Nonetheless, this week’s record $500 million jackpot makes for an interesting mathematics exercise as those of us who don’t normally waste money on lottery tickets ask ourselves, “is it worth it to buy one”?

Odds vs Expected Return

The Mega Millions website very clearly gives the odds of winning each prize. If you buy a single $1 ticket, you have a 1/40 chance of winning any prize at all and a 1/175 million chance of winning the jackpot.

But a different and, perhaps, more meaningful question is the expected return on your “investment” of a $1 ticket. In computing the expected return, we weight the odds according to the prizes.

Note that “expected return” doesn’t actually mean that you “expect” to receive that particular dollar amount. For instance, if I were to offer you the option to flip a coin and if it comes up heads, I will give you $5 and if it comes up tails, I will give you $10, your “expected return” is $7.50, even though there is no chance whatsoever that you will receive that amount. Nor is “expected return” the same thing as “most likely return” — your most likely return on buying a lottery ticket is, of course, that you have just made a $1 donation to the government and will get nothing.

So, consider the eight lower prizes (we’ll look at the jackpot separately):

So not counting the jackpot, your expected return or average return on a one dollar Mega Millions lottery ticket is 18.2 cents.

Computing the Jackpot Expected Return

You might expect that since the jackpot for Friday’s drawing is $500 million that the expected return is 500,000,000/175,711,536, or, $2.85 on a $1 ticket. Unfortunately, this is not the case. There are three considerations that we need to make:

1. The cash option vs. the advertised jackpot
2. Taxes
3. The possibility of multiple winners

Cash Option vs. Advertised Jackpot

The first consideration is the most obvious – $500 million is the projected future value of investing $359 million in an annuity made up of ultra-safe government bonds that, as long as the U.S. doesn’t default on its debt, are pretty well guaranteed to pay out. Despite last year’s hysterics, the United States has never been in any serious jeopardy of defaulting on its debt (even if we don’t raise the debt ceiling at some point, tax revenue more than covers debt payments) and so as long as the country exists, this annuity is safe.

Nonetheless, it doesn’t make sense to use the annuity value in ROI (return on investment) calculations any more than it would make sense for your employer to quote your salary in terms of what it would be worth in 20 years if you invest it in a particular stock. So the “real” jackpot is $359 million.

So we might expect that the expecting return is $359,000,000/175,711,536, or, $2.04 on a $1 ticket — still a bargain. Unfortunately, we next need to consider taxes.

Taxes on Lottery Winnings

You will often read, even from supposedly reliable news outlets, that there is some 25% “gambling tax” and so you can expect 25% of your $359 million to go to Uncle Sam. That is not correct. The source of this confusion is that the IRS requires a 25% withholding on gambling proceeds over a certain amount, but the actual tax that you owe is not going to be 25%. Gambling proceeds are treated as ordinary income and if you hit the jackpot, that will put you into the top bracket, which is currently 35%. All income over $388,350 is taxed at 35% and so if you make $359 million, your tax is approximately $125.6 million.

Similarly, in Virginia, even though only 4% is withheld, gambling proceeds are ordinary income and Virginia’s top marginal rate is 5.75%. So if you were to win Mega Millions in Virginia, you can expect to pay a total of 40.75% in taxes, or, $146 million.

This tax, of course, may be reduced if you donate a portion of your winnings or invest them in a tax-deferred asset. But if you simply picked up a check, you would pay $146 million in taxes. So we’re going to consider $213 million as our “after tax” amount.

The possibility of multiple winners

Finally, we need to consider the very real likelihood that you will not be the only winner.

Let’s look at a simple case first. Suppose that you and a friend each pick try to guess a randomly generated number from one to ten. I think we would agree that each of you individually has a 1/10 chance of guessing right. But there is a 1/100 chance that you are BOTH going to be right. So, the odds would be:

• 1/100 = both right
• 9/100 = you and you only are right (1/10 – 1/100)
• 9/100 = your friend and only your friend is right
• 81/100 = you are both wrong

So it’s only slightly more complicated when we look at the lottery. Suppose that you and your friend both pick one random ticket:

• 1/(175 million)² = both win
• 1/(175 million) – 1/(175 million)² = you and you only win
• 1/(175 million) – 1/(175 million)² = your friend and only your friend wins
• (1/(175 million) – 1/(175 million)²)² = you both lose

Now, if only two people in the whole universe played the lottery, it would be essentially impossible for them both to win. But when hundreds of millions play, you are actually more likely to have multiple winners than to just have a single winner.

