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Wednesday, December 31, 2008

How 2009 Powerball Changes Effect You

Introduction
In August 2008, the MUSL announced that the State of Florida would be joining the Powerball lottery. With the increased population of new players, Powerball expanded the set of white ball numbers and decreased the number of red Powerballs, in order to make the game more attractive. The minimum jackpot will be increased, and for those who purchase the Power Play Option, the second prize of matching all 5 white balls will be fixed at $1 million.

Tickets for the new Powerball format will go on sale on Sunday January 4, 2009, and the first drawing will be held on Wednesday January 7, 2009.

While players should be excited about these new changes, they should understand that this new format:

Benefits the Powerball States

Not the Players!


Summary of Publicized Changes
First, lets review the Powerball changes that will become effective in January.
  • White Balls increased from 55 to 59
  • Red Powerballs decreased from 42 to 39
  • Minimum annuity jackpot increased from $15 to $20 Million
  • Powerplay Match 5 multiplier (5+0) fixed at 5X, payable in $1 million cash
  • Chances of winning the jackpot increased to 195.2 million
  • Overall odds of winning any prize decreased to 35.1
  • Jackpot pool percentage increased from 30.3% to 32.5%.
Additionally, certain things will not change. The price per ticket will remain at $1 each. The prize payouts and combination structure will remain as is. The Power Play Option will continue to cost $1, and the bottom seven prize levels will still be drawn with values 2X to 5X. Lastgly, the annuity payment structure remains fixed.


Combination Changes
Table PB09-1 summarizes combinatorial changes implied by the changes in the quantity of white and red balls. As shown, the Powerballs decrease from 42 to 39 balls, a 7.1 decrease. At the same time, the white balls increase from 55 to 59, a 7.3% increase. This appears to be a net wash.

However, the number of white ball combinations has increased from 3.5 million to 5.0 million, which is a 43.9% increase. But because the Powerballs decreased, the total number of all 6 number combinations increased only by 49 million, or 33.6%.

Table PB09-1: Combination Changes
Item New
Matrix
Old
Matrix
Change Pct
Change
Dir
Tot Combos 195,249,054 146,107,962 49,141,092 33.6%
Powerballs 39 42 -3 -7.1%
White Balls 59 55 4 7.3%
5-Number Combos 5,006,386 3,478,761 1,527,625 43.9%



Winners Changes
Since the winning prize structure remains the same, the new format will produce more individual winners. While the number of combinations increased by 33.6%, the total number of winners increases by 39.3%. This is a 6.0% advantage for the players.

At the same time, the number of losers increases by 33.5%, about the same as the increase in combinations.

Further, the overall chances of winning any prize decrease from 36.6 to 35.1, which is 4.1% advantage for the players. This is reinforced by the fact that the percent of winners also increases by 4.4%.

Table PB09-2: Winners Chances
Item New
Matrix
Old
Matrix
Change Pct
Change
Dir
Tot Winners 5,560,464 3,991,302 1,569,162 39.3%
Tot Losers 189,688,590 142,116,660 47,571,930 33.5%
Overall Chances 35.11 36.61 -1.50 -4.1%
Pct Winners 2.85% 2.73% 0.12% 4.4%


Thus far, it appears that players will benefit from the game format changes.


Payout Information
But reviewing the payout information presented in Table PB09-3 below, one can begin to understand why the players do not really benefit. In the new format, $54.1 million will be returned to the players. This is only a 23.5% increase. Remembering that the total number of combinations increased by 33.6%, it becomes apparent that a full 10.1% of the new money raised remains within the Powerball organization. Since the number of combinations increased by 49.1 million and each combination represents a dollar, we quickly see that $4.9 million extra goes to Powerball, not the players.


This is reinforced by reviewing the Average Ticket Win, which at $9.73 (verses $10.97) is a 11.3% drop. Both of which re-iterate that players receive less money in the new game.

Table PB09-3: Payout Info
Item New
Matrix
Old
Matrix
Change Pct
Change
Dir
Tot Payout $54,112,290 $43,800,030 $10,312,260 23.5%
Avg Tkt Win $9.73 $10.97 -$1.24 -11.3%
Return per $ $0.28 $0.30 -$0.02 -6.7%
Jackpot/Odds $569,577 $409,763 $159,814 39.0%
Jackpot Parity $161,136,764 $117,307,932 $43,828,832 37.4%


Additionally, the Jackpot/Odds and Jackpot Parity percent changes of 39.0% and 37.4% indicate growth that exceeds the 33.6% increase in new combinations. Should the Minimum Jackpot be greater, these would be more in line, and help to benefit the player. But, since the Jackpot is fixed at $20 million, overall payouts to the players is minimized.


Power Play Jackpot Breakeven
Lastly, for completeness, the increase in combinations and payouts implies that the Power Play Jackpot Breakeven level is increased as well. From Table PB09-4, we learn that players should purchase the Power Play Option whenever the Jackpot is below $62.6 million. Above that level, players should always skip this option and go for the Jackpot itself by spending the additional dollar on an individual ticket.

Table PB09-4: Power Play Breakeven
Item New
Matrix
Old
Matrix
Change Pct
Change
Dir
Tot Payout $62,568,435 $43,200,045 $19,368,390 44.8%




Conclusion
While the new Powerball matrix format increases a players chance of winning a prize by increasing the number of winners, the amount of money returned back to the players is proportionately lower than the existing game. As we have seen, the average winning ticket will now be $9.73, which is 11.3% lower than present. Further, the actual percent of amount of money is 10% less than what has been increased.

Since nearly $5.0 million extra will be retained by Powerball, we believe the new format benefits the Lottery Organization rather than the players. To remain fair, either the minimum jackpot should have been set at $25 million, or lower tier prize payouts should have been increased.

