Are you thinking about buying a 1 in 302,575,350 chance to win a $1.6+ billion jackpot in the Mega Millions lottery today?
Mega Millions jackpot enters ‘uncharted territory’ at record $1.6 billion
Yes, that headline is correct: The Mega Millions jackpot is at $1.6 billion. With a B.
All eyes were on the latest drawing Friday night, when the jackpot was at an already mind-boggling $1 billion. However, with no ticket matching all six numbers drawn — 15, 23, 53, 65, 70 and Mega Ball 7 — the grand prize now swells to $1.6 billion....
The estimated cash option for a $1.6 billion jackpot — should a winner choose to take a one-time lump sum payment instead of annual payouts over 30 years — is about $905 million, according to Mega Millions officials.
That's quite a lot of money, which will very likely entice a lot of Americans who normally don't consider playing the lottery into the mix for the grand prize in tonight's Mega Millions lottery drawing. To give you an idea of how stiff the competition will be in the Tuesday evening drawing, about 57% (or 172,467,950) of the 302,575,350 possible combinations of numbers that could be played in the Friday, 19 October 2018 drawing were played, when only a $1 billion jackpot was up for grabs. And now with an even bigger prize at stake, it would be a safe bet that an even larger percentage of all the possible number combinations will be played in the next drawing.
But is the jackpot large enough to be worth your $2.00 to buy one chance to pick win the jackpot? Or to be worth sharing in winning the jackpot if there is more than one player who has also picked the winning numbers?
There are two big factors that factor into the answe to those questions: the odds of winning and the amount of taxes that you would have to pay on the prize you might win. In the following tool, we've plugged in the numbers that are projected to apply for Mega Millions' record high jackpot drawing on Tuesday, 23 October 2018, but you can change it to apply to any lottery drawing. If you're considering playing the Powerball lottery, whose own grand prize in its next drawing on Wednesday, 24 October 2018 will have at least $620 million at stake for whoever beats its 1 in 292,201,338 odds of winning, we another version of this tool set up with its default numbers to answer the same questions. [If you're reading this article on a site that republishes our RSS news feed, please click here to access a working version of the tool.]
In the tool above, we've set the federal income tax rate to 37%, which is the maximum income tax rate that applies for 2018. We've set the state and local income tax rates to 0%, which you'll need to change if you live in a state and/or city and/or county that taxes lottery winnings.
Running the default numbers we've entered, we find that the projected jackpot of $1.6+ billion is greater than the "magic" jackpot of $961 million that would make the Mega Millions lottery worth paying $2 for a ticket to play today. At the same time, because the jackpot is currently less than $1.82 billion (double the tool's magic jackpot figure), it's not worth buying a second ticket to play, nor is it at a level that would make it worth paying $2 to play only to have to share the grand prize with one or more additional winners who might pick the same winning numbers.
On the 1 in 302,575,350 chance that you do win, you'll have some decisions to make about how you want to collect your winnings. Be sure to check out this article to consider the relative merits of either taking the lump sum or of taking the annuity payout over 30 years.
Labels: lottery, personal finance, risk, tool
In 2008, Arizona became the first state in the U.S. to implement photo speed enforcement, where high speed cameras are used to photograph both the driver and license plates of vehicles exceeding posted speed limits on the state's roads.
The way the system works, the photos of speeding vehicles are examined by the contractor who operates the photo radar system to determine if the images are clear enough for an identification of both driver and vehicle to be made. If so, a notice of violation is mailed to the vehicle's registered owner, requesting that they waive their rights to contest the violation and pay a fine of $181.50.
That number is important, because that $181.50 becomes the prize in an unusual kind of lottery for drivers who decline to waive their rights.
The "lottery" works because if a month passes after the notice is mailed to the vehicle owner, who then declines to waive their rights and pay the $181.50 fine, the state's law requires that they be officially served notice of the violation in person. If they are not notified within 120 days of the issuance of the original notice, the speeding ticket, and the liability for paying the fine associated with it, goes away. Entirely.
If however they are served notice, then in addition to the fine of $181.50, they are also responsible for paying administration fees of $25.00 on top of it.
That $25.00 then is the cost of choosing to play what we'll call the Arizona State Photo Radar Lottery.
Here's what makes the lottery possible. There are so many potential photo speed enforcement violations being processed in the state at any given time that a good portion of those who have been mailed a notice of violation are never served notice in person within the period of time the state's law requires.
The Phoenix New Times reports that the odds of not being served notice in person are about 1 in 4.