In calculating the odds of multiple winners vs a single winner, we use something called a Poisson distribution.

This table shows the odds of having a particular number of winners, given the number of people who play the lottery. So if 150 million tickets are sold, there is a 42.58% chance of having no winners, a 36.35% chance of having exactly one winner, etc.

But now we have to ask, how many people are playing? As is no doubt obvious, the number of players varies from week to week depending on the jackpot size. Smaller jackpots yield a small number of players and large jackpots yield a large number of players.

The lottery doesn’t tell us exactly how many tickets were sold, but we can estimate the number of players based on how many of the lower-level prizes were handed out. On the most recent drawing, 2.53 million tickets won the $2 prize for matching only the yellow ball, which has approximately 1/74.8 odds, so we can extrapolate that there were around 190 million tickets sold. 1.35 million tickets won the $3 prize (1/141 odds), which also comes out to around 190 million.

So for the recent drawings going back through the beginning of March, here are the numbers of tickets purchased we have seen:

Now, the way the estimated jackpot is computed is that it is based on the number of tickets that the lottery expects to be purchased (as opposed to basing it on the previous drawing’s sales and then using this drawing’s sales for next week). So extrapolating previous jackpots vs ticket sales, we can guess that with a $500 million advertised jackpot, Mega Millions is expecting around 350 million tickets to be sold.

So what is my expected return?

Plugging our ticket sales guestimate into our table above, we can see that there is a 27.18% chance of exactly one winner, a 27.07% chance of exactly two winners, etc.

So presupposing that you do possess the winning ticket (an event that has a 1/175711536 chance of happening), your expected prize, after taxes, is:

$213 million / * 27.18% +
$213 million / 2 * 27.07% +
$213 million / 3 * 17.97% +
$213 million / 4 * 8.95% +
$213 million / 5 * 3.57% +
$213 million / 6 * 1.18% +
$213 million / 7 * 0.34% +
$213 million / 8 * 0.08% +
$213 million / 9 * 0.02%

That adds up to $106.3 million. But we’re double-counting the 13.64% chance that nobody wins, so actually, it’s $123.1 million. (Remember, we’re presupposing you have the winning ticket … so we’re not interested in the possibility that nobody wins.)

So your expected return for the jackpot is 70.1 cents. Added to the cumulative expected return on all other prizes of 18.2 cents, for your “investment” of a $1 lottery ticket, your expected return is 88.3 cents for this Friday’s drawing.

I want massive regulations on whatever industry I’m in because my big business can absorb it and just raise prices, but it will drive the little guy out of business. It’s simple math – if the government requires every widget manufacturer to spend $50,000 on a widget disgronifier, a small widget company that only grosses a few hundred thousand dollars a year will be put out of business, but I can buy it without batting an eye. Then once the small guy is out of business, I’ll double prices and blame (rolls the dice) an earthquake in Asia or (rolls the dice) the South American stock market.

I want the government to raise taxes on all income over $1 million such that an accumulation of wealth is impossible. I’ve made my billions and don’t need any more income. I’m one of the richest (and therefore most powerful) people in the country and so I want to slam the door behind me. My power will never be challenged if it is impossible to ever accumulate as much money as I have.

I want capital gains taxes raised through the roof. If small startups can’t get venture capital money, then I never need to worry about someone competing with me.

And all the while, I get to propose these things and sound compassionate because I’m somehow on the side of the little guy. So keep on voting for Democrats and confiscatory taxes on the upper middle class – I’ll just stay uber-wealthy. If you’re a member of occupy this that, and the other, and you want higher taxes and bigger government, you’re doing nothing but giving the people you hate exactly what they want.

Photo credit: Tracy Olson

Rule #2: See rule #1.

