A When to Buy Mega Millions or Powerball Guide

Introduction
On January 31st 2010, sales of Powerball and Mega Millions expanded into each other's jurisdictions. No longer are States classified as either one lottery or another. Now, players in most States have the opportunity to buy both games.

This cross-selling is great for players when the Jackpots are high and for the hard-core lottery players. But what about the regular or occasional player on a limited budget? Now they are faced with three important questions:

• Which Lottery is Better to Buy?
• Should I Buy the Powerplay or Megaplier Option?
• Can I Afford It?
  

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Whats' the Problem?
Initially when players could only buy one game, it was easy to set a budget. In most of the old Mega Millions states, folks could spend $5 per game, or $10 per week, or $520 per year. Those in Texas had the option of spending $1 extra per ticket to buy the Megaplier. For them, their budget would be $1,040 per year.

Similarily, everyone in the Powerball states could choose whether to buy an individual ticket or one with the Powerplay Option. But, they too could maintain a budget of $520 - $1,040 per year.

But now, the games are doubled, and so is the yearly expenditure. While we don't know if people can afford to spend $2,080 per year on the big prize lotteries, we expect that this is a lot of money for them. To us, this is a big problem.

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Difficult Choices
In previous articles and published webpages, we introduced the concept of Jackpot return. This number indicates how much money a lottery will pay out in prizes verses how much was collected.

Each lottery, and variation thereof, has it's own Jackpot return. This number increases linearly as the Jackpot grows. Thus, it is easy to calculate the implied breakeven of the Megaplier and Powerplay Options. And from this, we can recommend whether to buy these options or not.

However, when multiple games are compared, it becomes difficult to decipher one's choices.

Graph MMPB-GR01 below illustrates the Jackpot Returns for Powerball and Mega Millions, and their associated Powerplay and Megaplier Options. As seen, all of these returns appear to intersect at points where the Jackpots are somewhere between $47 and $65 million.






Addtionally, the Mega Millions and Powerball Jackpots do not move in parallel. Mega Millions may be $40M, and Powerball only $20M. So, what should one do?

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What to Buy Matrix
To help simplify this information we have created a "What to Buy Matrix" below. The data is organized horizontally by the Powerball Jackpot ranging from $20-$300 million.  Vertically is the Mega Millions Jackpots, with values for $12 to $300 million.

The cells are color-coded.
The light blue indicates that you should buy the Powerplay Opton;
The dark blue indicates that you should buy the Powerball Only;
The light red (pink) indicates that you should buy the Megaplier Opton;
The dark red indicates that you should buy the Mega Millions Only;

MM JP	Powerball Jackpot
	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
12	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
20	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
30	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
40	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
50	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
60	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
70	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
80	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
90	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
100	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
125	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
150	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
175	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
200	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
250	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300
300	20	30	40	50	60	70	80	90	100	125	150	175	200	250	300

The table assumes that a player is willing to buy the Powerplay or Megaplier Option. But, the player will only buy one lottery or another.

To read the table, you can locate the row with the Mega Millions Jackpot. Then, read across the columns to the current Powerball jackpot. If the intersecting cell is: red, then buy Mega Millions; blue, buy Powerball; pink, Megaplier; or light blue, Powerplay.

Returning to the example above when the Mega Millions is $40M, and Powerball only $20M, a player should buy Mega Millions with the Megaplier Option!

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Summary
In the beginning of this article, we raised three questions.

• Which Lottery is Better to Buy?
• Should I Buy the Powerplay or Megaplier Option?
• Can I Afford It?
  

We believe the first two are answered in the "What to Buy Matrix", which tells you which lottery is better to buy, and if you should buy the Megaplier or Powerplay option.

The "Can You Afford It" answer is really up to you. Our recommendation is that those on limited budgets should only buy one lottery or the other.  The matrix above indicates which lottery you should buy, and if you should buy the Powerplay or Megaplier Options.

Since these options are only recommended when the Powerball & Mega Millions jackpots are $50 million or under, we believe that it is not necessary to buy these all the time. This means that your budget will not substantially increase, and that Most Can Afford It!

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Let Us Know
We hope this information is helpful to everyone. During the past month, we have followed this advice, and we hope that you will as well!

