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Thursday, May 29, 2008

Teen Wins PB Now What? - An LPP Special Edition, Advice to a Winner

Introduction
As part of our "If You Won" series, we had planned to one day write a number of articles about what you should do if you actually won the lottery jackpot. We still intend to write this series, but since a young lottery player recently won a large PB jackpot, we thought it more timely to address his situation now. Our objective herein is to offer a conservative opinion that may help this winner (and others) sustain a true lifetime of wealth and happiness.

Brief Background
A young 19 year-old lottery player hit the $35.3 million Powerball jackpot on the May 17, 2008 drawing. In the Powerball.com release statement, the player says he intends to share: his prize with his family and invest the money". Looking at the Winner's Stories page, we learned that he elected to receive the cash payment of $17.175 million. After paying his Federal taxes, the player will get to keep an estimated $11 to $12 million. (For purposes of the remainder of this discussion, we will assume he retains $11 million to spend and invest.)

Wow, $11M is a lot of Money!
Not Really! With today's life expectancy of 80-100 years, our young 19 year-old can realistically live for another 70 to 80 years. This money has to be conservatively managed in order to provide continuous income throughout his lifetime. If properly done, this young man will always enjoy his riches and perhaps pass on a legacy to his heirs. How can he do this?

By remembering and obeying our following advice.

Your life is changed forever.
First and foremost, you must realize that everything is now different. Your job now, and forever, is to manage this money. There are too many stories of people who won the lottery and spent it all. If you blow $1M per year, you will be out of money in 11 years, at age 30! Don't become another "lottery winner" victim. Instead, dedicate you life to managing the financial welfare of yourself. Yes, many will think that you are stingy, but you must think of yourself, not them.

We believe that you must prepare yourself, and know what may lay ahead. For this, we have identified 7 rules that you should follow:
  1. Educate Yourself
  2. Avoid the Vultures
  3. Resist Temptation
  4. Be Conservative
  5. Protect Your Money
  6. Seek Qualified Advice
  7. Decide for Yourself
1. Educate Yourself
Now that you have this money, you need to educate yourself about money. You need to understand mathematics, and learn about various investment vehicles. To to this, we urge you to attend college and learn about business. If you are already attending college, Great, Stay there and complete your degree. If not, enroll in college today. Meet with the college admissions staff, and explain your situation. Tell them that your situation has changed and that receiving a degree is now an important priority in your life. You'll have to work hard and learn, but so what, you have a concrete reason to do so, and a real need to know. As a start, read the book: The Millionaire Next Door. You're now one of them.

2. Avoid the Vultures
Now that you have a sizable stash, realize: Everyone Else Wants It. This goes for family, friends, business owners, salespeople, bankers, insurance salesmen, financial advisers, charities, religious organizations, con-artists, and more. For now, avoid them all. Change you phone numbers. Park you money in short term interest paying accounts, and take time to think. Don't be imitated or embarrassed into forking over your hard-earned winnings to fast talkers or down-and-outs. Remember that when you are broke again, nobody will care about you or want to be your friend again. So, avoid them all.

3. Resist Temptation
On the front page of our website, Lottery Power Picks, we highlight the 4 things most people want to do if they win the lottery: (1) Buy a new car; (2) Buy a new house; (3) Travel; and (4) Invest. These are all great things to do, but resist the temptation of unwisely overspending. Remember Rule #2 above. The salespeople in all these businesses are out to make a living. If you have money, they want it. Forget buying a Hummer or Ferrari; gas prices and insurances are far too expensive. Don't buy everyone in your family a mansion. One day you'll need to buy a house of you own. Don't travel First Class, that's a waste of money, and join the travel rewards programs to get free rewards. Stay away from stocks, options, swaps and more until you understand what they're all about. Lastly, don't throw continuous parties, treat everyone to dinner, and buy drinks for the bar just to look like a big shot. Spend wisely and thriftly.

4. Be Conservative
Initially invest your money in short to medium term interest bearing accounts. These can be banks accounts, CD's, US Treasury Bills & Notes, or Municipal Bonds (not annuities). If you simply deposit $10 million (and keep $1 million for a rainy day) into one of these, at: 3% you'll earn $300,000 per year; 4% you get $400,000; and at 5% you get $500,000. Pay your taxes, reinvest 1/2 of your interest, and spend the rest. Do this, and you earnings will grow, and you'll have lots of fun not working. Unlike investing in stocks, you'll never lose your money in these risk free type vehicles.