Some sample FAQs to help you determine if the forwarded email is true:

Q: It sounds really bad, so it must be true, right?
A: It’s not true.

Q: It sounds just like the kind of thing those evil people in the political party I disagree with would do, so it’s probably true, right?
A: It’s not true.

Q: One of the guys who sent it said that he’s a doctor, lawyer, or friend of Bill Gates, so it’s true, right?
A: It’s not true.

Q: It was sent to me by a really smart person, so it’s true, right?
A: It’s not true.

Q: But it says that if I don’t forward it out, that I hate America, puppies, Christmas, and sick little kids?
A: It’s not true.

Q: But … but … but …
A: It’s not true.

A single person who makes $17725 (which equates to $8375 after deductions) will see their federal income taxes go from $837 to $1256. That’s a 50% tax increase on a person who is not exactly wealthy. A single person who makes $60K after deductions (equivalent to about $69350 if they take the standard deduction) will see their taxes go from $11181 to $12380. Do you really have an extra $1200 on hand to pay in taxes when we’re already in tough times?

Turbo Tax has a good summary of coming changes.  There are a lot of other tax increases coming that may affect you – like reducing the child tax credit and reducing the tuition tax credit. Capital gains and dividends taxes will also go up, further discouraging investment.

In terms of dollars, an ABC blog from last year said that these tax increases would represent $989 billion over ten years.  Do we really want to suck $100 billion out of the economy right now? Nancy Pelosi has the strange idea that unemployment benefits are a great stimulus to the economy.  It’s funny to hear Democrats argue that unemployment benefits stimulate growth, while tax cuts do not.  Rather, unemployment benefits discourage recipients from earnestly seeking a job and encourage those who are near retirement or otherwise looking to exit the labor force to instead pretend to look for a job just to collect a check.  When unemployment benefits ran out in June, the labor force actually shrunk by 652,000.  Those were 652,000 people who were looking for a job for the purposes of receiving unemployment, but once the check stopped, they stopped pretending to look.  The New York Times – not exactly a rightwing rag – had a blog entry about this in March.  The New York Times gets it, but Nancy Pelosi does not.

The President assures us that if we hadn’t spent trillions of dollars on pork projects for Democrat districts stimulus spending, we would have been even worse off.  Well, if this stimulus was so essential, it’s even more essential that we don’t rip hundreds or thousands of dollars out of the hands of ordinary Americans.  Again, we’re not talking about tax increases on those evil rich people the media loves to demonize – we’re talking about tax increases on everyone – including the poor and middle class.  Really, it’s a disproportional increase.  If you make some arbitrarily large amount of money ($1 billion) your effective tax rate goes from 35% (well, 34.999%) to 39.6%.  That’s an increase of 13%.  If you make $17725 – less than 200% of poverty – your income taxes go up 50%.

(If you’re curious how much your income taxes will go up, you can look at this site for the current marginal rates.  For 2011, the 10% rate goes away, the 15% rate stays the same, 25% goes to 28%, 28% goes to 31%, 33% goes to 36%, and 35% goes to 39.6%.  The cutoffs for each bracket will probably not change significantly – they are inflation-indexed and there isn’t any inflation right now.  Obviously, this does not include tax changes not tied to the income tax rate.)

Our current fiscal path is unsustainable.  Raising taxes during a recession is insanity.  We need a congress that doesn’t believe the lie that the government can tax and spend the country into prosperity.  I hate to say I told you so about Obama, but, well, I told you so.  We’re on an unsustainable path, but that can be changed.  I have no particular love for the Republican party – I don’t think anyone can deny that one-party rule in the 2000s was a disaster.  But one-party rule on the other side is an even bigger disaster.  I hope and pray that it’s not too late to reverse our path.

“MVP Level” donors received a commemorative “100th year of Scouting” football, which Coach autographed on the spot.

TIDEWATER COUNCIL

BOY SCOUTS OF AMERICA

BREAKFAST OF CHAMPIONS

Tuesday, March 23, 2010 7:15 AM

Virginia Beach Convention Center
1000 19th Street, Virginia Beach, VA

Featuring:
FRANK BEAMER
Head Football Coach of Virginia Tech
Emceeing the event is WVEC-TV 13 Sports Director Scott Cash

The Breakfast of Champions is a fundraising event designed to honor and support the efforts of over 4,000 adult volunteers who provide a quality year-round Scouting program to more than 9,000 Hampton Roads youth.