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

When Will Powerball States Begin Selling Mega Millions? (Lottery Trivia Question 2010-02)

This week's Lottery Trivia Question is about the Powerball and Mega Millions Lotteries.

Our Trivia Question #2010-02 is: 

A deal was struck last October allowing Powerball and Mega Millions States to sell both lotteries.

• When will States begin cross-selling tickets to both lotteries?
• Will there be any format changes to the games?

Enter your answer by leaving a Comment to this post below. Leave your name, and if you have a website or blog, provide it's URL and name.

We will provide the correct answer next Monday, January 18th, and will post your name and a URL link back to your site.

Have Fun,

JL.........

What Game Replaced Pennsylvania Match 6? (Lottery Trivia Question 2010-01)

This week's Lottery Trivia Question is about the Pennsylvania Lottery.

Our Trivia Question #2010-01 is: 

In March 2009, the Pennsylvania Lottery retired its Match 6 Game.

• What new lottery game replaced Match 6?
• What is the format of this new game?
• What are the chances of winning?
  

Enter your answer by leaving a Comment to this post below. Leave your name, and if you have a website or blog, provide it's URL and name.

We will provide the correct answer next Monday, January 11th, and will post your name and a URL link back to your site.

Have Fun,

JL.........

2009 Lottery Power Picks Year in Review

This past year of 2009 has presented lottery players with a number of exciting changes. Among the major highlights were:

• Powerball changed its format to 59 White Balls and 39 Powerballs,
  
• Canadian Super 7 was retired,
• Lotto Max was launched.

And, trying to keep pace, Lottery Power Picks provided analysis of:

• Lotto Max - When to Play Guide,
• How 2009 Powerball Changes Affect You, and
  
• 3 UK Lotto Oddities or Questining Camelot.

Our new developmental releases included:

• Hot / Cold Lottery Number Frequency Distribution for all our covered Lotteries,
• The Lottery Annuity Calculator Gadget,
• Packaging new RSS Feeds for easy access to our important research articles.
  

And for fun, we:

• Reactivated our AskTheBlogster blog, and
• Wrote a 12 part Lottery Trivia Question/Answer Series of Useless Facts.
  

As we look forward to 2010, we plan to:

• Introduce a variety of Lottery Research Strategies that analyze the probabilities of winning by playing subsets of numbers, and
• Expand our Lottery coverage into the Canadian Regional Lotteries, Texas, New Jersey and more.

Thanks for all your support during the past year and help us to make 2010 better than ever!

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





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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
Game	Population	Col A 50% Sure	Col B 99.9% Sure
Powerball	146,107,962	14,232.0	44,928.3
Powerball (Jan 09)	195,249,054	16,452.1	51,937.1
Mega Millions	175,711,536	15,607.3	49,270.1
Lotto 649	13,983,816	4,402.9	13,899.4
Super 7	62,891,499	9,377.4	29,476.7
Super Lotto Plus	41,416,353	7,577.3	23,920.5
Hot Lotto	10,939,383	3,894.3	12,293.6
EuroMillions	76,275,360	10,283.0	32,462.0
Irish Lotto	8,145,060	3,360.3	10,607.9
UK Lotto	13,983,816	4,402.9	13,899.4
Thunderball	3,895,584	2,323.9	7,336.2
Birthdays	365	22.5	71.0

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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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.

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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.

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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.

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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!

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

• Lottery Post Discussion Thread
• Odds and Probability - Brian Alspach
• Odds Slang for Probability? - Dr Math
• Lottery - Odds of winning (1 ticket and 2 tickets)- Ricci rec.gambling.lottery
• Lottery - Odds of winning (1 ticket and 2 tickets) - Perkis rec.gambling.lottery
• Lotteries: What are the odds?

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

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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.

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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.

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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.

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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.

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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.

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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).

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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.

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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 M	C$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.

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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.

• Canadian Lottery Comparison
• Atlantic 49
• BC 49
• Ontario 49
• Quebec 49
• Western 649

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

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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.

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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.


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.

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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.


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.

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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.



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.

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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.

• Powerball Power Play Analysis
• Hot Lotto Sizzler Analysis
• Mega Millions Megaplier Analysis

Focus for February: The Canadian Territories

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