by Iliya Bluskov, Ph.D.
Copyright
ISBN 9780968950289
All rights reserved under the PanAmerican and International Copyright
Conventions. This material may not be reproduced, in whole or in part,
in any form or by any means electronic or mechanical, including
photocopying, recording, or by any information storage and retrieval
system now known or hereafter invented, without written permission from
the publisher, Lotbook Publishing.
All inquires should be addressed to:
Lotbook Publishing
P.O. Box 23037
Prince George, B.C.
V2N 6Z2 Canada
or email: lotbook@telus.net
In his
new pick5 book, Dr. Bluskov’s once
again delivers the best known strategies to the lottery players; this
time his focus is on Pick5 lottery systems. Players who are interested
in systems for Pick6 lotteries should check his pick6 book. In this presentation of the pick5 book, some sections are omitted,
others are partially presented. The Contents lists the titles of all
sections except the titles of the systems; three (out of 126) systems
are presented here. The full text and the remaining 123 systems are in
the book.
Contents
Can you win the top
prize in your lottery by playing with a system?
Playing systems in
the big doublepick lotteries: Wheeling the bonus number(s)
Wheeling bonus
numbers in Euro Millions
Finding your way through the
book
Navigation table by
number of combinations
Navigation table by
quantity of numbers
PART I: Lottery systems
with a single guarantee
System # 26: 9 numbers,
12 combinations
(and 105 other
systems)
PART II: Lottery systems
with double guarantees
System # 108: 9 numbers, 18 combinations
(and 10 other
systems)
PART III: Lottery systems
with multiple guarantees
System # 126: 11 numbers, 11 combinations
(and 8 other
systems)
PART IV: More about the
book and systems
Is this the best book on
the market?
How a system is
constructed
Larger systems
Comments, reviews, testimonials
Ordering Information
Dr. Bluskov is a university professor. He has also worked as a freelance writer for a number of lottery publications in Europe and North America, and has spent many years in research in Combinatorics, a branch of Mathematics, which, among other things, deals with combinatorial lottery systems. He turned his lifelong fascinations with numbers and structures into groundbreaking strategy books for lottery players. Part of his research is on determining how to achieve a specific winning guarantee in a lottery in the minimum possible number of tickets. The results in his books originate from recent research in several areas of mathematics, and have been obtained by various techniques ranging from sophisticated combinatorial constructions to applying optimization methods via thousands of hours of computations. Although based on quite advanced knowledge in mathematics and related areas, the results are described in plain language and are accessible to virtually every lotto player or a group of players. Dr. Bluskov’s lotto books have been the best on the market for a long time, and we firmly believe he will keep it that way for the years to come. We hope you will agree with that statement when you go through the content and use some of the systems. Dr. Bluskov is the only author who has actually created world record breaking lotto systems. His books present a number of improvements and new features that cannot be found in any other book on lotto systems. These include the organization and the presentation of the material, the systems with multiple guarantees (never appeared before in a lottery publication) and the complete tables of possible wins. Each table has been generated by a complete experiment over ALL theoretically possible draws. A computer program has performed the experiment for every system in the book. The tables have been additionally abbreviated and custom designed "by hand". The complete tables appear also for the first time in a lottery publication. Wheeling the bonus number(s) in the Mega lotteries (Lucky Star numbers in EuroMillions) is completely new to the genre. Dr. Bluskov was the first to introduce and study several ideas that lead to establishing a number of properties defining a good lotto system. These include minimality, balance, and maximum coverage, features that are discussed in the text. Information about the availability of these features is provided in his comments for each system in his books. The book presented here is for pick5 lotteries and contains 126 systems (wheels) all of which are the current world records in terms of providing any particular guarantee in the minimum known number of combinations.
Readers are often interested to know whether I play
the lotteries, how I play and how much I have won. Indeed, I do play, and when I play I do use systems. I used to play a lot when I was younger.
Nowadays, I have a good
day job that keeps me busy even at nights, I am involved in publishing
books, both lottery and
mathematical ones and invest in the stock market; overall, I do not really need to
win a jackpot to have a comfortable life. Still, I do not mind winning
one! I do not think there is a single person on earth who minds winning one either. I have always looked at the
lottery as an
entertainment, not as a source of income. To get rich from the lottery
you have to be among the few lucky big winners; in other words, you must be a
jackpot winner, either alone or with a group of people. The purpose of my book is to show you, the readers, the strategies that many big winners, syndicates and
individual players alike, use regularly to play the lottery, scooping
some small wins along the
way, while waiting for the big hit. You might be one of them one day, it can happen.
