Why you should play the Pick 4 Lottery

The primary goal of a lottery player is to win money. However, the motive behind this goal varies from person to person. Some do this to win a large jackpot, and to be set for life. Others play to supplement their income by trying to continually win smaller prizes. And, a smaller group are addicted gamblers, hooked on the thrill of winning regardless of the prize.

This article is aimed at the second group of players, i.e. those who play to supplement their income. These are the people who treat the lottery expenditures as an investment. Their objective is to continually win smaller prizes and not to lose any of their own money. Their mindset is similar to those who invest in options. They know that they will:

• lose a little,
• lose a little,
• make a lot!

Play Pick 4
To accomplish a viable cash flow of winnings, we suggest that playing the Pick 4 lottery game in your individual states.

While there are slight variations in cost and payouts, the basic format of the game is identical in most states. To win, the player must select 4 numbers that range from 0 to 9 in each of the positions. This means that there are 10,000 possible combinations. In general, the cost of each ticket is $0.50 and the payout is $2,500. And, in most states, the Pick 4 drawings are held twice a day, seven days a week.

In some states, the cost of the ticket is double ($1.00), but the payout is also double ($5,000). Further, many states pay out a fixed prize, and others determine the winning prize on a pari-mutuel basis. In these instances, we can still assume that the average payout per $0.50 spent is $2,500.

A Winning Strategy
To limit one's costs, we recommend that a player select only number that they wish to play. Then, we suggest that they play that number in every drawing until it wins.

By doing this, a player will be spending only $0.50 to win $2,500. Thay is a return of 5,000 to 1.

However, we recognize that the players number may not be drawn immediately. This means that the player will be spending $1.00 per day until it wins. This represents $365 per year and 700 drawings. If the number is not drawn for a while, the player has approximately 6.9 years (6 years 10 months) until he reaches the breakeven level (which is 5,000) drawings.

Comparison
To help understand this strategy, we have prepared the table and graphs below comparing the Pick 4 lottery game to Powerball (PB), Powerball with Powerplay (X PB), Mega Millions, Mega Millions with Megaplier (X MM), Lotto 649 (L6), Lotto Max (LM), and Pick 3. The charts only consider prizes in those games where the player matches 4 balls.  

	Cost per Ticket	Prize	Odds	Winnings per $	Return	Dwgs per Week	Weeks to Prize	Years to Prize	Cost per Year
Pick 4	$0.50	$2,500	10,000	$5,000	$0.25	14	357.1	6.9	364.0
PB 4/5+	$2.00	$10,000	648,976	$5,000	$0.02	2	2,500.0	48.1	208.0
PB 4/5	$2.00	$100	19,088	$50	$0.01	2	25.0	0.5	208.0
PB 3/5+	$2.00	$100	12,245	$50	$0.01	2	25.0	0.5	208.0
X PB 4/5+	$3.00	$40,000	648,976	$13,333	$0.06	2	6,666.7	128.2	312.0
X PB 4/5	$3.00	$200	19,088	$67	$0.01	2	33.3	0.6	312.0
X PB 3/5+	$3.00	$200	12,245	$67	$0.02	2	33.3	0.6	312.0
MM 4/5+	$1.00	$10,000	689,065	$10,000	$0.01	2	5,000.0	96.2	104.0
MM 4/5	$1.00	$150	15,313	$150	$0.01	2	75.0	1.4	104.0
MM 3/5+	$1.00	$150	13,781	$150	$0.01	2	75.0	1.4	104.0
X MM 4/5+	$2.00	$40,000	648,976	$20,000	$0.06	2	10,000.0	192.3	208.0
X MM 4/5	$2.00	$400	19,088	$200	$0.02	2	100.0	1.9	208.0
X MM 3/5+	$2.00	$400	12,245	$200	$0.03	2	100.0	1.9	208.0
L6 5/6	$2.00	$2,478	55,491	$1,239	$0.04	2	619.5	11.9	208.0
L6 4/6	$2.00	$87	1,033	$44	$0.08	2	21.8	0.4	208.0
LM 6/7	$1.67	$6,973	299,305	$4,184	$0.02	1	4,183.8	80.5	86.7
LM 5/7	$1.67	$138	4,751	$83	$0.03	1	82.8	1.6	86.7
LM 4/7	$1.67	$20	214	$12	$0.09	1	12.0	0.2	86.7
LM 3/7+	$1.67	$20	230	$12	$0.09	1	12.0	0.2	86.7
Pick 3	$0.50	$250	1,000	$500	$0.25	14	35.7	0.7	364.0

As you can see, the games with the highest return to the players are both the Pick 4 and Pick 3 games.



