New Lotto Texas 2013 - Review of the Game Changes

Revised: Friday, April 26, 2013

For the 4th time since the game began in 1992, the Texas Lottery Commission (TLC) will be making changes to Lotto Texas.

These changes will become effective beginning with the April 17 2013 drawing.

This is our summary of the changes and our evaluation of them.

The basic Lotto Texas format will remain the same. 
Players will still be required to pick 6 numbers from a set of 54. If the full 6 number combination matches the one drawn that evening, the player will win the jackpot prize. Each single ticket will continue to cost $1 each, and the lower tier prizes will remain the same (i.e. those matching 3, 4, and 5 of the white balls). Should a player be lucky enough to win the jackpot, he will still have the option to receive either the lump sum cash payout, or the full advertised annuity amount paid over a number of years.

What Changes
However, there will be 4 differences in the new Lotto Texas 2013 game.

• First, a "Extra!" option is added to the game. Players can choose to pay $1 more for the chance to win higher cash amounts for the lower tier prizes. This means that those holding the Extra! option will earn higher prizes if they match 3, 4, or 5 balls. Plus, a new $2 prize payout will be added for those matching only 2 of the 6 balls. (This is in effect a "multiplier" option).
• Second, the minimum annuity jackpot prize will be increased to $5.0 million.
• Third, the annuity payout period will increase from 25 to 30 payments.
• Forth, the annuity jackpot will increase in increments of $250,000 rather than the current $1 million.

While we rarely like the idea of raising lottery ticket prices, we have found that those games with a "multiplier" option usually offer better returns to the lottery players. Since players have the option (or choice) to pay more for a ticket, they have more control over the amount of money they spend. Thus, we believe this is fairer to them because they can control their own spending.

To help players understand how these changes will affect them, we discuss each of these 4 changes below.

Summary of Lotto Texas 2013 Changes and Payout Structure
To begin, we have prepared the summary Table 1 below illustrating the prize payouts for a single $1 ticket and the new $2 Extra! ticket.

Table 1: New Lotto Texas 2013 Payout Structure
Match	Chances	Occurs	Probability	Single $1   Ticket	New $2 Extra!
6	25,827,165.00	1	0.000004%	Jackpot	Jackpot
5	89,677.66	288	0.001115%	$2,000	$12,000
4	1,526.43	16,920	0.065512%	$50	$150
3	74.66	345,920	1.339365%	$3	$13
2	8.85	2,918,700	11.300892%	-	$2
1	2.51	10,273,824	39.779140%	-	-
0	2.10	12,271,512	47.513972%	-	-
	Total	25,827,165	100.000000%	-	-

Here we can see that there is no change to the single $1 ticket set of prizes. However, the Extra! ticket offers increased prizes for those matching 3, 4, and 5 balls. The match 5 prize moves from $2,000 to $10,000; the Match 4 prize moves from $50 to $100; and the Match 3 prize moves from $3 to $10.

And, we can also see the new $2 prize for those matching 2 of the balls. The addition of this new prize is what makes the Extra! ticket attractive. Assuming all possible combinations were purchased, there will be nearly 3 million new winning tickets, an increase of 11.3% over those who did not buy Extra!. Further, those matching: 5 balls have a 5 times multiplier; 4 balls have a 2 times multiplier; and 5 balls have a 3.33 times multiplier.

On a $ return basis, we look to see what will be returned to the players if the jackpot prize is not won. In the case of the single $1 ticket, we find that 9.52% is returned. Whereas, the Extra! ticket returns 31.61% of the money back to the players. This is an increase of 3.32 times, and it exceeds the 2 times cost in Extra! ticket. Thus, we believe that the Extra! option is attractive and should be played.

The Breakeven: When to buy Extra! - Like all other multiplier games, the new Lotto Texas Extra! option has an implied breakeven value. This is the jackpot amount where the returns of a single ticket equals that of the Extra! ticket. For Lotto Texas, we calculate this value to be: $11.4 million. Thus:

Buy Extra! when the jackpot is less than or equal $11.4 million;

Do not buy Extra! when the jackpot is more than $11.4 million.

Minimum Jackpot Increases to $5 Million
There are two components to increasing the minimum jackpot. First, people tend to buy more lottery tickets when the jackpot increases. This means that increasing the minimum jackpot from $4 to $5 million will result in higher ticket sales.  Second, the addition of the new Extra! option will most likely increase the Texas Lottery Commission profits since many players will be willing to pay $2 for their ticket rather than $1 because of the improved prize payouts.

Thus, it is noteworthy that the Texas Lottey Commission recognized the potential for increased profits and raised the minimum Jackpot accordingly.

Annuity Payout Period increases to 30 payments.
However, changing the annuity payout period from 25 to 30 payments only benefits the Texas Lottery Commission, not the players.

On the surface, players may be indifferent to this change because most jackpot winners opt for the cash value payment. But, the value of the cash prize offering is directly proportional to the length of time established by the annuity. This means that for any given annuity value, the longer the annuity term to maturity (years of payments), the lower the cash value will become.

Thus, even though we have a higher annuity value, the corresponding cash value payout will be proportionately lower than what currently exists.

In theory, the Texas Lottery Commission (TLC) should not care whether a player chooses to take the cash option or the annuity payment. The reason is that the cash value should be valued at the amount the TLC must invest in order to achieve the annuity payments.

But since the discounted cash value will be lower after the 2013 changes are implemented, the TLC will profit more from the difference it is saving.

Further, some players who would have previously opted for a 25 payment annuity may shy away from a 30 period annuity: First because it is 5 years longer (which increases the uncertainty period); and Second because the yearly annuity payment will be lower.