In a year when lottery sales have declined, it is not surprising that the Powerball organizers revised the format in order to increase their retained profits.

While the lure of winning a minimum of $20 million is nothing to sneeze about, players should understand who profits and who loses.

We hope you have found this study to be informative.

Learn More
To learn more about this subject, visit our in-depth pages that provide the detailed numbers behind each of these options.

Focus for February: Oddities in the UK Lotto



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Saturday, December 13, 2008

November Entrecard Droppers

Merry Christmas
&
Happy New Year
To all of our Readers.

With special thanks to our dedicated daily visitors, and especially our Top 10 Entrecard droppers in the month of November 2008:


November EC Dropper Awards

Small Town Mommy31
BMWF1Blog31
Bingo Games and Women CommunityBingo Games and Women Community31
Tiddly Winks29
Lottery Power Picks News/Blog28
iWalk,U2?28
My note's27
San Diego Backroads27
In The Presence of Vultures27
THE WORLD ACCORDING TO JAY27

We hope your Holidays are Joyous.

Noel

Friday, November 14, 2008

Top Entrecard Droppers

We sincerely thank all of you who have visited and dropped on our site each day. In particular, we wish to publicize our Top 10 visitors:


October EC Dropper Awards

Small Town Mommy31
Alluricious Blog30
From the Eyes of my Heart30
Metallman's Reverie30
Lottery Power Picks News/Blog29
512 Apple Memo28
Blog Contest Station28
Septagon Studios Inc News Blog27
San Diego Backroads27
Money Maker Times27


In addition, we wish to thank everyone else who took the time to visit and drop on our site. We hope to continue seeing all of you every day possible.

Thanks Again

Friday, October 31, 2008

Florida Lotto Plus Analysis. Should you buy the $2 or $3 Option?

Introduction
The Florida Lottery enhanced the Florida Lotto by introducing the $2 and $3 LOTTO PLUS jackpot levels on March 2, 2008. This gives players of that game the option to "Super Size" their jackpot winnings. This means that rather than strictly buying a single $1 ticket, players can instead:
  • Spend $2 per ticket, and increase the base jackpot payout by $10 Million if that combination wins; or
  • Spend $3 per ticket, and increase the base jackpot payout by $25 Million if that combination wins.
Shortly after these options became available, the first $2 Lotto Plus jackpot winner increased his winnings from $6 million to $16 million in the May 10th 2008 drawing. However, since that time to date, there have been no additional Lotto Plus winners.

The lure of increasing the size of the Jackpot purse for only $1 or $2 more seems to be very attractive on the surface. Thus, we asked ourselves two questions:

Would We Buy the Lotto Plus Option?
And, If so, Which One?

Our analysis found that:

Yes, We Would Buy
the Lotto Plus Option
in Certain Instances

but it would depend on the size of the Base Jackpot being offered. As for which one to buy, we found that:

The $3 Lotto Plus Option is the Best
(If You Can Afford It)

How would you know when to buy the Florida Lotto Plus Option?
You should always buy the plus option whenever the current jackpot value is below its Jackpot Breakeven level.
  • For $2 Lotto Plus, Breakeven is $5.8 million: Buy the $2 Lotto Plus Option whenever the Jackpot is below this value. Never above this. Buy 2 tickets instead.
  • For $3 Lotto Plus, Breakeven is $8.3 million: Buy the $3 Lotto Plus Option whenever the Jackpot is below this value. Never above this. Buy 3 tickets instead.
Why is that?
The reason these levels can be calculated is because ONLY the Jackpot prize is increased for those winners who purchased the option. No other lower level prizes are increased. So, as the Jackpot increases above its minimum, only the probability weighted amount of jackpot money returned to players increases. At some point, which we call Jackpot Breakeven, the Single $1 Ticket jackpot return outweighs the increased Jackpot payments per dollar spent. Once this point is reached, buying the Lotto Plus option is not a good investment. Remember, because the option costs $1 or $2 more, it is necessary to divide these probability weighted returns by 2 or 3 before comparing them to single $1 tickets. When the jackpot is above the breakeven level, the per dollar return of Florida Lotto Plus tickets becomes less and less valuable compared to that of a regular $1 ticket.

As lottery players, we want to play the option that returns the most money back to us, the players. As you will see below, your option changes depending on the jackpot level.


Florida Lotto Plus
When a player buys the Florida Lotto Plus Option only the Jackpot will be increased. For the $2 option, jackpot payout increases by $10 Million. For the $3 option, jackpot payout increases by $25 Million.

However, the Florida Lotto has 22,957,480 unique combinations. Only one of these will be selected in any particular drawing. Excluding duplicates, there will be only 1 winning combination.

To play, the Florida Lotto requires a player to select 6 numbers from a set of 53 (there is no bonus ball). Prizes are only paid out to players who correctly match 3, 4, 5, or 6 of the numbers. This means that of the nearly 23 million combinations, only 340,798 will return any prize payout.

The graph below illustrates both the expected Lotto Plus $3 Return (in blue) and the Lotto Plus $2 Return (in red) against the expected return of a Single Ticket (in green).

When the advertised jackpot is set to the minimum $3 million, the $3 Lotto Plus returns the most money, $0.467 of each dollar received, back to the players. By comparison, the $2 Lotto Plus returns the $0.374 of each dollar received, and a Single $1 Ticket returns $0.313.

When the jackpot level reaches $5.8 million, the returns of the $2 Lotto Plus and a Single Ticket are equal, at $0.436 each. However, both of these are substantially below the $3 Lotto Plus's $0.508 return. (Note that above this breakeven level, the single ticket returns out pace that of the $2 option.)