5. Protect Your Money
Who knows what the future holds. On day, you get married. Then a few years later, your wife files for divorce and wants half of your money ($5 million gone like that). To avoid this, think about having a pre-nuptial agreement. Also, think about putting the money into a trust. This may protect you and your assets from future lawsuits from a wife, other family members and friends as well. Also, begin to shop now for and buy a Personal Liability Insurance which will protect you if someone wants to sue you (this is cheap); and, make sure you have enough insurance on your car.

6. Seek Qualified Advice
We're not experts, but know that other people are. Seek FREE qualified advice from various professionals on every subject. For example, you will now need an accountant. Talk to a few, and find out what they do, and what they cost. You don't want to spend too much ($250-$1000 per year), but you will need to retain one of them. Look and ask around for other people who know about trusts, insurance, banking and investing. Don't stick with friends or family, they don't need to know your business. Qualified people will be happy to work for you at reasonable costs, and help you retain your winnings.

7. Decide for Yourself
If you follow the above 6 Rules of Advice, you'll have the confidence and understanding to buy, spend, invest, and enjoy what you want. If you listen to other people, and do as they say, you will most likely spend or lose most of your money (that's not what you want). Instead, listen to those who give advice. Analyze what it will cost you. Determine what you have to lose. Choose the best action that will insure your everlasting happiness and protect your money. You may make mistakes along the way, but in doing so, you'll learn. You won't be a fool for blindly doing what others told you to do, and you'll never be mad at anyone except yourself!



Lastly, We Offer You Our Best Wishes

We hope you have enjoyed our advice and have gained a bit of confidence on how to approach your future. Remember your goal is to have that money forever, and to live off the interest. With $11 million, there's enough money for you and your future family (wife and children), but not enough to support everyone else in the world! This may sound cruel, but it is all yours. Make sure it stays that way!

Congratulations to You
and

We Wish You the Best in the Future.


J.L. ..........


PS: Think about starting a daily journal, and keeping notes about all your offers, adventures, etc. Then, someday, 5 to 10 years from now, write a book on what it's like to be a Lottery Winner!



Here's another link that provides good advice:



Regular Bimonthly Focus for June : Analysis of the Powerball Cash verses Annuity Options



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Saturday, April 26, 2008

How Lottery Odds Change When Buying Multiple Tickets

Introduction
Over the past several years, I have read many posts on the internet from people who have wondered how their odds of winning the large lottery jackpots improve when they purchase multiple tickets. Most often, the replies stated that you should simply:

Divide the
Number of tickets you purchased for that drawing.
by the
Total number of combinations


Is this correct?
The answer is: Absolutely yes. This is the basic formula for computing the probability.

For example:
If you play Powerball, the chances of your tickets matching the winning Jackpot combination when you buy:
  • 1 Ticket, will be: 1 in 146,107,962 or 1 in 146,107,962
  • 2 Tickets, will be: 2 in 146,107,962 or 1 in 73,053,981
  • 3 Tickets, will be: 3 in 146,107,962 or 1 in 48,702,654
  • 4 Tickets, will be: 4 in 146,107,962 or 1 in 36,526,990.5
  • 5 Tickets, will be: 5 in 146,107,962 or 1 in 29,221,592.4
  • and so on.
Similarily, if you play Mega Millions, the chances of your tickets matching the winning Jackpot combination when you buy:
  • 1 Ticket, will be: 1 in 175,711,536 or 1 in 175,711,536
  • 2 Tickets, will be: 2 in 175,711,536 or 1 in 87,855,768
  • 3 Tickets, will be: 3 in 175,711,536 or 1 in 58,570,512
  • 4 Tickets, will be: 4 in 175,711,536 or 1 in 43,927,884
  • 5 Tickets, will be: 5 in 175,711,536 or 1 in 35,142,307.2
  • and so on.
Note that because this is a simple division formula, it is mathematically correct to reduce the numerator and denominator to the lowest terms. Whether the terms are reduced or not, the resulting probability value will be identical.

If this is so simple, why do people argue about it?
Because of the definition of the word "Odds". If you visit the AllExperts.com post: Probability & Statistics, you will read that we are in agreement. However, you will note that the article speaks in terms of "Chances" and "Probability", but not "Odds".

The question by Daren Henning in Dr. Math's Powerball Odds When Buying More Tickets, also alludes to this confusion, but the answer is not clarified.

