This morning in Sunday school someone threw out that a substantial fraction of Americans have a lottery win comprising their retirement plans. (“How did we get to talking about gambling in Sunday school?” you might ask. It was just a chance discussion, that's all.)
I just shook my head at that statistic. I figured it wasn't far from the truth, but looked around a little bit to verify. This three-year-old article over at the Motley Fool cites a survey survey by the Opinion Research Corporation for the Consumer Federation of America that found about one-quarter of those surveyed thought that winning the lottery was the most practical way to amass $200,000 or more. (Here is a summary of the survey.)
Since I'm a math-oriented guy, I thought it'd be neat to figure out the return on “investing” in Powerball® tickets. Tickets cost $1 each. The odds of winning different prizes, plus the average payout for each prize, are as follows (PB = red Powerball, W = white ball):
| If you match… | You win… | The odds are… | Avg payout per $1 spent… |
| PB | $3 | 1 in 61.74 | $0.0486 |
| PB + 1W | $4 | 1 in 123.48 | $0.0324 |
| PB + 2W | $7 | 1 in 787.17 | $0.0089 |
| 3W | $7 | 1 in 359.06 | $0.0195 |
| PB + 3W | $100 | 1 in 13,644 | $0.0073 |
| 4W | $100 | 1 in 19,030 | $0.0053 |
| PB + 4W | $10,000 | 1 in 723,144 | $0.0138 |
| 5W | $200,000 | 1 in 5,138,133 | $0.0389 |
| PB + 5W | $5,455,000 | 1 in 195,249,054 | $0.0279 |
| Any prize | — | 1 in 35.11 | $0.203 |
The five white ball + red Powerball win is the Jackpot. This varies from week to week and I calculated the payout by taking the sum of the cash payouts for all the Jackpots in 2008 (a little over half a billion dollars) and dividing by 104 (two drawings per week). The payout is about 20 cents for each dollars' worth of tickets bought, or a return of minus 80%. (Add a few percent perhaps if you take the annuity.)
The loss gets a little bit less if you chip in an extra buck per ticket to get the Multiplier. Each week the Multiplier is 2, 3, 4, or 5; the chance of each multiplier showing up is 25%. If a winning ticket is a Multiplier ticket, then the payouts (except the Jackpot) will be multiplied by the Multiplier. These tickets cost twice as much, but the average Multiplier is 3.5, which means that the payout of the first eight prizes is multiplied by 1.75. This ends up being a loss of “only” 67%.
Ok, that's pretty a bad return, as one should expect: the average lottery player should get taken for a ride. But how did the Standard and Poor's 500 Index do last year? It was pretty bad, too.
The S&P was 1,411.63 on January 4th, 2008. It was 931.80 on January 2nd, 2009, a loss of 34%.
So, investing in the S&P 500 was (on average) better than putting an equivalent amount of money into Powerball tickets. But certainly our investments can aspire to better things than just outperforming the lottery, can't they?
Great job on looking at the lotto 'returns'. It worries me to read that some people are still playing the lotto in this economy, but don't have ANY savings for a safety net.
Why people buy lottery tickets is one of those questions economists have been arguing about for a long time. It should be pretty obvious that they are a terrible deal, otherwise why would the states run them? And people seem to actually prefer the lotteries with very very long odds of giant payouts, rather than short odds of modest ones.
I think it is a symptom of innumeracy. People just can't wrap their heads around what 1 in 195,000,000 really means.
I did some quick math and found that the $1 spent on a lottery ticket biweekly for forty years put into a savings account instead with 5% compound interest would gross >$13,000. Not too shabby!
Amazing post. I must admit I play the lotto here and there but I never seem to win but then again, I can't win in the stock market either, so I don't know which one to choose 😉
I view the lottery as a tax on people who don't understand math. Where I live, it's the people who can least afford such poor odds that play the lottery the most!
I love the lottery. I just wish the money made by the states actually went to what they claimed they would and not pet projects. Keep paying my taxes dumb people!
Great post! I played lottery few times in past but now I just do not have time for that.
I've actually been playing the lottery pretty regularly for the past 6 months or so out of sheer boredom at work. Unlike most people who play the lotto, I've been keeping a detailed spreadsheet recording all activity. To summarize, I've spent roughly $300 on lotto tickets and I've recouped 64% of it. The ROI falls to lower than your estimate if you take out the one time I won $150.
If you were to play the lottery only when the pot exceeds $50 MM or something like that, the payout would look a little better, but then you run the additional risk of having multiple winners splitting the prize.
Personally, I'd rather take my 401K to Las Vegas and play craps with it.
I love craps! So far it's the one table game I've actually won at AND had fun.
I always say I'll play the lottery if it hits $100m, but never do. I bet even more will be playing due to the economy, further reducing your potential winnings.
It sure would be nice to win though.
the lottery is a hard game to win.. but often it is a better bet then casinos
good post
Can't beat savings accounts/CD's that don't eat the principal and you are guaranteed a return in these hard times. Of course, not a bad time to buy a few shares at depressed rates on quality companies either!
Wow great job on all this data. Lottery tickets are for people who are really bad at math. Most of the time the stockmarket makes money over the long haul.
Most people I know don't play the lottery because they think they'll get rich…they're just in love with the idea that they could get rich from it. It's the attraction to fantasy that gets them.