When the advertised jackpot level reaches $8.3 million, the $3 Lotto Plus and a Single Ticket returns are equal, at $0.544 each. This jackpot level is the $3 Lotto Plus breakeven. From the graph, it is clear that either of these two scenarios are preferable to the $2 Lotto Plus option which only returns $0.490 per dollar spent.

Above the $3 Lotto Plus breakeven point, single tickets purchased without either option return more to the players. When the jackpot grows to $23 million, $1.184 is returned to single ticket holders, compared to only $0.810 for $2 Lotto Plus, and $0.758 for $3 Lotto Plus.


Players should purchase Lottery Tickets like they would any other investment, and always seek the highest return on their dollars. Thus, when the Florida Lotto jackpot is below $8.3 million, the $3 Lotto Plus should be purchased. Above $8.3 M, always buy single tickets. If you cannot afford the $3 option, you should consider the $2 Lotto Plus. In this case, breakeven is at $5.8 million. Buy the $2 option below this level, and single tickets above it.


Alternate Analysis
Since the only prize that is increased by $2 and $3 Lotto Plus is the actual Jackpot paid to winners, we can alternately analyze the jackpot payout on a per dollar basis. For this, a simple algebraic relationship is defined as:

JackpotAmount = (JackpotAmount + OptionPayout)/CostPerTicket

As seen, the OptionPayout and CostPerTicket variables are fixed but depend upon whether we are analyzing the $2 or $3 option. This means that we can solve for the optimal Jackpot amount for either of these options.

Solving for the $2 Lotto Option, our formula changes to: JackpotAmount = (JackpotAmount + 10)/2 which implies the $2 Plus JackpotAmount of $10 Million.

Similarily solving for the $3 Lotto Plus Option, our formula changes to: JackpotAmount = (JackpotAmount + 25)/3 which implies a $3 Plus JackpotAmount of $12.5 Million.

If you prefer this analysis to breakeven returns, we advise that you NEVER purchase either option when the base jackpot is above $12.5 million. At this level, go for the Jackpot, and purchase multiple combinations, giving yourself increased chances of winning.


Conclusion
To conclude, the decision to buy the Florida Lotto Plus option is dependent upon the jackpot size. When the jackpot is below its breakeven level, players are encouraged to buy the plus option. But, when the jackpot is above its breakeven level, players should forego this option, and buy 2 or 3 straight tickets instead (depending on whether you are considering the $2 or $3 option).

Our belief is that both of these options have value to the Florida Lottery player and should be considered.

Looking back at the May 10th 2008 $2 Lotto Plus winner, we believe the player made a very good choice, not only for his winnings, but because the base jackpot level was approximately equal to the $2 breakeven level of $5.8 million. Rounding this number to the nearest million, the player was indifferent to buying the option or not. Having purchased the option and having the winning combination, the player won a $16 million annuity jackpot, consisting of the $6 million base amount plus the $10 million option payout. Well done!


Learn More
To learn more about this subject, visit our in-depth pages that provide the detailed numbers behind each of these options.

Focus for December 2008: The New Powerball Changes, What They Mean to You



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Friday, September 26, 2008

Chances of Duplicate Lottery Tickets - Special Edition

Introduction
We've often wondered what the likelihood of different lottery players having the same combinations in a single drawing actually was. Looking for an answer, we searched the internet, but could not find it. So, we decided to conduct our own research. This was performed by studying the classic Identical Birthday Problem, identifying the underlying mathematical formula, applying this formula to individual lotteries, and summarizing our results.

Birthday Problem
How often have you been in a group of people and discovered that two of you shared the same birthday? Was this purely coincidence, a random event? Or, was it in fact highly likely?

The classic form of the Birthday Problem, which is familiar to most everyone, quantifies the chances of two people sharing the same birthday. Given a probability of certainty, the Birthday Problem solution calculates the size of smallest group necessary to meet that probability.

Thus, when in a group of 23 (22.5 actually) people, you can be 50% certain that two or more of you share the same birthday. To be 99.9% sure, you need a group of 71 people!

The Mathematics
The formula behind this solution is fairly simple, and in terms of Excel is written as:

SQRT(2*PopulationSize*LN(1/(1-Probability)))

We solve the Birthday Problem by substituting the PopulationSize with 365 days and the Probability of 0.50 or 0.999 to acheive the answers above.

Calculating the Chances of Duplicate Lottery Tickets
We applied the formula above to the various lottery games that we cover and produced the Chance of Duplicates Table below.

The first column identifies the lottery Game. Next is the Population (total number of possible combinations) for that game. The 3rd and 4th columns are our results. Column A identifies the minimum number of tickets that must be issued in order to be 50% sure that there at least one duplicate. Column B is similar, but identifies the minimum number of tickets that must be issued in order to be 99.9% sure that there at least one duplicate.

Chance of Duplicates
GamePopulationCol A
50%
Sure
Col B
99.9%
Sure
Powerball146,107,96214,232.044,928.3
Powerball (Jan 09)195,249,05416,452.151,937.1
Mega Millions175,711,53615,607.349,270.1
Lotto 64913,983,8164,402.913,899.4
Super 762,891,4999,377.429,476.7
Super Lotto Plus41,416,3537,577.323,920.5
Hot Lotto10,939,3833,894.312,293.6
EuroMillions76,275,36010,283.032,462.0
Irish Lotto8,145,0603,360.310,607.9
UK Lotto13,983,8164,402.913,899.4
Thunderball3,895,5842,323.97,336.2
Birthdays36522.571.0

The Chances
As shown, the chances that duplicate lottery tickets will be sold are very likely. For example, there is a 50% chance that duplicate Powerball tickets will be issued when only 14,232 tickets are sold. And, you can be 99.9% sure that there are duplicates when only 45,000 tickets are sold. When Powerball changes format in January 2009, the total number of possible combinations will increase by over 49 million. Even so, you can be 99.9% sure that there will be duplicates when only 52,000 tickets are sold. By reading the table above, you can determine the likelihood of duplicate tickets in your favorite lottery, whether it be: Powerball, Mega Millions, Super Lotto Plus, Hot Lotto, EuroMillions, Irish Lotto, UK Lotto, or Thunderball.