Mr. Henning says that he and his friend are arguing about the odds when buying 10 tickets in a hypothetical 80,000,000 Powerball lottery. The friend says the odds are 10/80,000,000 or 1 in 8,000,000. However, Henning thinks the odds are to 79,999,990 to 1. Dr. Math agrees with the friend and explains why.

To be correct, Henning should have stated that he believed the odds were 10 to 79,999,990. In this case, he too would be correct.

How can they both be correct?
Once again, because of the definition of the word "Odds"
It is context dependent.


Statistical Definitions
When you buy a Lottery Ticket, you are buying a "chance" to win the jackpot.

In Dictionary.com, chance is defined as:
  1. the absence of any cause of events that can be predicted, understood, or controlled: often personified or treated as a positive agency: Chance governs all
  2. luck or fortune: a game of chance
  3. possibility or probability of anything happening: a fifty-percent chance of success
Measuring Chance
"Chance is measured using either probabilities (a ratio of occurrence to the whole) or odds (a ratio of occurrence to nonoccurrence, or for and against)."
  • Probability = events/(events+non-events) values range from 0 to 1
  • Odds = events/non-events values range from 0 to infinity
From sources: Measuring chance and Primer on Probability, Odds and Interpreting their Ratios

Example
As an example, assume that we are rolling a single 6 sided dice.

We wish to measure the chance that a "5" will appear. The probability that a 5 will appear is 1/6, or 0.1666667. Whereas, the odds that a 5 will appear are 1/5, meaning one change for, and 5 against.

Next, let us measure the chance that an even number will appear. The probability that an even number will appear is 3/6, or 0.50. Whereas, the odds that an even number will appear are 3/3 or 1/1 meaning one change for and one against.


Confusion Abounds
Just looking at the numbers above, one cannot tell if we are viewing an expression of probability or odds. While all these numbers are correct, we need more information in order to interpret their meanings properly.

Returning to Mr. Henning's question about the lottery odds above, both the friend and Dr. Math are asserting the correctness of the probability definition. In this, they are correct, but should have clearly stated that they are speaking of Probability, not Odds.

Whereas, according to the above definitions, Mr. Henning is correct in asserting the odds, because he is referring to the occurrences for verses occurrences against.


Resolving the Ambiguity of the Word Odds
We cannot change City Hall. In the Lottery World, the use of the word Odds is often synonymous with Probability or Chances.

If you visit the Minnesota Lottery Figuring the Odds or the Powerball - Prizes and Odds pages, you will see that they incorrectly define your odds in terms of Probability.

Conversely, when you read the Mega Millions How to Play and BCLC How play Lotto 6/49 pages, you will learn that they are correctly presenting your Chances.

In order to resolve the ambiguity of the word Odds, we believe the meaning is "sub-language" dependent.
  • Within the Lottery Context, we suggest that Odds be interpreted as Lottery Odds (which is the same as Probability)
  • Within the Gambling Context, such as horse racing, we suggest that Odds be interpreted as the defined Odds (Chances For verses Chances Against).
The easiest and least confusing thing to remember about Lottery Odds is to:

Always think in terms of Chances.
That way, you can't go wrong!


To learn more about the Odds / Chances discussions, you can read the following:



Focus for June : Analysis of the Powerball Cash verses Annuity Options



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Monday, March 31, 2008

Special Edition: Power Play 10X Promotion

Introduction
During the month of April 2008, the The Multi-State Lottery Association (MUSL) is offering Powerball players who buy the Power Play option a chance to win 10 times the non-jackpot prizes.

Prior to every drawing, the Power Play wheel is spun to determine that drawings Power Play number. The wheel typically contains: (4) 2's,(4) 3's, (4) 4's, and (4) 5's.

In this promotion, Powerball will replace one of the 5's with a 10, giving players a 1 out of 16 chance to get a 10x multiplier, and 3/16 chances to get a 5x multiplier.

Based on this information, the average PowerPlay multiplier during the promotional April 10x period will be 3.8125. This is determined by taking the probability weighted average of the four possible multipliers: 0.25*(2+3+4)+(3/16*5)+(1/16*10)=3.8125

Is it worth buying the Power Play 10x Megaplier?