Are those odds good enough to justify disregarding the original notice of violation for Arizona's speeders? After all, once a vehicle owner is served a notice of violation in person, they've lost the lottery, so to speak. They must pay the fine.
To find out, we've modified our tool for determining when it might make sense to buy a regular lottery ticket, and entered the relevant numbers into it. As with all our tools, you're welcome to change the values to run whatever scenario you wish. For the Arizona State Photo Enforcement Lottery however, we'll have more comments below the tool....
Using the default data for Arizona, we see that with a 1 in 4 chance of not being served in person should the registered vehicle owner choose to ignore the original notice of speeding violation, it makes more sense for them to risk the $25.00 additional fee to gain the chance of not having to pay $181.50. We find that with the same odds, the fine would have to be less than $100 for it to be more worthwhile to simply pay the fine.
We infer from this finding that the state of Arizona got greedy when setting the amount of the fine for photo speed enforcement.
It then comes as almost no surprise to find that Arizona drivers have largely chosen to ignore mailed notices of violation for speeding. As of June 2009, just 24% of drivers in the state who had been mailed such notices had paid them, down from the figure of 38% from when the system first went into operation in October 2008.
From a public policy perspective, if Arizona chooses to continue operating its system of photo enforcement, we find that it either needs to lower the fine for speeding below $100 or lower the odds of "winning" by increasing the number of people served in person.
Alternatively, the state could increase the amount of fees it charges to serve potential violators in person. We note however that this latter change would carry with it the unintended consequence of effectively increasing the amount of the "prize" to be won by ignoring the mailed notices of violation.
Unless and until such changes are made, we should expect that Arizona drivers will continue to choose to play the state's unofficial lottery.
With too few people playing the lotteries in California on account of too many people winning smaller jackpots too often, and so much of the state's finances dependent upon its take from the lottery, we thought we'd do our part and help spark lottery fever in the Golden State!
As we've previously observed, people really don't get excited about the lottery until the grand prize reaches a considerable value - and we've observed that the magic number for a lottery jackpot seems to be tied to three things: the cost of a ticket, the odds of winning the jackpot and the percentage of the winnings that the winner(s) will have to pay in taxes.
Now, we realize that these factors go far beyond California, so we thought we'd modify the previous generation of our lottery tool to go one step further. Because we really find that it's a hassle to look up the odds of winning the grand prize in the lottery from umpteen different state and lottery web sites, we thought we'd just look at the games themselves and calculate the odds "live"! All you need to do is to enter the numbers that matter for your preferred lottery game, and we'll work out all the rest: the odds of winning, and most importantly, the magic jackpot value for which it's worthwhile to buy a ticket (and where the math says that "lottery fever" really begins.)
And there you have it! The default data for our tool above is for California's Super Lotto Plus game, but you can easily adapt it for whatever typical lottery you might find throughout the U.S. (and many places throughout the world.) As a special note, California does not levy its state income tax against lottery winnings. This is not true of most (but not all) states!
Now all you have to do is wait until the grand prize in your lottery of interest gets above the Magic Jackpot Number. Otherwise, it just isn't mathematically becoming to get overly excited about the lottery....
About the Tool
Our tool above can help you find the odds of winning a typical lottery, including the kind with a Power or Mega ball. In the case where the lottery you're running numbers for doesn't have a Powerball or MegaBall option, just enter 0 and 0 for this set of numbers.
In the math behind the tool, we assume that the sequence in which the numbers are drawn is not a factor in determining the winner. This increases the odds of winning considerably over a lottery in which the order the numbers are drawn matters.
California has a problem. Not enough people are playing the state lottery because too many people are winning. From the Contra Costa Times:
... players haven't won any monster jackpots lately despite California's much-touted entrance into Mega Millions in mid-2005.
Lottery officials said the problem that is hurting their operation and allocations of revenue to schools is puzzling -- there just haven't been any huge jackpots.
At an unusually fast pace, players have been nabbing Mega Millions and in-state Super Lotto prizes while they are still relatively small and before they can build up.
[snip]
During the last half of 2006, there was an "unusual absence" or "drought" of large jackpots to fuel "lotto mania" -- ticket-buying sprees that bolster revenue for the state agency that runs on a July 1 to June 30 fiscal year, according to lottery spokesman Rob McAndrews.
"Jackpot levels are out of the lottery's control and have been significantly below average this year," the Lottery Commission said in a statement.