Next, we examine the Per Dollar Prize amounts. Here, we see that only 4 prize levels return as much money per dollar spent as that of Pick 4. These are the Powerball and Mega Millions payouts for matching 4 white balls and the Power or Mega ball.



Now lets consider the amount of time we have before we reach the $0 (zero dollar) profit level. Of the 6 prizes that exceed the 6.9 year level, total amount spent is substantially higher than the Pick 4 total of $2,500.



Lastly, we illustrate the yearly cost of purchasing one single ticket for each of the games. Here, we see that the Pick 4 and Pick 3 cost is highest. However, this is primarily a function of there being 14 drawings held in a week verses 2 for most games (and 1 for Lotto Max).



Summary
In summary, we believe that playing 1 Pick 4 combination continually in each drawing is a viable strategy for those lottery players looking to earn investment income at a relatively low and affordable cost!

JL ..............

Introducing the Lottery Probability Surface

In an effort to help players find a financially feasible strategy for playing the lottery, we discovered an important organization inherent in all lottery games.  By reducing all the combinations of a particular game into individual sum and range buckets, and then totaling those occurrences, have identified each game's "probability surface".

The surface is constructed using the only the primary white balls and not the bonus balls.  One axis of the surface consist of the Sum of all the balls.  And, the second axis is defined by subtracting the last ball from the first ball (the X and Y axis are interchangeable).

Doing this, for Pick 3 and 4 games which allow all selection for replacement, the resulting surface is that of a diamond. The reason for this pattern is that the last ball may be less than, equal to, or greater than the first ball, thus allowing the Range to progress from negative to positive values.  The illustration below is a 3-D view of the Pick 4 probability surface.

3-D Image of Pick 4 Lottery Probability Surface

For those games which do not have replacement (such as Mega Millions, Powerball, Lotto 649, Texas 2 Step, etc), we ignore the order drawn and sort the numbers from lowest to highest value. Doing this, we define a shape that is trapezoidal in shape. The illustration below is a 3-D view of the Texas 2 Step probability surface. This shape similar to that of Powerball, Mega Millions, etc. However, its scale is more condensed.

Texas 2 Step Lottery Probability Surface (3-D)

During the coming months, we will publish the probability surface characteristics for each of the lottery games that we cover.  In addition, we will be adding new analytic pages to our website summarizing the historical data of each game.

Our first application using this new discovery will be the Pick 4 games. We are well into the development of studying the New Jersey Pick 4 and hope to release this in the next few weeks. Following that, we will apply the same template to analyzing the Pick 4 games which we can easily obtain the complete drawing histories (California, Texas, North Carolina).

JL ..........

Lottery Power Picks turns 6 year old this September

This has been an exciting year for us at Lottery Power Picks. It began with the announcement that Powerball was going to change its format. With that, we wrote an analysis of the new format and projected anticipated jackpot growth. Along with that, we added a "Which Game Should You Play" page, and provided our users with a new 2012 Powerball playing guide (all of these are available on this blog).

Our overall suite of products (website and blogs) has consistently maintained a level of 5,000 page views a day throughout the year.  However, when the Mega Millions jackpot reached the $400 million level, we found that search traffic jumped dramatically. Our daily traffic at the peak for: the Lottery Power Picks website had a record level of 8,137 visits; our news blog had 265 visits; and this blog received 2,470 visits.

During that period, we realized a few important things about lottery related sites. First, we learned that when jackpots are low, consumer interest is also low. People only become fanatics when the jackpot levels reach the $200 million level. Second, we learned that all the information that we provide is sought after during high times. Third, although daily visitor levels are relatively low most of the time, it is important to be positioned for the extraordinary times. Lastly, we learned that our information is valuable.

This had brought new enthusiasm to us. And, we responded by re-writing our Lottery Power Picks website. Although this is not fully complete yet, we have released it beta.  We expect this to be fully functional in the upcoming months and will cut it over to our live site by the end of 2012.

Additionally, we have been working on a Pick 4 strategy that we believe will help you win those prizes. It differs from our Pick 3 strategy because the cost of playing too many combinations is not cost effective. We will release our Pick 4 pages and write a blog entry about this by Thanksgiving.

Lastly, our web hosting company moved our site to a new server last Spring. Since then, our up-time has been nearly 100%, and more importantly, hacking attempts have dropped to a minimum. This allowed us to spend less time monitoring the traffic and more time developing our lottery brand.