All proceeds benefit the Tidewater Council, Boy Scouts of America.

IT’S FOOTBALL TIME IN HAMPTON ROADS

THE THROW…

March 23, 2010 marks the 10th Annual Tidewater Council, Boy Scouts of America’s Breakfast of Champions. Game day starts with breakfast at 7:15 AM leading up to this year’s featured speaker, Virginia Tech coach Frank Beamer!

THE TOUCHDOWN…

The Breakfast of Champions is a unique fundraising event in that there is no ticket price for attendance. Rather, attendees come to the breakfast, hear a brief story of Scouting and enjoy the morning with featured speaker Frank Beamer. Attendees are asked to make a contribution to Scouting of whatever they feel comfortable giving. Because most people wait until the day of the breakfast to make their donation, a Player’s Scorecard (Donation Form) is available at each place setting. There are several suggested giving levels provided on this form, the bottom line request being $167, the cost to support one youth in Scouting for one year. As a special recognition, anyone contributing $365 or more will receive a football to be autographed by Coach Beamer at the event. The minimum contribution to attend the breakfast should be $50.00 to cover the cost of the event per person.

TEAM STATS

As you probably know, the mission of the Tidewater Council is to provide a quality year-round Scouting program to our over 9,000 youth, their parents and over 4,000 adult volunteers throughout Hampton Roads. What you may not know is that donations from the community are the Tidewater Council’s primary funding source for operations. In short, this mission cannot survive without each of you!

For further information

• For more about the event, including how to become a STAR PLAYER, please see the Star Players Handbook
• To make your gift to support the work of the Boy Scouts, please see the Donation form
• Please contact Danielle Hughes at 757-534-8500 or danielle.hughes@scouting.org for more information

Different people are of different opinions about whether or not we are better off, if we lose to GT, with playing the opening round game.  I’m of the opinion we are not – we are going to get little, if any credit from the NCAA for beating the last place team and a loss would absolutely ensure we make a third straight NIT trip.

My personal opinion is that with a win over GT, we’re in and with a loss, we would need to make it to the finals in the ACC tournament.

Below, for anyone who really cares, are all of the scenarios:

Scenario #1: VT over GT and Miami over FSU

If Virginia Tech wins @Georgia Tech this weekend, and Florida State LOSES @Miami, we will finish third.  After our first round bye, we will play the winner of the 6-11 game.  In this scenario, North Carolina would most likely finish #11 and Wake Forest would finish #6.  So we would get the winner of that game.

Scenario #2: VT over GT and FSU over Miami

In this scenario, we would finish fourth and would play the winner of the 5-12 game.  The 12-seed is going to be Miami in this scenario and the 5-seed would be the winner of Saturday night’s game between Clemson and Wake Forest.

Scenario #3: GT over VT, Miami over FSU, and WFU over Clemson

In a four-way tie among VT, GT, FSU, and Clemson, Tech would finish fourth in the conference and again, play the winner of the 5-12 game.  Florida State, who beat Virginia Tech in the only meeting of the two teams this year, would be our opponent.  Either North Carolina State or Miami would be the 12-seed.

Scenario #4: GT over VT, Clemson over WFU

Regardless of the outcome of FSU’s game with Miami we would finish fifth.  Our opening round game would be against either by the NCSU or Miami and if we win this opening round game, we would get a rematch with FSU.

Scenario #5: GT over VT, FSU over Miami, WFU over Clemson

Tech would finish in a three-way tie for fourth with Clemson and Wake, having beaten both teams earlier in the season.  Tech would get the 4-seed and would face the winner of #5 Wake Forest or #12 NCSU or Miami.

According to Wikipedia, WordPress is used on 202 million websites. And, as we all know, millions of anonymous teenage kids slouching towards an encyclopedia are never wrong.  So what’s one more?  202 million of us out there think we have something worth saying.  Make that 202 million and one.