DQYDJ

  • About Us
    • Contact Us
    • Resources
    • Disclosures
  • Tools & Research
    • Stocks and Investments
    • Personal Finance
    • Economics
  • Blog
    • Investing
    • Economics
    • Personal Finance
      • Debt
    • Politics
    • Real Estate
    • Offbeat
      • Weekender

No, Business Insider, The Mega Millions Drawing Isn’t A Positive Expected Value. Here’s What You Need to Know.

Economics     December 17, 2013 by PK

In case you’ve been on the weird part of the internet today, you probably already know that the Mega Millions drawing’s jackpot tonight is for a prize of $636,000,000 and a cash option of $341,000,000.

I’ll admit shedding a single tear on behalf of math when reading Business Insider’s piece today on the Mega Millions having a positive expected value.  Folks, listen: there is no positive expected value in the Mega Millions tonight, nor will there be next time there is a massive prize.

We originally covered this in a post calculating the expected value for the last huge Mega Millions drawing, and we even followed it up with a calculator so you can determine what the expected value is for the Mega Millions yourself.  (Click it, it won’t hurt).

Here’s Where The Math is Wrong

Our calculation?  Here you go, from our Mega Millions expected value calculator:

Mega millions expected value on 12/17/2013We estimate that with every dollar you spend (and a 39.6% federal marginal tax rate and 5% state tax rate), you’re throwing 56 cents down the drain.  Get that?  EV = 44 cents per ticket.  That’s well below $1.00.

Even in a Randian fantasy with $0 federal and $0 state taxes (where do you live? Sealand?) you’d only have an expected value of 78 cents per ticket – essentially throwing away 22 cents in that fantasy land.

So I Don’t Have to Go to That Page and Read the Methodology, Explain it to Me Simply?

(This math is simplified – scroll to the end for the advanced [read: more correct, kinda] math).

Sure, here’s the TL;DR: if you’re going to use the $636,000,000 number you’re not comparing like quantities with the $1 you are spending on the ticket.

The Mega Millions pays you immediately then for 29 years after (0, 1, 2 …. 29 – not 30 years, basically), so to get from $341,000,000 to $636,000,000 we have to do some compounding – the math is:

rate = ( (future/present) ^ (1/ number of periods) ) – 1

or

rate = ( (636 / 341) ^ (1/29) ) – 1

rate = 2.1726%

Okay, but what does that mean?

It means you need to either use the $341,000,000 number when you do your calculations, or apply the compounding rate to your $1 – making each of your tickets actually cost $1.87 today.

Well, It’s Too Late Now.  I won.  Now What?

Take the cash.  I know that we used a 10% discount rate on our stock fundamental value calculator, but there’s a way easier trade to beat 2.17% – buying 30 year treasuries, which closed today at 3.88%.

You’re welcome.

Now: stop thinking you have a positive expected value.

(End of article)

Still Reading?  The Advanced Math.

If you are already convinced, here’s the minutiae on why the ‘take the cash’ option is better, but not by as much as estimated.  It’s also math on why your EV is even lower when you do the math with the $636M – your discount rate will end higher; you’ll see.

In the section above I did the math by ‘buying’ $636,000,000 to be paid out with $341,000,000 today.  That’s not correct, as our friend Jason Hull pointed out on Twitter (his site here).  He later sent me the page explaining how the payouts work, found here.

So, we can model this and find the internal rate of return to figure out what our ‘return’ would be.  To do this, we set up a spreadsheet like the following, with ‘$-341,000,000’ our initial ‘investment’ since we are assuming we’ll win (ha) and payments increasing 5% a year, including a payment which we get “today”:

Investment-$341,000,000.0012/17/13
0$9,572,712.7112/17/13
1$10,051,348.3512/17/14
2$10,553,915.7612/17/15
3$11,081,611.5512/17/16
4$11,635,692.1312/17/17
5$12,217,476.7412/17/18
6$12,828,350.5712/17/19
7$13,469,768.1012/17/20
8$14,143,256.5112/17/21
9$14,850,419.3312/17/22
10$15,592,940.3012/17/23
11$16,372,587.3112/17/24
12$17,191,216.6812/17/25
13$18,050,777.5112/17/26
14$18,953,316.3912/17/27
15$19,900,982.2112/17/28
16$20,896,031.3212/17/29
17$21,940,832.8812/17/30
18$23,037,874.5312/17/31
19$24,189,768.2612/17/32
20$25,399,256.6712/17/33
21$26,669,219.5012/17/34
22$28,002,680.4812/17/35
23$29,402,814.5012/17/36
24$30,872,955.2312/17/37
25$32,416,602.9912/17/38
26$34,037,433.1412/17/39
27$35,739,304.7912/17/40
28$37,526,270.0312/17/41
29$39,402,583.5312/17/42

So, in your favorite spreadsheet program, do the XIRR (or IRR, since it is uniform) on that and get: 3.80%.  A closer match to the 30 year bond, but it still reigns supreme (more on that in a second).  Also, you would do the original math using 3.80% versus $1 to come up with an actual discounted cost of $2.95 a ticket(!) today… so all the articles saying there is positive EV should use $2.95.  Isn’t finance fun?