We wish to thank all of our users who visit us on a regular basis and have taken the time to write us and give us feedback.  Additionally, we thank Google for providing us with a wide range of development and monitoring tools, and helping us appear in search results.

We look forward to releasing our new website and analytical lottery coverage articles during the next year. Hopefully, one or more of us will win a jackpot prize as well!

JL ............

Is is Time for a Euro Millions Super Draw?

Expect to see a Euro Millions Super Draw during May 2012

One of the special features of the Euro Millions lottery is the Super Draw. These are named "Super" because the minimum jackpot prize is typically set at �100 million, regardless the level of the previous jackpot.

In these drawings, only the Jackpot prize amount is increased.

What if there is no winner?
What happens to the Super Draw Jackpot prize it there is no jackpot winner depends on the Super Draw designation:

• Super Draw One means that the jackpot will roll forward to the following drawing; and
• Super Draw Two means the jackpot prize will be allocated to the winners of the next lowest tier in which there is a winner.

How are these funded?
After every Euro Millions drawing, 50% of the gross ticket revenue is allocated to the Common Prize Fund. Of this, 8.6% is placed in the EuroMillions Reserve Fund (also called the Booster Fund).

When the amount of money in the booster fund is sufficient, it is withdrawn and used for a Super Draw.

On the average, approximately �1million are added to the booster fund after each drawing. This means, it will take about a year for �100 million to accumulate.

To make Super Draws more frequent, the Super Draws are typically designated after the anticipated jackpot reaches �40M to �50M and the booster fund contains the remainder.

Why now?
The last Super Draw was held on October 4, 2011, approximately 6 months ago.

At present, we have calculate the value of the Reserve Fund to be around �57 million, which means that we would expect to see a new Euro Millions Super Draw sometime soon in the month of May 2012 (or whenever the jackpot nears �50 million).

Probability of a Mega Millions rollover or having a single winner decrease as sales approach 600M

As tonight's record Mega Millions drawing approaches, ticket sales are going off the charts. We originally expected that 400 million tickets would be sold, but with the recent increases in the jackpot prize from $476M to $540M $640M, we now believe that up to 600 million tickets may be sold.

Thus, we asked ourselves two questions:

1. What is the probability that there will be no winner in tonight's drawing?
2. What is the probability that there will only be one sole winner?

Using our brute force duplicate ticket estimator, we have produced two tables for your reference.

The first summarizes the probabilities of: 0 to 8 individual winning tickets. As shown, the probability of not having a winner tonight and rolling over again drops from 18% to 3% as ticket sales increase from 300 million to 600 million. Similarly,  we can see that the probability of having a single winner decreases from 39% to 27%, while that of two winners decreases slightly from 28% to 26%. Interestingly, we find the probabilities of 3 to 5 winners rapidly increase as sales approach 600 million. We believe the likelihood that 6 or more winning combinations will be sold is rather slim.

	Table 1: Probability of Mega Millions Winning Tickets
Winning Tickets	300M Sold	400M Sold	500M Sold	600M Sold
None, No winner	18.1%	10.3%	5.8%	3.3%
1 Winner Only	39.3%	35.4%	31.2%	27.4%
2 Winner Only	28.2%	29.5%	28.2%	25.9%
3 Winner	12.4%	18.4%	21.5%	22.2%
4 Winner	1.9%	5.9%	11.0%	14.9%
5 Winner		0.5%	2.3%	5.6%
6 Winner			0.1%	0.6%
7 Winner
8 Winner
Total Probability	100.0%	100.0%	100.0%	100.0%

The second table summarizes the distribution of the tickets sold. It estimates the absolute number of tickets in each category. Here we find that approximately 31.9 million combinations will not be generated when sales are at the 300M level, but only 5.8 million combinations will be unsold when 600M tickets are printed. In all other cases, the absolute number of tickets per category increase as sales increase. Interestingly enough, we can see how the size of the 6 and 7 tuplets begins to grow.

