequently. Should I select these numbers?
A: Not necessarily. Each combination of numbers is equally likely to win. Of course over time some numbers are drawn more than others because that is what true randomness looks like. However, the picks in the past give no insight into which numbers will be drawn next.
Every lottery ticket is equally likely to win. You are less likely to share the jackpot if you choose numbers larger than 30 because so many people pick numbers based on birthdays. The picture below indicates that while each number is equally likely to be drawn, each number is not equally likely to be selected for a ticket. Choosing numbers greater than 30 will give you a more “unique” ticket that offers a high probability of winning the full jackpot.
Lottery numbers as chosen by lottery players are far from uniformly distributed
Q: A lottery expert said: “The only advice I can really give people is buy as many tickets as you can afford.”
A: While it’s true that your odds are winning strictly go up with each additional ticket you purchase, in general buying lottery tickets is not a good investment. I’d recommend investing in mutual funds or education, or saving for retirement or a rainy day over playing the lottery.
If you are playing the lottery, it’s best to go into a pool with other people. The goal is really to come out ahead, not to win it all. Each ticket has a 1 in 292 million chance of winning, so you can increase your probability of winning by tenfold if you go into a pool with 9 other people and split any winnings amongst yourselves.
Q: What is the cash lump sum payout associated with the Powerball? If I win, should I choose the lump sum payout or the annuitized prize paid over 29 years?
A: The lump sum payout is about $806M (now $903M). The $1.3B (now $1.5B) payout is paid out over 29 years (the first payment is immediate). The tax situation is similar for these two options, so I would recommend the annuitized prize. In either case, you would be in the highest income tax bracket (39.6% for Federal and 7.65% in Wisconsin). This means that you’d come out with about half of your winnings. If you take the lump sum, on average you’d come out $0.54 behind for each $2 ticket you purchase if you live in Wisconsin. And that is an optimistic number since you will probably have to share the prize. So it’s not a good investment. The annuitized payment is a better deal, although the future earnings you would collect will be worth less than the money now.
There are some weird lottery tax rules according to which state you lived in or bought your ticket (see Forbes for more). An article on Arizona Central summarizes financial advice and personal happiness levels after winning the lottery. Spoiler: winning the lottery probably won’t make you happier.
Q: Will you be playing the Powerball?
(Updated on January 13, 2015)
Q: As the jackpot gets bigger does expected value of ticket get larger or smaller due to an increased possibility of multiple winners?
A: Almost certainly bigger. The increased probability of multiple winners grows slowly with the number of tickets sold. I have a picture below. 440 million tickets were sold when the jackpot was $700M and early reports suggest that around the same number of tickets were sold when the jackpot rose to $1.5B. I made a figure of the conditional expected winnings for someone who wins the jackpot, which takes the possibility of multiple winners into account. I included a few different values of the jackpot for comparison. I don’t take taxes or smaller prizes into account here (the smaller prizes would add a constant to all the numbers here).
Your expected lottery winnings conditioned on you winning.
(Updated on January 14, 2016)