Summary
This study identifies the number of tickets that must be sold in order to be 50% and 99.9% mathematically certain that one or more people will have duplicate combinations. While this information is not sufficient to estimate the total number of duplicate tickets, it provides a guideline to understand the chances. If you live in a small town of around 50,000 people, and everyone buys 1 lottery ticket, don't be surprised if you discover that someone else has the same combination as yours.

JL .........




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Friday, August 29, 2008

MM Cash or Annuity? The LPP Analysis of the Mega Millions Jackpot

Introduction
Mega Millions players are required to choose whether they wish to receive Cash or Annuity Option at the time of purchase. In most States, the players who choose the Annuity Option may opt to take the Cash Value within 60 days of winning, but those who originally chose the Cash Option may not change their mind. After asking around, we confirmed that most people select the Cash Option, believing this is the best choice. So, if you play Mega Millions, what do you choose:

The Cash or Annuity Option?

Since the beginning of 2002 through Aug 24 2008, seventy-five (75) jackpots have been won by individuals and groups. These are listed in the Mega Million Jackpot History of Winners page. However, the Mega Millions website does not indicate whether these winners had chosen the cash or annuity payouts. But, it does feature profiles of 19 winners in their Winners Gallery. Of these 19, three have chosen the Annuity, and the rest have taken the Cash Option.

This means that around 85%
of Mega Millions players
take the Cash Option.
Is this the best decision?

Or, would they have more money by taking the Annuity?


Real World Example
For purposes of this paper, we have chosen to analyze the Jul 25 2008 Mega Millions drawing. We believe this Jackpot Analysis is relevant because it represents the minimum jackpot payment as defined by the rules, and is current as of this writing.

Graph MM0808a illustrates the Jackpot Offerings for the Jul 25 2008 Mega Millions drawing.


In this drawing, Jackpot winners choosing to receive the Annuity option will be paid $12 million in 26 equal installments spread over a 25 year period. Those who elect the Cash option will receive only one lump sum payment of $7.1 million. Comparing the amounts of both options presented, the Cash to Annuity Ratio for this drawing is 59.2%.

Having little other information, most winners will elect to receive the Cash Option, believing that the $7.1 million is a fair amount within the current interest rate environment.

However, this Cash Option may not be fair.

Therefore, the purpose of this paper is to provide Mega Millions players with more information about their two options. In this, we shall examine both the tax implications of each, and explain how fluctuating interest rates influence the size of the offered Cash Option, and more. By

Analyzing and Comparing the
Cash and Annuity Mega Millions
Options

we believe both players and winners will have a better understanding of the fairness of the estimated cash option being offered in any particular Mega Millions drawing.


How the Cash and Annuity are Paid
In Mega Millions, a Jackpot annuity winner receives 26 equal payments over a 25 year period. This differs from Powerball whose payments are graduated over a 29 year period. Taxes are paid yearly on receipt of each payment, meaning that all accrued interest earned remains tax free until payment is made to the winner.

Conversely, players who choose to receive the Cash Option will receive a single lump sum payment whose estimated value is stated on their web site. Taxes on this full amount is payable in the year received.

Mega Millions describes these different payment options on their page: "Differences Between Cash Value and Annuity".


Mega Millions Annuity Yearly Cashflow Payments
Because each of the Mega Millions Annuity Payments is fixed, the amount of money that the Mega Millions organization must deposit varies, depending on the: length of time until payment is made, and interest rates earned on this money. However, the payments made to the winner is always fixed. This means that players who won $12 million and elected the annuity option, would receive an 26 annual payment of $462 thousand every year.

Assuming that the prevailing interest rates are at an even 4% per year, Graph MM0808b illustrates the 26 annuity cash deposits that would be required by Mega Millions in order to meet these payments.

We have chosen the 4.0% interest rate level because this is the rate that the competing Powerball assumes its reinvestment. By using this same rate, we can reliably compare the cash values of both of these lotteries.




Note: This graph is for an $12 M annuity, but is scalable. If the annuity is $30 M, multiply payments by 2.5; if $84 M, multiply by 7; if $240 M, multiply by 20; etc.

As shown, the blue horizontal line illustrates the constant payment of $462K made to the winner. The vertical green bars illustrate the money required to be deposited. Notice that as the time increases, the amount of money Mega Millions must deposit is reduced. This is because compound interest is being earned on each deposited cashflow. When interest rates are 4.0%, Mega Millions would need $462K for the first payment; $365K for the 5th year; $289K for year 10, ... and finally $143K for the 26th and final payment. The differences between the deposited amount and the $462K payment is the interest earned.

To be fair to the players, the total the 26 deposits should equal to the Cash Value Offered at the time the tickets are being sold. Since we are assuming 4.0% as a fair interest rate, Mega Millions must aside $7.672 Million in order to make these payments of $12 M to you.

We shall define this value of $7.672 million as Par.
The Par Cash to Annuity ratio is 63.9%.


Jul 25 2008 Jackpot Revised
Adding the $7.672 M Par Value to our Jackpot Graph (MM0808c) provides us with a relative measure by which to judge the fairness of the $7.1 million cash option offering. As shown, the Cash Option is $0.572 million below Par. This means that those who elect the Cash Offer immediately lose $0.572 of their winnings. In terms of ratios, we are offered 59.2% verses the par 63.9%, or a 4.7% loss.


Without knowing the prevailing interest rates by which to reinvest our Cash Option, we cannot yet say with certainty that the $7.1 offering is unfair.