Using the Powerball "Multiplier Jackpot Breakeven Formula" defined on the Powerball Powerball Play Multiplier Breakeven Analysis page, the jackpot breakeven will be

J = O*(m-2)*c
J = 146,107,962*(3.8125-1)*0.197
J = 52,169,674


So should you buy the Power Play for a chance to win 10x?
During this promotional period, it depends where the Jackpot is.
  • For Powerball 10x, Breakeven is $52.2 million: Buy the Power Play Option whenever the Jackpot is below this value. Never above this. Buy 2 tickets instead.

Why is that?
The goal of all players is to have the most money played returned back to the players. In a previous post and a website page, we explained this in detail. If you wish to learn more about this subject, then read our 2 entries:


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.




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Monday, February 25, 2008

Analysis of the Canadian Lotteries

Introduction
I have received many e-mails from players in Canada asking if we would offer Lottery Power Picks for the smaller Jackpot Provincial lotteries: Atlantic 49, BC 49, Quebec 49, Ontario 49, Quebec 49, and Western 649. Initially, we felt that these games were insignificant, but after reading one person's comments, we realized that we needed to take a closer look. He had said that even though the Ontario 49 Jackpot was fixed at C$1.0 million, he preferred to play Ontario 49 because it only cost C$0.50.

This made us think. Were these provincial lotteries with smaller jackpots a better or worse value than Lotto 649 and Super 7?

One would normally think that bigger is better. But after conducting this research, we have changed our thinking to:

Bigger is better ONLY WHEN the Jackpots are High.

How would you know which to buy?
If you have an unlimited amount of money and want to win a lottery jackpot, you should buy tickets for every lottery available to you.

But, if you're like most folks on a budget, you'll want to spend your lottery dollars wisely. For this purpose, we have prepared the breakeven return table below to help you decide. Each row indicates when you should buy the provincial lottery instead of Lotto 649 or Super 7.







Table 1: Provincial vs Multi-State Breakeven
Buy
When
Lotto 649

is below
When
Super 7
is below

Atlantic 49
C$9.7 M
C$8.4 M

BC 49
C$8.1 M
C$5.9 M

Loto-Quebec 49
C$8.1 M
C$5.9 M

Ontario 49
C$7.5 M
C$5.0 M

Western 649
C$12.4 M
C$12.4 M
  • Buy Atlantic 49:
    • When Lotto 649 is below C$9.7 M
    • When Super 7 is below C$8.4 M
  • Buy BC 49:
    • When Lotto 649 is below C$8.1 M
    • When Super 7 is below C$5.9 M
  • Buy Quebec 49:
    • When Lotto 649 is below C$8.1 M
    • When Super 7 is below C$5.9 M
  • Buy Ontario 49:
    • When Lotto 649 is below C$7.5 M
    • When Super 7 is below C$5.0 M
  • Buy Western 649:
    • When Lotto 649 is below C$12.4 M
    • When Super 7 is below C$12.4 M
Why is that?
To make the smaller Provincial lotteries attractive to the players, they typically return more of the money received back to players. Thus, when the Lotto 649 and Super 7 jackpots are low, you get more for your money from the provincials.

However, as the Lotto 649 and Super 7 jackpots grow, the money returned back to players also grows. When their returns exceed the fixed returns of the provincials, you should buy the larger mult-states.

Why is it difficult to know which to buy?
It is difficult to know which lottery to buy because everything varies: the ticket price, the odds, the payout, etc. In order to give you an indication of the variety in each of the Canadian lotteries, we have graphed 6 aspects of the games. Looking at these, you can quickly see that without some strict measure, it is difficult to determine which game to play.



1. Minimum Jackpot Size
Graph CS1 illustrates the minimum jackpots for each of the 7 Canadian lotteries. For Super 7, C$2.5 M is the fixed minimum, while C$3.0 M is the Lotto 649 minimum. Since both of the lotteries are nationwide, their jackpots will grow each time a drawing fails to produce a jackpot winner. Whereas, the provincial lottery jackpots are fixed at: C$1.0 M for the Atlantic 49, Ontario 49, and Western 649; and at C$2.0 M for BC 49 and Quebec 49.


2. Price per Ticket C$
Ticket prices for each of the lotteries also vary. The most expensive is Lotto 649, which costs C$2.0 per ticket. Next are BC 49 and Quebec 49, at C$1.0 per entry. While Super 7 sells 3 plays for C$2.00, the individual ticket costs C$0.67 each. Lastly, Atlantic 49, Ontario 49, and Western 649 tickets only cost C$0.50 each. Note however that Western 649 requires players to buy 2 games at once.