This "unusually" fast pace of winning would seem to be a good thing, but it isn't working out that way. With so many smaller jackpots, fewer people are playing the lottery, which is sharply reducing the money the state's lottery fund was projected to provide to California's schools. The state's lottery commission is projecting that it will collect substantially less revenue from lower ticket sales:
The panel, largely due to drops in lotto game sales, lowered projected 2006-07 revenue from $3.6 billion to $3.2 billion.
It's the first such mid-year change in a decade and follows a record sales year in 2005-06 of nearly $3.6 billion.
At the outset of Mega Millions participation, there were jackpots of $170 million, $258 million and $315 million. But recently, there have been fewer attention-grabbing prizes.
As a result, public schools -- which are required to get at least 34 percent of sales -- will receive less.
Education will get an estimated $1.13 billion -- $136 million less than last year.
But, get this, apparently state-sponsored gambling has some unintended consequences beyond not meeting education funding projections from poor lottery ticket sales! It turns out that legalized gambling increases the number of people who have gambling problems.
This presents a special problem for the state, which the California Research Bureau, having been commissioned by the State Attorney General's office, recently reported to a state senate committee:
The report found California's efforts to deal with gambling-related problems is inadequate and underfunded.
It also suggested the government's slice of revenue from gambling operations should be weighed against the true costs of the woes it causes -- primarily those related to problem gamblers.
The report provides information for that comparison.
The government makes a few billion dollars a year -- at best -- on its cut of gambling revenues.
Meanwhile, setting aside the expenses of imprisoning those who commit crimes and other liabilities, problem gamblers cost California about $1 billion annually in jobless benefits, welfare, health care and bankruptcies alone.
So, in addition to not providing enough funding for the state's education system, gaming in California costs the state's taxpayers money - and should cost more if the state were adequately meeting the needs of the people with gambling-related problems.
Who's the big loser in all this? It would seem that the California taxpayers are the ones on the hook. It would also seem that the politician's dream funding device of collecting revenue through lotteries and the state's take of gambling revenues, without either controlling spending or increasing more stable forms of revenue, isn't all it's cracked up to be.
That means the taxpayers are likely not going to get the things they were promised for their tax dollars. And if they do, then a growing problem that was made worse by the state and who's solution is already underfunded by the state will be left unattended and will only continue to get worse.
But Californians can always hope that maybe a round of lottery fever will fix the whole thing....
Labels: lottery
The conventional wisdom, where the lottery is concerned, is that it's a fool's game. We here at Political Calculations have a different view. We think it's a fool's game up until the jackpots get really gi-normous (how do you spell that anyway?!)
The real question isn't about whether or not you should consider playing the lottery, but instead how huge does the grand prize need to be to have the potential for winning the jackpot to be worth the cost of playing the game? And that's where our tools come in - we can work out just what the jackpot has to be to worth the price of a single ticket!
But that's not all - we can also find out whether it would make more sense for the winner of that grand prize to take the money as a lump sum or have it paid out over a number of years!
| Playing the Lottery |
|---|
| Subcategory | Title | Description |
|---|---|---|
| Cost Benefit | The Cost of Risk vs. Benefit | Our first cut at finding the prize amount for making the lottery worth the cost of playing. Odd, in that the same math can be used to determine whether the remote benefit of a given medical procedure is worth its cost! |
| Cost Benefit | Revisiting the Lottery | Our improved tool for finding the magic jackpot number that would make the lottery worth playing! The only trick is to not play at all until it hits the big number.... |
| Getting the Payout | The Lottery Winner's Dilemma | Maybe you've won the lottery, or maybe you've just come into an unexpected windfall with different payout options. Either way, our tool can help you decide which is better: taking the money over time or as a lump sum today. |
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Labels: lottery
Have you just won the lottery? Or maybe you've come into some other kind of windfall where you now face the same dilemma that the lottery winner does: should you take the money all at once or spread out over a number of years?
The key to answering this question lies in comparing the effective rates of return that you could receive from investing the amount of the lump sum against what you would be getting if you opted for the annual payout plan. The best choice is to select the option that provides a higher rate of return.
The problem though is that while it's pretty easy to find out what a typical range of annualized rates of return are for a typical investment in the stock market, it's not so easy to figure out what interest rate you're getting from the annual payment option, even though you know how much it will pay out each year and how many years the money will be paid out. The reason why is because the math it takes to get the answer is horrendous! (And we're not even factoring in taxes!)