Lets assume the annuity value is set at $5 million and the investment yield is 2.80%. Under the current rules of 25 payments, the cash value will be $3.66 million and each of the annuity payments will be $200,000.

However, under the new 2013 rules of 30 payments, the cash value will be lowered to $3.45 million and each annuity payment will be reduced to $167,000.

Under this scenario, the TLC will profit by $210,000 simply by the difference in the cash values. And, the players yearly payment will decrease by $33,000.

Table 2: Annuity to Cash and Yearly Payouts Scenarios
Jackpot	Yield	Old  Cash	New  Cash	Cash   Diff	Old Yearly Payout	New Yearly Payout
$4M	2.8%	$2.93	$2.76	-$0.17	Old Yrly	- na -
$5M	2.8%	$3.66	$3.45	-$0.21	$0.200	$0.167
$5M	4.0%	$3.25	$3.00	-$0.25	$0.200	$0.167
$5M	6.0%	$2.71	$2.43	-$0.28	$0.200	$0.167
$10M	2.8%	$7.32	$6.89	-$0.43	$0.400	$0.333
$10M	4.0%	$6.50	$5.99	-$0.51	$0.400	$0.333
$10M	6.0%	$5.42	$4.86	-$0.58	$0.400	$0.333

Table 2 above illustrates various annuity to cash values for 3 different yield values: 2.8% (current value); 4.0%; and 6.0%. As we can see, the new jackpot cash value for 30 payments is always less than the current 25 payout structure. Additionally, we can see that the annuity payout in the new 2013 game will be less than what winners receive now.

Jackpot Increases by $0.250 million
The last major change with the new 2013 Lotto Texas will be the increments by which the annuity jackpot will grow.

Under the new rules, the jackpot will grow in increments of $0.250 compared to the existing $1.0 million increment. This does not mean that the jackpot will only grow by 1/4 million dollars between consecutive non-winning drawings. Instead, it means that the annuity will be set to the closest 1/4 million.

While this may appear to be a detriment, we believe it is a good improvement to the game because it will be fairer to both the Lotto Texas players and the TLC as well.

The reason is that the annuity can be adjusted more proportionately to actual ticket sales.

For example, when the jackpot is set to the minimum, ticket sales are low. But, as the jackpot increases, the ticket sales increase as well.  Thus, when the jackpot is set at $5.0 million, the next drawing jackpot may only be $5.25 or $5.50 million. But, when the jackpot grows to $10 million, the subsequent jackpot might be set at $10.750 or $11.250 million.

In the past, the TLC would have to adjust jackpot growth more randomly because increments would be rounded to the nearest $1.0 million. This would have the effect of the TLC offering a lower annuity jackpot than what its profits would permit.

Setting the Lotto Texas jackpot increment to $0.250 will now be the same as that of Texas Two Step. A review of that game's jackpot history shows that growth appears to be exponential, rather than linear. We believe this same pattern will be repeated by the Lotto Texas game as well.

Summary
In summary, four new rules to Lotto Texas will go into effect beginning with the April 17, 2013 drawing.

These changes include: offering a new Extra! option that will increase the non-jackpot prize payouts; increase the minimum annuity jackpot to $5 million; lengthening the annuity payout period from 25 to 30 payments; and, lowering the minimum annuity jackpot growth to $0.250 million.

Overall, we believe these changes will be beneficial to lottery players in Texas, and to the Texas Lottery Commission as well. The Extra! option increases payout returns to the players and will increase the potential number of winners by 3 million. Increasing the minimum jackpot amount will help to attract more players when the annuity is at its minimum. And, changing the jackpot growth will help to increase the annuity offerings because it eliminates precautionary rounding.  The only detriment to the new rules is the lengthening of the jackpot payout period. This may influence more players to choose the cash value payment. But, we believe the annuity is still better because the cash value will be lower than what it is today.

Please not that at the time of this writing, the official rules have not been published on the Texas Lottery website. When they become available, we will add the link to this post and make any modifications necessary.

Sources:

• Lotto Texas Change Announcement
• The Lotto Report review of changes
• Lotto Texas 2013 Complete Odds and Return to Players
• When to buy Lotto Texas Extra - Recommendation Analysis
• Texas Two Step Jackpot Growth History

Introducing the Lottery Annuity Calculator

We are pleased to announce the release of our new Lottery Annuity Calculator Gadget. This new product is available for your use directly on your iGoogle home page, your websites, or blogs.

A screen shot is displayed below.






As shown, the gadget is divided into two halves of information. The left side contains 4 editable fields, the:

1. Jackpot Annuity Value
2. Offered Cash Value
3. Ratio of Cash to Annuity, and
4. Implied Yield.

Only two of the 4 may be entered for calculation. The Check Boxes next to the fields identify which value to use.

Once you have entered your data, press the "Calc" button and all other information will be computed.

At the right side of the screen, you will see the number of annuity payments that that will be made to the winner. Under it will be the amounts of the first and last payments.

To add this gadget, simply press the



button here or above.

We believe this new gadget will be a valuable tool to all lottery players, and especially those who are lucky enough to win! In addition, we welcome all Lottery providers to take advantage of this gadget when projecting future cash and annuity values.

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?

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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.

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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".

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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%.

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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.

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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.

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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.

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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.

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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.

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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!

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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.


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.


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.

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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:

• Mega Millions Game Rules (from NJ Lottery)
  
• USAMega.com - Mega Millions Frequently Asked Questions
  
• What to do when you win the lottery
  
• CASH VS.ANNUITY: WHICH ONE IS THE BEST ONE TO TAKE IF I WIN?
  

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