I would like to make it perfectly clear that I do not promote
any particular lottery and am not connected to any of the existing lotteries. The book itself does not promote playing with a
(large) number of tickets. It is a book for those players (or groups of
players) who have ALREADY decided to play with more than two tickets.
You are probably interested in this book,
because you are going to throw a couple of bucks at the next jackpot anyway, right? So, my
question is: Why not try the
strategies of the big
winners? This book will lead you through
the widely used highly entertaining and precise strategy of using lotto
systems.
The book
came as a result of long years of experience in creating and improving
lottery systems. I have worked as a freelance writer for a
number of lottery publications in Europe and North America, and I have
spent many years in research in Combinatorics, an area of Mathematics, that
among other things deals with combinatorial lottery systems (or coverings, as they call them in
Combinatorics). I hold an M.Sc. and Ph.D. in Mathematics and work as a
university professor. All of my publications, including both my
master's thesis and doctoral dissertation, are related to lottery
systems. The objects in
this book originate from the most recent
research in the area, and are based on expert knowledge of the subject.
That is why this book has
no match among the publications and software in existence.
Back to my playing experience: Indeed, I played, both
individually and in pools, and I played enough to win: a couple of
second tier prizes, a number of third tier prizes; I even hit the top
tier once, a small jackpot, back in Europe, but I am still chasing the elusive Big Jackpot. The
"small" jackpot that I won was actually a car. I never drove that car.
I chose to receive the equivalent of the value of the car in money and
continued playing until I hit a 5win (in pick6 lotto), first with another player and then
another one, just by myself, winning multiple smaller prizes along the
way. That was over 30 years ago; the cost of a ticket was 10 cents and
it was quite affordable to play a system. I was a student at the time,
young and excited about many things in life; I spent a good portion of
my winnings on partying nonstop for months, and, of course, on some
more lottery play. I believe I made many people happy to know me and
made many new friends as well. Perhaps, I was luckier than average at
that time; still, I did not become rich; after all, it was a car and
some small to medium wins. Nevertheless, these were good size wins for
the time and I had a lot of fun dealing every day with sums higher than
my monthly allowance. Overall, I was happy to have had this experience,
because it earned me a lifetime interest in a subject that later became
my area of research and studies and kept me quite busy over the years.
I had already been using lotto systems, but it was at that time that I
really became interested in the subject, and I started thinking on how
to improve the performance of these systems to the absolute maximum, by
reducing the number of combinations for any given guarantee to the
absolute minimum. I had a lot of success in this direction and I am
still fascinated by the subject. Many users of lotto systems are
enthusiastic about my book, others are cautious; I believe this is the
case with every gambling book. I just offer my knowledge and expertise
to the players and groups who are willing to use it. The book might
help you win more prizes or win prizes more often. In any case, I am
happy to offer you a new perspective on the lottery, new ways of
enjoying the lottery as a game, and not just as the five minutes thrill
of watching the draw on TV. I believe that playing lotto should be fun,
just like any other game of chance, and I am glad that my book is a
step in this direction.
Here is a bit more history in support of my credentials: Back
in 1987, I started writing for a weekly newspaper on sport and
lotteries, and then I started a column devoted to lottery systems in a
second, similar, newspaper. I moved to Canada in 1993 and continued my
contributions to these two newspapers for several years after that.
After spending over 10 years in studies and research in Combinatorics,
working mostly on coverings (the mathematical term for lottery
systems), in 2001, I published the first edition of the book Combinatorial Lottery Systems (Wheels) with
Guaranteed Wins, which quickly became the Amazon bestselling book
on lotto systems for pick6 lotteries. (A pick6 lottery is one where
the main draw has 6 numbers, plus possibly one or two bonus numbers.) A
second edition of that book was published in 2010 (you can order the
new edition of the pick6 book here). A
pocket version called The Ultimate Guide to
Lottery Systems was published in 2009 and translated into several
languages including German, Spanish, Portuguese, and Japanese.