But we know for sure that if we take the Annuity, $7.672 M will be set aside for our winnings. If we take the Cash Option, we immediately lose nearly $600,000. This comes out to losing $22 thousand per year.



Fair Value of Mega Millions Cash Option at Varying Interest Rates
Both the Mega Millions organization and us recognize that interest rates vary. Because of this, the value of the cash option will move in the opposite direction of interest rate movements. This means that if interest rates go up, the cash option goes down, and vice-versa. Knowing the fair value of the cash option at various interest rate levels further will help us to judge the fairness of the Cash Option being offered.



Graph MM0808d illustrates the fair value of the cash option value at interest rates varying from 2% to 10%. Note that when interest rates fall below 4%, the cash option increases above our $7.672 M Par Value (green line).

This graph tells us that when interest rates are at 2%, Mega Millions must invest $9.472 million to fund our $12 million annuity. At 3% interest, $8.498 must be deposited for funding. And, when interest rates rise to 10%, only $4.651 needs to be invested.

Referring to this graph, we observe that the July 25 2008 Cash Option of $7.1 M equates to an interest rate environment of slightly less than 5%. Considering that interest rates have fallen substantially during January 2008 and May 2008 (from 4.25% to 2.00%) and continue to remain low, this 5% investment level appears to be rather high.

Thus, the July 25 2008 $7.1 Million Cash Option begins to appear to be rather low.

Note: This graph is for an $12 M annuity, but is scalable. If the annuity is $30 M, multiply amounts by 2.5; if $84 M, multiply by 7; if $240 M, multiply by 20; etc.


Tax Implications
Regardless which option a winner selects, taxes represent a large portion of the income. Winners are automatically moved into the highest tax bracket, and both standard and itemized deductions become limited.

Because of this, we assume that Federal Taxes will consume 35% of one's winnings.

This means that those who elect the $12 million Annuity Option will pay a total of $4.2 million to the IRS. Without paying State taxes (many states do not tax those residents who win Mega Millions),

Annuity winners keep $7.8 million

to spend and invest. One important benefit of taking the annuity is that taxes will only be paid on the amount of money given to the winner each year. All other interest being earned will remain and grow tax free until it is paid out later.

Conversely, those who decide to take the Cash Option will be taxed immediately. In the case of the July 25 2008 cash jackpot, the winner will immediately fork over $2.5 million to the IRS. This means that the cash winner will only pocket $4.6 million. Typically, Mega Millions withholds only 25% of the jackpot winnings. This means that winners will be liable for the remaining 10% when they file their taxes. Most winners do not realize this and are unhappily shocked when they learn about the additional tax consequences.

The website USAMega.com provides excellent Mega Millions Jackpot Analysis pages that summarize both the Federal and State Tax implications on the Annuity and Cash Options.


Cash Value Implied Yield Curves
Knowing that $12 M annuity winners will retain $7.8 million of their winnings after taxes, it is possible to construct the associated Implied Yield Curves that will provide the cash option winners with the same amount of money. Using this $7.8 M value as a target, the Blue Curve displays the Tax Free Rates for varying cash offerings, meaning that the earned interest is not taxed until paid. Whereas, the Green Curve indicates the Taxable Equivalent Curve. The horizontal axis indicates the cash value offering in millions. The vertical axis indicates yield rates.


Note: These Cash Jackpot values are based on a $12 M annuity, and are scalable. If the annuity is $30 M, divide the offered amount by 2.5; if $84 M, divide by 7; if $240 M, divide by 20; etc.


Returning to the July 25 2008 drawing, the Cash Jackpot offering is $7.1 million.

Assuming that this is the fair value, it will be the same amount that Mega Millions will invest for the Annuity winners. From the graph MM0808e Blue Curve, we can guesstimate that Mega Millions will invest this money at approximately 5.0%. The interest earned on the annual payments will compound tax free at this rate and will generate a total of $12 M in payments to the winner. After paying taxes, the player will get to keep the $7.8 million.

However, if the player selects the cash option, he will receive $7.1 million, pay $2.5 M in taxes, and invest the remaining $4.6 million. The Green Curve in graph MM0808e already takes the reduction of taxes into account. So, to find the taxable equivalent yield the player must earn, we locate $7.1 M on the horizontal axis, then find the point on the Green Line above it. Doing this, we find that the cash option winner must receive approximately 6.5% on the remaining $4.6 M in order to earn $7.8 million.


Evaluating the July 25 2008 Cash Offering
Considering the Federal Reserve has reduced interest rates substantially, we know that short term rates are around 2.3%, 10-year Treasuries less than 4.0%, and 30-year treasuries below 4.5%. Thus, it is impossible for Mega Millions to earn an average rate of 5.0% on the annuity deposits at this time. Therefore, we conclude that:

The $7.1 million cash offering is extremely undervalued,
and should be at least $7.7 or more million.


Cash Loss per Million (Mar 14 - Aug 29 2008)
To test the correlation of the Mega Millions Cash Option Jackpot offering against actual changes in interest rates, we have constructed the Cash Loss per Annuity Million graph at right.


We define Cash Loss as the difference between the expected Cash Par Value and the Offered Cash Value, normalized to a single $1.0 million in annuity value.

As shown, the graph covered the 49 drawings beginning March 14 2008 and ending August 29 2008. The magnitude of the loss is displayed on the y-axis, and ranges from $10,000 to $60,000 per annuity equivalent million dollars. The vertical Green Lines indicate when a Mega Millions Jackpot was won and was reset to the minimum $12 M. The horizontal Blue Line indicates the average loss of $30,000 per million.

During this period, the FOMC reduced the Federal Funds Target rate twice:
  • Mar 18 2008 - from 3.00% to 2.25%, and
  • Apr 30 2008 - from 2.25% to 2.00%.
These are indicated by the magenta dots on the graph.