That's why we here at Political Calculations' have stepped up to provide our newest tool, which you may use to find that effective rate of interest! Just enter the amount of the lump sum payout, the amount of the annual payments you would receive and the number of years the payments would be made - we'll take care of the rest! (Warning: It's best to use actual numbers rather than guessing - it doesn't take much to throw the results out of range!)
Now, all you have to do is to compare this rate of return against the historical best, worst and average rates of return from an investment in the stock market. For the 20 year payout period default entry in the tool above, these rates of return for an investment in the S&P 500 index are:
- Worst case: +1.6%
- Average: +9.4%
- Best case: +19.2%
The figure to use for comparison is the average rate of return - the best and worst rates of return are provided simply to illustrate the extreme ends of the possible range.
HT: Oak Road Systems for the math!
Previously on Political Calculations
- Revisiting the Lottery
Our improved tool for determining what the prize needs to be to make the lottery worth playing!
- The Cost of Risk vs. Benefit
- Our original tool for finding whether the benefit (the grand prize in the lottery) is worth the price of a ticket when the odds are taken into account.
A conversation recently overheard at a gas station:
Man 1: Hang on, I'm going to get a lottery ticket.
Man 2: Okay. Hey, what's it at?
Man 1: It's like over $100 million. Want any?
Man 2: No. I only get interested when it's over $200 million.
So much for lottery fever, right? Do you remember when a prize of 100 million dollars would have people lining up wherever lottery tickets were sold, and even streaming across state lines to where they could play the lottery for that kind of prize? What's happened? Why don't we see that kind of frenzy anymore when the lottery reaches that level?
Not that long ago, I looked at the cost of risk versus the value of the benefit for taking the risk, and noted that the math involved for deciding whether or not to take a risk would be ideal for deciding whether or not to play the lottery. Using the tool I created, I found that for a $1.00 ticket, the amount of the grand prize had to be at least equal to the odds for winning it. In the case of the Powerball lottery, that means the grand prize has to be at least worth $120,526,660 to make the value of the benefit worth the $1.00 cost of the risk. The table below has the odds for the Powerball lottery for all its prizes:
| Powerball Odds | ||
|---|---|---|
| Match | Prize ($USD) | Odds of Winning |
| 5 Regular + Powerball | Grand Prize | 1 in 120526770 |
| 5 Regular | $100,000 | 1 in 2939677 |
| 4 Regular + Powerball | $5,000 | 1 in 502195 |
| 4 Regular | $100 | 1 in 12249 |
| 3 Regular + Powerball | $100 | 1 in 10685 |
| 3 Regular | $7 | 1 in 261 |
| 2 Regular + Powerball | $7 | 1 in 697 |
| 1 Regular + Powerball | $4 | 1 in 124 |
| Powerball Only | $3 | 1 in 70 |
| Any Winning Combination | $??? | 1 in 36 |
So, why don't people get excited anymore when the prize levels get to the level where it would seem that the grand prize makes it worth taking the $1.00 risk? Are people really that blase' about the lottery these days? After thinking about it for a bit, one possible answer for the apparent apathy came screaming into my head: taxes!
Here's my thinking: income taxes substantially reduce the value of the benefit for the lottery's higher dollar prize winners. Winners of the grand prize will most likely have their winnings taxed at the highest income bracket levels, so to make the value of the benefit more compelling, the grand prize has to be much higher. This higher level will be directly related to the marginal tax rate that coincides with the amount of the prize.
So, I re-engineered my original calculator to directly solve for the value of the benefit that justifies the cost of the risk with the given odds and the federal, state and local income tax rates that may apply for the user. I've also simplified the interface so users may directly enter the odds of winning without having to enter a formula. You may alter the data to examine whether the grand prize of the lottery in your part of the world is worth playing:
Using this new calculator with the odds of winning the grand prize for the Powerball lottery and the federal, state and local maximum income tax rates given as default values, we find the the amount of the grand prize that makes the lottery worth the cost of taking the $1.00 risk is $213,321,717 - strangely near the level that Man 2 in the conversation I overheard indicated it would have to be for him to be interested in playing. It may just be coincidence, but it makes me wonder if people might naturally be finding their way to the "optimum" risk level in deciding what values justify the cost of taking this kind of risk. Definately food for thought.
Welcome to the blogosphere's toolchest! Here, unlike other blogs dedicated to analyzing current events, we create easy-to-use, simple tools to do the math related to them so you can get in on the action too! If you would like to learn more about these tools, or if you would like to contribute ideas to develop for this blog, please e-mail us at:
ironman at politicalcalculations
Thanks in advance!
Closing values for previous trading day.
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