Meanwhile, readers kept asking about a similar book for pick5
lotteries, and now this book is a reality, you can order it right here.
This book can be used for any pick5 lottery in the world. It
can be used in almost any English
speaking country, as there are such lotteries in each of Canada, USA, United Kingdom, South Africa, and Australia. There are pick5
lotteries in almost any country
in Europe, and also in many other places, including Antigua, Argentina, Barbados, Dominican Republic, Ghana, Jamaica, Japan, India, Mexico, Philippines, Taiwan, Turkey, Trinidad and Tobago, to name a
few. A pocket version of this book has
been produced and it is available in English and French.
Some of my readers might wonder why I decided to write books
on this subject. Well, I have been in the business of creating and
publishing lotto systems for a long time, so that the idea of writing a
book was not that foreign to me; nevertheless, I did not really intend
to write books, not until I realized that there are several such books
in existence and I saw them: they all shared the same characteristics:
quite outdated and poorly written; often giving misleading information
to the reader. They all exploited lotto systems from older, European
sources, such as the Bulgarian Lottery Corporation Book, or a similar
book from Hungary. Systems from these sources were recycled and
published as new material by a number of authors. More recently, some
of these authors updated their collections from Internet sources and
published slightly more uptodate editions; still the state of the art
was out of reach for them and consequently for the lotto players. It
was at that time that I decided to make some difference by writing new
books not only for lotto players who were already familiar with using
lotto systems but also for players who were willing to start
experimenting with them. I was up to the challenge. Before I started
writing, I carefully studied what other sources had to say about lotto
systems (wheels). During my career as a professional mathematician and
creator of lotto systems I collected every imaginable piece of
literature and software on the subject. I also collected and studied
pretty much everything written in the area of coverings (the
mathematical term for lotto systems or wheels). I was quite happy to
discover that many of my systems are better than the existing ones in
terms of performance. At that time, I realized that I should start
publishing my findings. In the process, I found many more new record
breaking wheels and published them in various lotto publications. I was
not in a hurry to publish books. I realized that the process of
"getting the big picture" might take several years, and several years
it took. Finally, in 2001, the first edition of my pick6 book was published. It came out at a
time when I was absolutely satisfied with the content and the quality
of the product, at a time I considered its level to be well above the
level of any competing product. The book quickly found its permanent
place in the lotto products market and has been the number one
bestselling book on lotto systems for a long time. The tradition of
superior quality has been fully maintained in the second edition of my pick6 book (2010) and in the present, pick5 book (2011).
Odds
of being struck by lightning are better than the odds of winning a
lottery.
Lottery Myth
The number of possible draws in any lottery is huge and the probability of winning the jackpot is small. Still not as small as the probability of being struck by lightning, as the following excerpt from Duane Burke's address, Top Ten Myths About Lottery (and Why They Are Not True) suggests: "Statistics gathered by NASPL (North American Association of State and Provincial Lotteries) indicate that in one year alone (1996) 1,136 people won a million dollars or more and an additional 4,520 won $100,000 or more by playing North American lotteries. By contrast, 91 people were killed by lightning during that same year in the United States." This was in year 1996, but the number of people struck by lightning probably remains about the same over the years, while many new lotteries are created every year, and therefore many more opportunities for winning a top prize arise. You would probably agree that the myth is busted. Indeed, the probability of winning the jackpot ranges from the relatively high 1/15,104 in a 5/20 lottery to the staggering low 1/175,711,536 in the multistate doublepick lottery Mega Millions. Aside from winning a Jackpot, the players have other ways to win something with their tickets; in many lotteries, they can even enter a draw and win a prize with a nonwinning lottery ticket, and, as Burke continues: "What kind of a second prize does a lightning strike offer?'' To be fair to the supporters of the myth though, I will finish this "lightning" diversion with a comment from a reader of Burke's article: "The truth is: There are way less people trying to be struck by lightning (than those trying to win a Jackpot). If you were really trying, your odds are pretty good!'' The chances of winning prizes smaller than the jackpot in any lottery are much better. That is why, in the quest for the elusive jackpots, many players prefer to play with a wellorganized group of tickets, so that they can win guaranteed smaller prizes. Such a group of tickets is what we call a lottery system. Lottery systems can be thought of as an interesting and entertaining, but also very precise strategy for playing the lottery. Although the best lottery systems were created by using quite advanced mathematics and computations, they are very easy to use. In fact, to use lottery systems, all you need to know is how to count up to the number of balls used in your lottery. No mathematical knowledge is either assumed or required for playing a lotto system. In this book, I will explain what a lottery system is and how to use it, and I will also provide you with a number of excellent lotto systems to diversify your lotto experience. A lottery is a game. Games are entertaining. I hope this book will show you, among other things, how to extract more entertainment value from your lottery playing experience.