Because the interest rates were lowered, we would expect the Ratio of the Cash Offered Jackpot to Annuity to the closer to the Par Jackpot ratio of 63.9%, thus bringing the Loss per Million closer to zero.

But in reality, the Cash offering by Mega Millions appears to be random. During the period March 18 and April 30 when Fed Funds was 2.25%, the loss spiked to $60K, then dropped to $10K. After the April 30 cut, the losses remained constant, around $30K. Afterwards, the losses grew until the June 13th jackpot win, then fell. When the jackpot was reset on July 25th, the loss unexpectedly jumped to $47 K. Again in this cycle, as the Annuity jackpot has risen, the cash option loss has fallen to only $20 K per million.

Since players and winners had no basis to evaluate the fairness of the cash prize offering, complete trust was placed in the Mega Millions estimate, which appears to be arbitrary, and not really correlated to actual interest rates. Based on all of this, we believe that the:


Mega Millions Annuity Offer is Best!



Summary
To summarize, Mega Millions winners who elect to receive the Cash Option are usually penalized because: the Cash Option Value is under estimated; interest rates are typically lower than that offered by the Annuity; and, taxes erode the both the cash payment and interest earned.

MM Cash Option Breakdown
To visualize the July 25 2008 Cash Offering payout, Graph MM0808g illustrates the Cash breakdown against the comparative $12 million annuity prize. Notice that the player will retain a total of $6.7 million in winnings, consisting of the $4.6 M cash payment and $2.1 M of interest earned. A total of $3.6 million will be paid in taxes. And, $1.7 million will lost to Mega Millions .

Conversely, Mega Millions players who win $12M and elect to receive the Annuity payments will retain $7.8 million in cash, and will pay $4.2 million in taxes.

MM Annuity Breakdown
The net difference in money retained by the winner will be $1.1 million spread over the 26 payments.

This equates to approximately $42.3 thousand dollars per year. This is a lot of money.

Note: All amounts shown are based on a $12 M annuity at 4% interest. These values are scalable. Thus, if the annuity is $30 M, multiply amounts by 2.5; if $84 M, multiply by 7; if $240 M, multiply by 20; etc.



Conclusion
In this discussion, we have: illustrated how the Mega Millions Annuity payments are made; identified the fair cash value Par value of $7.672 million; described the fair cash jackpot offerings at varying interest rates; created the non-taxable and taxable implied break-even yield curves; shown the historical cash loss per million; and summarized the breakdowns of money retained, taxes paid, and money lost.

By focusing on the July 25 2008 cash and annuity jackpot offerings of $7.1 M and $12 M, we have concluded that winners in this drawing are far better off by receiving the Annuity Payments instead of the Cash Option.

Lastly, our advice with regard to this Mega Millions drawing (and most likely others) is to:

Take the Annuity,
You'll have alot More Money
Unless things change.

And remember, if you check the Annuity Option when you buy your tickets, you can change your mind and take the Cash Option (depending in which state you purchase the ticket). Those originally selecting the Cash Option cannot reverse that decision.

Learn More
We have not found many sites that provide detailed Mega Millions Jackpot information. However, you can learn more by visiting the following:
Focus for October: Florida Lotto Plus



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Friday, June 27, 2008

PB Cash or Annuity? The LPP Analysis of the Powerball Jackpot

Introduction
Playing Powerball requires players to make many immediate choices: What numbers to play? Buy the Powerplay? Play quick pick numbers? And, if the player is lucky enough to win the jackpot, the player must then choose whether to:

Take the Cash or Annuity Option?

Since the beginning of 2003 through Jun 18 2008, there have been 76 different winners (groups or individuals) that needed to make this choice (Powerball Winners). Of them, only three have opted for the Annuity; 70 have taken the cash option; 1 is still deciding; and 2 have mixed payments.

Since most players take the Cash Option,
they must be right.

Or, Are they wrong?


Real World Example
For purposes of this paper, we have chosen to analyze the May 31 2008 drawing. We believe this Jackpot Analysis is relevant because it represents the minimum jackpot payment as defined by the rules, and is current as of this writing.

Graph GR0606a illustrates the Jackpot Offerings for the May 31 2008 Powerball drawing.


In this drawing, Jackpot winners choosing to receive the Annuity option will be paid $15 million in 30 installments spread over a 29 year period. Those who elect the Cash option will receive only one lump sum payment of $7.1 million. Comparing the amounts of both options presented, the Cash to Annuity Ratio for this drawing is 47.3%.

Having little other information, most winners will elect to receive the Cash Option, believing that the $7.1 million is a fair amount within the current interest rate environment.

However, this Cash Option may not be fair.

Therefore, the purpose of this paper is to provide players with more information about these two options. In this, we shall examine both the tax implications of each, and explain how fluctuating interest rates influence the size of the offered Cash Option, and more. By

Analyzing and Comparing the
Cash and Annuity
Powerball Options

we believe both players and winners will have a better understanding of the fairness of the estimated cash option being offered in a Powerball drawing.



How the Annuity is Paid
Beginning on October 9, 2002 (Colorado Lotto Powerball Information), Powerball made two significant changes to the annuity payout structure. First, the annuity period for paying the Jackpot was extended from 25 to 30 payments (paid over a 29 year period). Second, each payment (after the first) is gradually increased at a predetermined interest rate of 4%. Previously, each payment was in equal amounts.

The Powerball FAQS/Contact Us page explains the reason for these changes:

"Each payment is 4% higher than the previous year's payment to help keep up with inflation. The annuity prize used to be paid out in equal payments. Persons who elect to take the annuity prize do so because they don’t want to worry about investing the money. They want to maintain their lifestyle for the term of the annuity. In fact, our past practice of equal installments did not really meet the needs of these winners."