Also, the annuity and the Treasury bond don’t just “wait” 30 (or 29) years to pay you off (that would be a ‘no coupon’ bond, if you’re paying attention) – they give you cash flows every year.  If you’re reading this site, I guarantee you’ll reinvest that money.  That means you’ll see somewhere north of 3.88% if you buy the 30 Year and reinvest when it pays coupons.  Please see our ten year Treasury coupon reinvestment calculator for details on why reinvested yields will be higher than effective yields.

Related Posts:

  1.   Adventures in Lottery Playing – What Was The Expected Value of Mega Millions Tickets?
  2.   The Saturday Powerball Drawing: You Do Not Have a Positive Expected Value!
  3.   Mega Millions Expected Value Calculator
  4.   Should Engineers and Business Majors Pay Higher Tuition?
  • Twitter Transparent PNG
  • Facebook Transparent PNG
  • LinkedIn Transparent PNG
  • Reddit Transparent PNG
  • twitter
  • facebook
  • linkedin
  • google+
  • reddit

Filed Under: Economics

Comments

  1. moneycone says

    Take the cash, always! I don’t think there is ever a story of someone not taking the cash!

    But good to know the math backing it up!

    • PK says

      While that’s true, I’m more concerned with the fact that people convinced themselves that it’s a good deal to buy a ticket. It was never a good deal… the expected value was always negative, as the odds of a split pot means the jackpot maxes out at around $450,000,000.

      • PK says

        Should say, “and” the odds. My chart is on thie piece if you scroll down: http://yourdayjob.net/mega-millions-expected-value-calculator/

      • moneycone says

        Good point! Never was much of a lottery-buying type!

      • Elroy says

        The better question is [….] what does one expect from winning the lottery? I’ve got a post coming up on the hedonic treadmill, and I link to an interesting lecture where they compare winning the lottery ($316MM opposed to $341MM) to becoming a paraplegic. Turns out, we would all want to win the lottery given those 2 choices, but reality is both parties are equally happy down the road.

        • PK says

          Interesting – maybe winning a few million in a subprize is better? No random relatives coming out of the woodwork as you’re a bit more out of the spotlight – I imagine that sort of pressure gets to a lot of winners.

  2. This Life On Purpose says

    We don’t pay taxes on lottery winnings in Canada. Canada = fantasyland?! haha but no, the math still doesn’t work out, and you are better off just investing your $1 than to buy a ticket.

    • PK says

      America’s Hat just gets more and more attractive to me by the day… but yeah, don’t even buy tickets. Funnily enough, I did a post on Canadian Gambling: http://yourdayjob.net/who-gambles-in-canada-gambling-stats-by-income/

  3. krantcents says

    There was a moment I thought about playing, but I didn’t! I wasn’t interested in losing the $2. If I won, I would definitely take the lump sum because I can invest it better than receiving payments.

    • PK says

      And.. you did win, roughly 56 cents a ticket!

Trackbacks

  1. Carnival of Personal Finance #434: The Happy Festivus Edition – The Holiday (Links) For the Rest of Us

Join Our Mailing List Today

ABOUT PK  1000 Posts

I turn caffeine into useful tools and interesting posts. I also designed (and started) Don't Quit Your Day Job...

Contact PK
Follow PK on Twitter

TRENDING

  • +287%   Should You Include Your Primary Home in Net Worth?
  • +140%   A Calculator: Income Distribution by Age for 2015 in the United States
  • +79%   Income by Age: How Income Changes and Increases Over a Career
  • +69%   Full-Time Individual Income Percentile Calculator for the United States in 2017
  • +56%   Nikkei Return Calculator, with Dividend Reinvestment
  • +47%   Correlation of Income and Net Worth for Age Groups in America in 2016

Featured Articles

  • Substitution vs. Income Effect (and its Implications)
  • Milton Friedman’s Permanent Income Hypothesis
  • Dollar Cost vs. Lump Sum Investing: Where Dollar Cost Averaging Fails.
  • 45-49 Years Old: The Peak of Your Financial Prowess
  • All About Credit Cards and the Perfect Credit Card Spending Strategy
  • The Four Pillars of Personal Finance

POPULAR  IN THE LAST WEEK

  • Income Percentile Calculator for 2017 US Data
    Economics
  • S&P 500 Return Calculator, with Dividend Reinvestment
    Investing
  • United States Net Worth Brackets, Percentiles, and Top One Percent in 2017
    Economics
  • Net Worth by Age Calculator for the United States
    Economics
  • Net Worth Percentile Calculator for the United States in 2017
    Economics

Recent Comments

  • Clint on Inflation Expectations as of 4/12/2018
  • PK on Inflation Expectations as of 4/12/2018
  • PK on American Retirement Savings by Age: Averages, Medians and Percentiles
  • Clint on Inflation Expectations as of 4/12/2018
  • David @ Zero Day Finance on American Retirement Savings by Age: Averages, Medians and Percentiles
  • PK on Average American Retirement Savings, Medians and Percentiles
  • Clint on Average American Retirement Savings, Medians and Percentiles
  • jim on Average American Retirement Savings, Medians and Percentiles

About DQYDJ

        

We're a finance blog with a twist: we write articles, but we also create calculators and visualizations to help you understand your finances and take control of your investments.

[ Read More About Us ]

Quick Links

  • Contact Us
  • Advertise on DQYDJ
  • Disclosures
  • Recent Posts
                 

Search DQYDJ

DQYDJ Categories

© Copyright 2018 DQYDJ.com