3. Number of Tickets for C$2.00
To make these purchases equivalent, let's assume that a player will purchase C$2.00 worth of tickets. For this amount: Lotto 649 players will have 1 chance to win the C$3.0M jackpot; the BC and Quebec 49 players will receive 2 chances to win C$2.0 M; Super 7 players will have 3 chances to win C$2.5 M; and the Atlantic 49, Ontario 49, and Western 649 players will have 4 chances to win C$1.0 M.



4. Overall Odds of Winning
The overall odds of winning any prize also vary. Super 7 offers the best chances, giving players a 1:17.66 to win something. Super 7 odds are 1.8 times better than Lotto 469, BC 49 and Quebec 49 whose odds are 1:32.31. Further, Super 7 odds are 3.0 times better than the Atlantic, Ontario and Western 49 odds of 53.66.



5. Average Ticket Payout
Although Super 7 contains more winning tickets, the average ticket payout is C$4.92. Whereas, Lotto 649 tickets average the highest payout of C$20.54 (4.2 times better than Super 7). As for the provincials: Ontario 49 pays C$12.81 per ticket ( 2.6 times Super 7); Atlantic 49 pays C$14.97 (3.0 times); BC and Quebec 49 pay C$16.14 (3.3 times); and Western 649 pays out C$17.54 per ticket (3.6 times more than Super 7).



6. Total C$ Returned to Players
The total dollars returned to players is displayed as cents per dollar. These indicator is important because it allow us to compare value on an equivalent basis. As shown, Lotto 649 returns the least back to the players, at only C$0.32 per every dollar received. Next comes Super 7 at C$0.42 per dollar, and Ontario 49 at C$0.48/dollar. Both the BC and Quebec 49 give back 1/2 of their take. Atlantic 49 returns C$0.56 to players. And, Western 649 pays out a whopping C$0.65 per dollar received, mor than twice as much as Lotto 649.



What about Lotto 649 verses Super 7?
Table 2 below provides you with a guideline as to when you should buy Super 7 of Lotto 649. To utilize this information, find out what the current Super 7 jackpot is. Then, look down the left column for this number. When found (or interpreted), read the right most column. If the Lotto 649 jackpot is below the number shown, then buy Super 7 tickets. If it is equal to or greater, then buy Lotto 640 tickets.












Table 2: Super 7 vs Lotto 649 Breakeven
If Super 7
Jackpot
is
Then Buy Super 7
whenLotto 649
is below
C$2.5 M
C$5.8 M
C$5.0 M
C$7.5 M
C$10.0 M
C$10.8 M
C$15.0 MC$14.1 M
C$17.0 M
C$15.5 M
C$20.0 M
C$17.5 M
C$25.0 M
C$20.8 M
C$30.0 M
C$24.1 M
C$40.0 M
C$30.8 M
C$50.0 M
C$37.5 M
  • When the Super 7 Jackpot is C$12.0 million or lower, you should buy Super 7 unless Lotto 649 is greater than shown
  • Above the C$12.0 million breakeven cross-over point, buy Super 7 only when its jackpot is higher than the Lotto 649 levels shown.


Conclusion
As you can see, the decision to buy the Provincial lotteries or the larger multi-territorial national lotteries depends on the current jackpot size and how much money you wish to spend. If you are not on a budget, buy every available lottery. But, if your funds are limited, consult Tables 1 and 2 above to determine which lottery will give you the most for your money.

Don't ignore the Canadian Provincial Lotteries just because the jackpots are low!
They are often a very good value to play.

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 April: How Your Probability of Winning Changes when you buy Multiple Tickets



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Wednesday, December 19, 2007

Should You Buy the Power Play, Sizzler, or Megaplier?

Introduction
Very often, someone asks me whether they should buy the Powerball Power Play Option. Not knowing the mathematical answer, my gut feeling was to tell them No. However, since one popular website encourages players to sign a petition to add a Megaplier Option to the Mega Millions lottery, I had my doubts. At present, the State of Texas offers this option. More recently, I read that Hot Lotto would be adding a Sizzler Option beginning in January 2008.

Realizing the importance of this topic, it was time to conduct research on this topic. What I learned is that for each of these three lottery options, the answer to the question:

Should I Buy the Power Play, Sizzler, or Megaplier?

The correct answer is both Yes and No!
It depends on the size of the Jackpot.