Changing the jackpot annuity payment structure to meet the needs of the winners sounds like a noble cause, but since few winners have ever elected this type of payment, this change has not benefited many players.

Other Powerball Rules
In addition to the above annuity payment schedule, Powerball has defined several rules of play. To summerize:
  1. The Minimum Annuity Jackpot is $15 Million. Payments to players will never be lower than this amount.
  2. The Minimum Increase in the Annuity Jackpot between Drawings will be $5 Million.
  3. Payment of the Annuity Option will be delivered in 30 unequal installments, spread over a 29 year period.
  4. Each Annuity Payment will be 4% higher than the previous.
  5. Amounts of both the Cash and Annuity Options are Estimated Values Only. Actual payments may be higher or lower than stated (with the exception of the minimum $15 M)
  6. $0.30 of every ticket sold goes to the Jackpot pool.
  7. Player has 60 days to decide which option to take. (This is important)
  8. The method of payment is binding. Once a winner as chosen, the option cannot be reversed.


Powerball Annuity Yearly Cashflow Payments
Using the above information, we have constructed a cashflow diagram of a $15 million annuity. Graph GR0806b illustrates the 30 annuity payments that would be made to the winner of this $15 million regardless of interest rates. While Powerball says they estimate the annuity, we know that the minimum jackpot annuity payment is $15 million. Thus, these payments are fixed.


Note: This graph is for an $15 M annuity, but is scalable. If the annuity is $30 M, multiply payments by 2; if $75 M, multiply by 5; if $150 M, multiply by 10; etc.

The first payment is delivered immediately and those following increase by 4.0% each year. If we assume that the fair interest rate level was also 4.0% per year, then Powerball would need to create 30 buckets of $267 thousand each. The first $267,000 (rounded) would be paid to you when you were declared the winner, and all the rest would be invested in 4% annual paying interest Treasury Bonds or Strips. Looking at the above graph, the blue horizontal line illustrates the amount of money that was deposited. Everything above that line is interest earned. The total of all 30 payments, which include both the value of the cash deposited and the interest earned, will equal $15 Million (which is what you won).

But since Powerball only needs to allocate 30 $267 K buckets for payment, it only needs to aside $8.024 Million in order to make these payments (totaling $15 M) to you.

We shall define this value of $8.024 million as Par.
This has a Cash to Annuity ratio of 53.5%.



May 31 2008 Jackpot Revised
Adding the $8.024 M Par Value to our Jackpot Graph (GR0606c) provides us with a relative measure by which to judge the fairness of the $7.1 million cash option offering, which is $0.924 million below Par. In terms of ratios, we are offered 47.3% verses the par 53.5%, or a 5.2% loss.


Without knowing the prevailing interest rates by which to reinvest our Cash Option, we cannot yet say with certainty that the $7.1 offering is unfair.

But we know for sure that if we take the Annuity, $8.024 M will be set aside for our winnings. If we take the Cash Option, we immediately lose nearly $1.0 million. This comes out to losing $61.6 thousand per annuity million won.



Fair Value of Cash Option at Varying Interest Rates
Both the Powerball organization and us recognize that interest rates vary. Because of this, the value of the cash option will move in the opposite direction of interest rate movements. Thus, if interest rates go up, the cash option goes down, and vice-versa. Knowing the fair value of the cash option at various interest rate levels further will help us to judge the fairness of the Cash Option.


Graph GR0806d illustrates the fair value of the cash option value at interest rates varying from 2% to 10%. Note that when interest rates fall below 4%, the cash option increases above our $8.024 M Par Value (green line).

This graph tells us that when interest rates are at 2%, Powerball must invest $10.784 million to fund our $15 million annuity. At 3% interest, $9.262 must be deposited for funding. And, when interest rates rise to 10%, only $3.992 needs to be invested.

Referring to this graph, we observe that the May 31 2008 Cash Option of $7.1 M equates to an interest rate environment of slightly less than 5%. Considering that interest rates have fallen substantially during January 2008 and May 2008 (from 4.25% to 2.00%), this 5% level appears to be rather high.

Thus, the May 31 2008 $7.1 Million Cash Option begins to appear to be extremely low.

Note: The Cash Fair Value amounts in the graph are based on a $15 M annuity, but these are scalable. If the annuity is $30 M, multiply amounts by 2; if $75 M, multiply by 5; if $150 M, multiply by 10; etc.



Tax Implications
Regardless which option a winner selects, taxes represent a large portion of the income. Winners are automatically moved into the highest tax rates, and both standard and itemized deductions become limited.

For purposes of this analysis, we assume that Federal Taxes will consume 35% of one's winnings.

This means that for those who elect the $15 million Annuity Option, they will pay a total of $5.25 million to the IRS. Without paying State taxes (many states do not tax those residents who win Powerball),

Annuity winners keep $9.75 million

to spend and invest. One important benefit of taking the annuity is that taxes will only be paid on the amount of money given to the winner each year. All other interest being earned will remain and grow tax free until it is paid out later.

Conversely, those who decide to take the Cash Option will be taxed immediately. In the case of the May 31 2008 cash jackpot, the winner will fork over $2.5 million to the IRS. This means that the cash winner will only pocket $4.6 million. Typically, Powerball withholds only 25% of the jackpot winnings. This means that winners will be liable for the remaining 10% when they file their taxes. Most winners do not realize this and are unhappily shocked when they learn about the additional tax consequences.

The website USAMega.com provides excellent Powerball Jackpot Analysis pages that summarize both the Federal and State Tax implications on the Annuity and Cash Options.