	Table 2: Distribution of Mega Millions Tickets Sold
Numbers	300M Sold	400M Sold	500M Sold	600M Sold
All Combinations	175,711,536	175,711,536	175,711,536	175,711,536
Unsold	31,864,733	18,036,279	10,209,010	5,778,566
1 Only (Singles)	143,846,803	157,675,257	165,502,526	169,932,970
2  (Doubles)	103,460,042	131,466,722	149,526,982	160,511,932
3 (Triples)	45,526,185	82,214,057	114,388,867	137,818,542
4 (Quadruples)	7,022,773	26,431,098	58,127,495	92,689,034
5 (Quintuples)	144,138	2,198,990	12,023,012	35,013,149
6 (Sextuplets)	59	13,876	430,590	3,988,410
7 (Septuplets)	0	0	528	45,963
8 (Octuplets)				0
Sum	300,000,000	400,000,000	500,000,000	600,000,000

We wish everyone the best of luck tonight and hope your dreams come true. But, as we can see from the above, remember to set your expectations according to the probability that you may have to share the jackpot prize with somebody else.

Cheers,

JL...............

Should I buy all the 175.7M Mega Millions combinations?

In the Tuesday night Mega Millions lottery drawing on March 27, 2012, an estimated 170 to 240 million tickets were sold. We obtain these numbers by doubling the increase in the cash (from $255M to $341M) and annuity (from $356M to $240M) prizes from the 27th to the Friday March 30th drawing. (Note that while the Mega Millions annuity has been increased to $500M and cash to $359.4, we have chosen to use the original prize levels to estimate ticket sales).

However, for purposes of this discussion, we will assume that 200 million Mega Million tickets were sold for that drawing.

Since our ticket sale estimate is well above the total number of allowable Mega Millions combinations (175.7 million), one can logically ask:

Why was there no Mega Millions Jackpot winner?

The answer is: Duplicates!

Because of randomness, the percent of duplicate tickets increases rapidly as the number of tickets are sold. In Mega Millions, this increase begins to level off after sales exceed 400 million. As the illustration below shows, approximately 40% of the combinations printed are duplicates when 200 million individual tickets are sold.

Graph 1: Percent of Mega Millions Duplicates per Million Tickets Sold

This means that of the 200 million sold, 80 million are duplicates, and only 120 million are unique. If we divide the 120 million by the 175 million Mega Millions combinations, we find that approximately 68.6% of the combinations were generated. Subtracting 68.6% from 100%, we learn that there is a 31.4% chance that the number picked in the drawing will be a loser.

Graph 2: Chance of Losing Mega Millions per Million Tickets Sold

Given the fact that the new Mega Millions annuity jackpot is set at $476 million for Friday night, we can expect ticket sales to potentially reach or exceed 300 million. At this level, about 52% of these tickets will be duplicate combinations, and there will be an 18% chance that there will be no Jackpot winner at all.

So, getting to our title question:

Should I buy all the 175.7M Mega Millions combinations?

The answer depends on how you purchase them. If you purchase every single unique combination, then Yes, you are guaranteed to win the Jackpot. In this case, there will be no losing tickets. However, you have to worry about sharing the jackpot prize with others. Using Graph 1 above, we can say that at the 300 million ticket sales level, you have 50 - 50 chance of winning it alone or sharing it with one or more others.

If you take the Cash Option, you will lose money if you have to share it with 1 other person.

And, if you take the Annuity, you lose money if you share it with 2 others.

However, if you are lazy and just buy 175.7 million Quick Picks, you are not guaranteed to win the jackpot. As stated above, approximately 40% of these will be duplicates and you will have a 31.4% chance of losing.

The last thing to remember is that you will have to pay taxes on the money you receive. If you win the jackpot, you will be in the highest tax bracket possible, which means that you will be paying 28% to the federal government.Then, depending on the State where you purchased your winning ticket and live, you may have to pay state taxes as well.

So in summary, our advice is NO. You should not purchase the 175.7million Mega Millions combinations unless the jackpot becomes substantially higher to cover your taxes and the possible loss of sharing it with others.

Multiple Lottery Ticket Odds Calculator Released

With all the excitement of winning the large Mega Millions and Powerball jackpots recently, we realized that many players were searching for a calculator that would show the odds (or chances) of winning when multiple tickets are purchased.

In response, we created and released a new Multi-Ticket Lottery Odds Calculator gadget which can be found on the right hand sidebar of this blog (about 1/4 down the page), on our Lottery Power Picks News blog, and in the Google gadgets directory.  To use this calculator, simply enter the number of tickets that you purchased and press the enter (or return) key. The odds of winning the top 2 prizes will automatically be displayed.  In our rush to release this gadget, we sacrificed making this a "pretty" display.

You can either use the calculator directly on this blog, or you can add it to your own iGoogle home page  by clicking on the "+ Google" button directly under the calculator.

Let us know what you think. 

Thanks, JL ......