How do you know when to buy it?
You should always buy the multiplier option whenever the current jackpot value is below its Jackpot Breakeven level.
  • For Powerball, Breakeven is $43.2 million: Buy the Power Play Option whenever the Jackpot is below this value. Never above this. Buy 2 tickets instead.
  • For Hot Lotto, Breakeven is $2.59 million: Buy the Sizzler Option whenever the Jackpot is below this value. Never above this. Buy 2 tickets instead.
  • For Mega Millions, Breakeven is $47.2 million: Buy the Megaplier Option whenever the Jackpot is below this value. Never above this. Buy 2 tickets instead.

Why is that?
The reason is that the Jackpot prizes in each of these lotteries are not multiplied. 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 jackpot returns outweigh the sum of the payouts of all the other prizes. Once this is reached, buying the multiplier option is not a good investment. Remember, because the multiplier option costs $1 more, it is necessary to divide these probability weighted returns by 2 before comparing them to single $1 tickets. When the jackpot is above the breakeven level, the per dollar return of multiplier tickets becomes less and less valuable compared to that of a regular 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.


Powerball Power Play
When a player buys the Power Play option, any prize that the player wins, except the Jackpot, will be multiplied by either 2, 3, 4 or 5. The odds that any one of these multipliers will occur is (typically) a constant 25%, which means that a player can expect an average 3.5 times multiplier on average.

Based on this assumption, the graph below illustrates both the expected Power Play return (in blue) against the expected return of a single Ticket without the Power Play (in red).

When the jackpot is set to the minimum $15 million, Power Play returns $0.396 of each dollar received, compared to $0.300 for those without the option.

When the jackpot level reaches $43.2 million, both tickets with and without the Power Play returns $0.493 for each dollar received. We refer to this $43.2 million as the Jackpot Breakeven level.

Above this breakeven level, tickets purchased without Power Play return more to the players. When the jackpot grows to $90 million, $0.813 is returned to straight ticket holders compared to only $0.653 to those who bought the Power Play.

PowerPlay chart

Players should purchase Lottery Tickets like they would any other investment, and always seek the highest return on their dollars. Thus, when the Powerball jackpot is below $43.2 million, the Power Play should be purchased. When the jackpot is above this level, never purchase the Power Play. Go for the Jackpot instead.


Hot Lotto Sizzler
When a player buys the Sizzler option, any prize that the player wins, except the Jackpot, will be multiplied by a fixed 3 times.

Given this, the graph below illustrates both the expected Sizzler return (in blue) against the expected return of a single Ticket without the Sizzler (in red).

When the jackpot is set to the minimum $1 million, Sizzler returns $0.401 of each dollar received, compared to $0.329 for those without the option.

When the jackpot level reaches $2.59 million, both tickets with and without Sizzler returns $0.474 of each dollar received. We refer to this $2.59 million as the Jackpot Breakeven level.

Above this breakeven level, tickets purchased without Sizzler return more to the players. When the jackpot grows to $5 million, $0.694 is returned to straight ticket holders compared to only $0.584 to those who bought the Sizzler.

Sizzler chart

Players should purchase Lottery Tickets like they would any other investment, and always seek the highest return on their dollars. Thus, when the Hot Lotto jackpot is below $2.59 million, the Sizzler should be purchased. When the jackpot is above this level, never purchase the Sizzler. Go for the Jackpot instead.


Mega Millions Megaplier (available only in Texas)
When a player buys the Megaplier option, any prize that the player wins, except the Jackpot, will be multiplied by either 2, 3, or 4. The odds that any one of these multipliers will occur is not constant, but on the average, a player can expect an average 3.476 times multiplier.

Based on this assumption, the graph below illustrates both the expected Megaplier return (in blue) against the expected return of a single Ticket without the Megaplier (in red).

When the jackpot is set to the minimum $12 million, Megaplier returns $0.350 of each dollar received, compared to $0.250 for those without the option.

When the jackpot level reaches $47.2 million, both tickets with and without Megaplier returns $0.451 of each dollar received. We refer to this $47.2 million as the Jackpot Breakeven level.

Above this breakeven level, tickets purchased without Megaplier return more to the players. When the jackpot grows to $90 million, $0.694 is returned to straight ticket holders compared to only $0.523 to those who bought the Megaplier.

Megaplier chart

Players should purchase Lottery Tickets like they would any other investment, and always seek the highest return on their dollars. Thus, when the Mega Millions jackpot is below $47.2 million, the Megaplier should be purchased. When the jackpot is above this level, never purchase the Megaplier. Go for the Jackpot instead.