Cash Value Implied Yield Curves
Knowing that $15 M annuity winners will retain $9.75 million of their winnings after taxes, it is possible to construct the associated Implied Yield Curves that will provide the cash option winners with the same amount of money. Using this $9.75 M value as a target, the Blue Curve displays the Tax Free Rates for varying cash offerings, meaning that the earned interest is not taxed until paid. Whereas, the Green Curve indicates the Taxable Equivalent Curve. The horizontal axis indicates the cash value offering in millions. The vertical axis indicates yield rates.


Note: These Cash Jackpot values are based on a $15 M annuity, and are scalable. If the annuity is $30 M, divide the offered amount by 2; if $75 M, divide by 5; if $150 M, divide by 10; etc.

Returning to the May 31 2008 drawing, the Cash Jackpot offering is $7.1 million.

Assuming that this is the fair value, it will be the same amount that Powerball will invest for the Annuity winners. From the graph GR0806e Blue Curve, we can guesstimate that Powerball will invest this money at approximately 4.8%. The interest earned on the annual payments will compound tax free at this rate and will generate a total of $15 M in payments to the winner. After taxes, the player will get to keep the $9.75 million.

However, if the player selects the cash option, he will receive $7.1 million, pay $2.5 M in taxes, and invest the remaining $4.6 million. The Green Curve in graph GR0806e already takes the reduction of taxes into account. So, to find the taxable equivalent yield the player must earn, we locate $7.1 M on the horizontal axis, then find the point on the Green Line above it. Doing this, we find that the cash option winner must receive approximately 6.2% on the remaining $4.6 M in order to earn $9.75 million.



Evaluating the May 31 2008 Cash Offering
Considering the Federal Reserve has reduced interest rates substantially, we know that short term rates are around 2-3%, 10-year treasuries less than 4.1%, and 30-year treasuries below 4.7%. Thus, it is impossible for Powerball to earn an average rate of 4.8% on the annuity deposit at this time. Therefore, we conclude that:

The $7.1 million cash offering is extremely undervalued,
and should be at least $8 or more million.



Cash Loss per Million (Jan 2 - Jun 18 2008)
To test the correlation of the Cash Option Jackpot offering against actual changes in interest rates, we have constructed the Cash Loss per Annuity Million graph at right.


We define Cash Loss as the difference between the expected Cash Par Value and the Offered Cash Value, normalized to a single $1.0 million in annuity value.

As shown, the graph covered the 49 drawings beginning January 2 2008 and ending June 18 2008. The magnitude of the loss is displayed on the y-axis, and ranges from -$10,000 to -$60,000 per annuity equivalent million dollars. The vertical Green Lines indicate when a Powerball Jackpot was won, and was reset to the minimum $15 M. The horizontal Blue Line indicates the average loss of $40,000 per million.

During this period, the FOMC reduced the Federal Funds Target rate:
  • Jan 22 2008 - from 4.25% to 3.50%
  • Jan 30 2008 - from 3.50% to 3.00%
  • Mar 18 2008 - from 3.00% to 2.25%, and
  • Apr 30 2008 - from 2.25% to 2.00%.
These are indicated by the magenta dots on the graph.

Because the interest rates were lowered, we would expect the Ratio of the Cash Offered Jackpot to Annuity to the closer to the Par Jackpot ratio of 53.5%, thus bringing the Loss per Million closer to zero.

But in reality, the Cash offering by Powerball appears to be random. During the period January 30 and March 18 when Fed Funds was 3.00%, the loss became larger, and then smaller. After the March 18 cut, the loss narrowed, as expected. After the last lowering to 2.00% on April 30, the loss widened to a high of $60,000 per annuity million.

Since players and winners had no basis to evaluate the fairness of the cash prize offering, complete trust was placed in the Powerball estimate, which appears to be arbitrary.

Returning to our May 31 2008 example, we observe that the Jackpot Loss on that date was at its largest. Knowing that the interest rates had declined, we would have expected that the Cash Offering to increase. Because it decreased, we further believe that the:

Annuity Offer is Better!



Summary
To summarize, winners who elect to receive the Cash Option are usually penalized because: the Cash Option Value is under estimated; interest rates are typically lower than that offered by the Annuity; and, taxes erode the both the cash payment and interest earned.

Sample chart
To visualize the May 31 2008 Cash Offering payout, Graph GR0806g illustrates the Cash breakdown against the comparitive $15 million annuity prize. The player will retain a total of $7.9 million in winnings, consisting of the $4.6 M cash payment and $3.3 M of interest earned. A total of $4.3 million will be paid in taxes. And, $2.8 million will lost to Powerball.

Conversely, winners who elect to receive the Annuity payments will retain $9.75 million in cash, and will pay $5.25 million in taxes.

Sample chart
The net difference in money retained by the winner will be $1.85 million spread over the 30 payments.

This equates to approximately $61.7 thousand dollars per year. This is a lot of money.

Note: All amounts shown are based on a $15 M annuity at 4% interest. These values are scalable. Thus, if the annuity is $30 M, multiply amounts by 2; if $75 M, multiply by 5; if $150 M, multiply by 10; etc.



Conclusion
In this discussion, we have: illustrated how the Annuity payments are made; identified the fair cash value Par value or $8.024 million; described the fair cash jackpot offerings at varying interest rates; created the non-taxable and taxable implied break-even yield curves; shown the historical cash loss per million; and summarized the breakdowns of money retained, taxes paid, and money lost.

By focusing on the May 31 2008 cash and annuity jackpot offerings of $7.1 M and $15 M, we have concluded that winners in this drawing are far better off by receiving the Annuity Payments instead of the Cash Option.

Lastly, our advice with regard to this Powerball drawing (and most likely others) is to:

Take the Annuity,
You'll have alot More Money.



Learn More
We have not found many sites that provide detailed Powerball Jackpot information. However, you can learn more by visiting the following:
Focus for August: Analysis of the Mega Millions Jackpot



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