Conclusion
As you can see, the decision to buy the Power Play, Sizzler, or Megaplier multiplier option is dependent upon the jackpot size. When the jackpot is below its breakeven level, players are encouraged to buy the multiplier option. But, when the jackpot is above its breakeven level, players should forego this option, and buy 2 straight tickets instead.


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: The Canadian Territories



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Saturday, November 17, 2007

Hot Lotto to Add Sizzler

We read on the Kansas Lottery website that beginning January 3, 2008:

Hot Lotto will be adding a Sizzler Option

This will be similar to the Powerball Power Play. You pay $1 more, and all prizes EXCEPT the Jackpot will be Tripled.

Is this a good option? We will analyze both the Sizzler and Powerplay options in our December 2007 BiMonthly Article. Don't miss it!

Also, note that beginning in January 2008, Lottery Power Picks will be adding 6 new lotteries for you to get your numbers:
  • California Super Lotto Plus
  • Hot Lotto
  • EuroMillions
  • Irish Lotto
  • UK Lotto
  • Thunderball
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Sunday, October 21, 2007

The 2007 LPP Lottery Value Rankings

Introduction
Both the Lottery Power Picks Home Page and its Gadget display a graph of the up-to-date jackpots from select worldwide lotteries. Visitors can instantly see which ones are high and which are low, giving them a sense of where the money is. However, this sampling contains a mix of mini, mid-size, and jumbo lotteries, making it difficult to identify their intrinsic value when choosing a game.

People tend to play the lottery with the highest jackpot and skip the low jackpots.

Are they making the right decision?

After reading the following article, the answer may surprise you because Lottery Power Picks has calculated and created a simplistic value ranking of its lotteries. Using this information, we believe that our: Canadian members can more confidently decide if they should play Lotto 649 or Super 7; Californians can choose to play Super Lotto Plus or Mega Millions; UK residents can select the best of EuroMillions, Lotto, or Thunderball; borderline state residents can pick either Powerball or Mega Millions; and more.

Because players have a diverse choice of lotteries to play, this post is intended to help them find the best place to invest their lottery dollars. It is not meant to hinder or solicit sales, but to simply help lottery players understand their favorite games a little better. We hope you enjoy it.

The 2007 LPP Worldwide Lottery Value Rankings
The following lists our 2007 Lottery Value Rankings of our 10 sample Worldwide Lotteries. These lotteries are ordered from the best (lowest number) to the worst value (highest number) for the players. Note that there are 3 ties. In these cases, the lotteries are simply listed in alphabetical order.
  1. Canada Super 7
    EuroMillions

  2. Thunderball
  3. Powerball
    UK Lotto

  4. California Super Lotto Plus
  5. Canada Lotto 649
    Irish Lotto

  6. Hot Lotto
  7. Mega Millions


Ranking Components
In order to calculate these rankings, five statistical components were individually ranked according to value, and their sum was equally averaged. These average values were then ranked from lowest to highest, and each lottery were was assigned that ranking. The final ranking was ordered from lowest to highest, where the lowest represents the best value for lottery players, and the highest represents the least valuable for players. In the case of ties, our ranked list presented the lotteries in alphabetical order, and was not meant to imply any empirical order. The following table summarizes the individual components and rankings we calculated for each lottery. These are discussed in more detail below.

Component

MM

PB

CDA
649
CDA
S7
CAL
SL
HL

UK
649
TB

EM

IRL
645
1. Overall Win Odds
87624110359
2. ReturnOn$10981672145
3. AvgPayout/$53498101672
4. Jackpot/Odds32654791018
5. Cash or Annuity2211221111
Average5.64.653.64.85.44.64.23.65
Rank 10471694317



Component 1: Overall Winning Odds (Overall Win Odds)
To calculate the Overall Winning Odds, we assumed that each combination was sold and that there were no duplications. Next we counted the total number of winning combinations. By dividing the total combinations by the winning combinations, we derived the Overall (Winning) Odds. For this statistic, the lower the Overall Odds number, the better for the player.

For each lottery, we have calculated these values, and matched those stated by each lottery. The chart below graphically displays these results. Note that UK Lotto towers over the others, giving those players the worst chances of winning. This is followed by the Irish Lotto, and Mega Millions. The lotteries giving players the three best chances to win are: Thunderball, Canada Super 7, and Hot Lotto.





Component 2: Average $ Returned to Player on $ Spent (ReturnOn$)
Having calculated the complete set of winning combinations above, we next determined the total value of the prize money paid back to the players by multiplying the prize cash values paid times the the number of winning combinations. We summed the total money paid and divided it by the total number of combinations to determine the Return on $ invested. The chart below summarized our findings. When reading this, please note that the higher the value, the better the player ranking.

For each $ a play spent on the lottery, Thunderball offers the highest returns with 0.54 for each $ spent. The second and third best returns were the UK Lotto and the Canadian Super 7.
Mega Millions returns the least back to the players, returning only 0.25 of each $ spent. Next comes Powerball, and then Canadian 649.





Component 3: Average Ticket Payout per $ Spent (AvgPayout/$)
The cost that each lottery charges for a single ticket varies. Many charge $1 for 1 ticket, and others charge $1 for 2 tickets, $2 for one ticket, and $2 for 3 tickets (ignoring the foreign exchange considerations). In order to compare the lotteries on a common basis, we have calculated the prize dollar return per winning ticket. Using this type of cost basis, players are neutral to the actual cost of a particular lottery ticket, and can concentrate on the average value of a winning ticket per dollar they spent. Thus, when viewing the graph below, the average payouts are consistently presented. Please note that when reading this graph, the higher the value, the better the player ranking.

The calculations used to determine this information was to total the total cash value all of a lottery's prizes, divide it by the number of winning tickets, and then dividing the result by the cost of a single ticket.

As we can see, the first place UK Lotto average winning ticket payout is nearly $10 higher than the second place Irish Lotto. Third is Powerball. The 10th place lowest paid winning ticket is that of Hot Lotto. The Canadian Super 7 is in 9th place, and the California Super Lotto Plus is eighth.





Component 4: Jackpot $ per Odds (Jackpot/Odds)
Each lottery offers a minimum jackpot prize. These vary from as low as $0.25 million to $15 million. Additionally, the odds of winning any also prize also varies. For comparative purposes, the graph below illustrates the the ratio of the jackpot to odds. Thus, one's jackpot expectation per odd is similarly quantified. Again, the higher the value, the better for the player.

As shown, the three major jumbo lotteries lead this risk/reward measure. First comes Euro Millions; second is Powerball; and third is Mega Millions. On the low side are: Thunderball whose payoffs are extremely small; and followed by the UK Lotto and the Irish Lotto.





Component 5: Cash or Annuity (Cash/Annuity)
Of the 10 lotteries being ranked, six pay the stated cash jackpot prize. The other four: Mega Millions, Powerball, California Super Lotto Plus, and Hot Lotto, each pay the stated prize as an annuity which is a heavily discounted cash prize. This means that the actual cash paid to a jackpot winner in each of these is considerably less than what is stated.

To adjust this discrepancy, we have assigned a value of 1 to all lotteries paying cash, and penalized those who pay annuities by assigning a value of 2 for this measure. Thus, for this measure, the lower the value assigned, the better for the players.



Summary
After ranking our 10 lotteries by each of the above measures and then finding their average placement, we derive an unbiased overall ranking that we call the LPP Lottery Value Ranking. In 2007, we believe that our summary informs the players which lotteries offer the best value for their investments. The list below re-iterates our findings and presents our rankings from best to worst value for players.

1. Canada Super 7
1. EuroMillions

3. Thunderball
4. Powerball
4. UK Lotto

6. California Super Lotto Plus
7. Canada Lotto 649
7. Irish Lotto

9. Hot Lotto
10. Mega Millions

After reviewing this list again, it is clear that we can't judge a lottery by it's jackpot size. Tied for Number 1 are: Canadian Super 7, whose minimum jackpot is $2.5 million; and EuroMillions, with a starting jackpot of �15 million. In third place is Thunderball, with a fixed jackpot of only �0.25 million. At the end are the Hot Lotto jackpot of $1.0 million, and lastly Mega Millions, offering $12 million.

As we can see, when looking Lottery Value Rankings list, the jackpot sizes are mixed and appear in an almost random order.

In our introduction above, we posed a question:

Should people play the lotteries with the highest
jackpot and skip those with low jackpots?

Based on our study herein, our answer clearly is:

No! Never judge a lottery simply by its jackpot size!

If you wish to learn more details about any one of these lotteries, read our detailed pages by clicking the links above.


Focus for December: The Powerball Powerplay




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