We start with a brief discussion on lotteries. A pick5 lottery is a game where one has to correctly guess several (usually 2 or more) of the numbers (5 in our case) drawn from a larger set, of, say, 39 numbers, for example. In various places of the world, there are lotteries with 20, 25, 30, 31, 32, etc., up to 90 numbers. The size of the lottery often depends on the size of the country (or state) where the lottery is played. Some lotteries introduce bonus (supplementary) numbers, which might be drawn from the same set as the main 5 numbers (such as Maryland's Bonus Match 5, Road Island Wild Money, New Mexico Roadrunner Cash, etc.), or from a different set (Powerball, Mega Millions, EuroMillions, Loto, Thunderball, California SuperLOTTO Plus, Hot Lotto, Megabucks Plus, Wild Card2, Kansas Cash Lottery, Tennessee Cash, etc.). You can use the lottery systems presented in this book for ANY such lottery in the world, even for lotteries that might be introduced in the future and have a number of balls outside the range 2090.
In this book we focus on 5numbersdrawn lotteries, but most of the existing lotteries operate on the same principles as the 5numbersdrawn lotteries. If the main draw consists of 5 numbers, the lottery is usually referred to as a pick5 lottery. If the main draw consists of 6 numbers, the lottery is called a pick6 lottery. There are also pick3, pick4, pick7 and even pickmore lotteries (Keno, for example). In any lottery, players fill out slips containing one or more tables, each containing all of the numbers of the lottery. For example, in a 5/39 lottery, each table has all 39 numbers, and the player fills 5 numbers in each table. We also refer to these tables as tickets. (Other sources use terms such as games, plays, or boards.) A combination is the set of 5 numbers filled in a particular table. When the draw comes, 5 numbers are drawn from the set of all numbers in the lottery. Players win whenever they correctly guess usually 2 or more of the numbers drawn in one of their tickets. The number of tables on a playing slip does not really matter for the application of our lottery systems.
If you watch morning shows or check your lotto publication regularly, you have probably seen it already, a syndicate of 7, or 10, or any number of people, won the big jackpot; or a smiling individual holding the big check and sharing his/her joy with the world. You have dreamed of you being there on the picture, right? I have dreamed about that too; still do, as a matter of fact. Occasionally, the winners will mention how they got there, some of them will praise their lucky numbers, and others will claim they used a lottery system. Yet others may have used a lottery system, but they will shy away from mentioning it to the public, they will just enjoy the money and try to win it again. So, what is the hype about? It is about the fact that if you want to play more numbers and you want to have certain guaranteed wins, then you have to use a lottery system (or a lottery wheel, as some authors call it) to organize (or wheel) your numbers. What is a lottery system and how can it help you diversify your lottery playing experience? In what follows, the lottery systems will be demystified for you, and you will be provided with a nice collection of great lotto systems.
Lottery systems are sought and used by lottery players throughout the world. Lottery systems are considered to be not only entertaining, but also a very wellorganized way of playing the lottery. This book introduces the bestknown systems (also called trapping systems, or wheeling systems, or wheels in short; mathematicians call these objects coverings). I will talk more about what "best" means in the next two sections. The process of using a lottery system (or wheel) is sometimes referred to as wheeling. There is a reason for that which originates from the construction of some systems; I will talk more about it later, in part IV of the book. Lottery players like using a system, because a system guarantees wins in the same way a single ticket does, while it allows playing with many numbers (6,7,8,9,10,11, etc.). I believe that using a lottery system from this book is more entertaining than just using a system from other sources or playing a random collection of tickets, and one of the reasons is the following: The possible wins for each system can be studied in advance from the Table of Possible Wins, a feature that has been fully developed and implemented for the first time ever in my books. Players like the fact that playing with systems provides a steadier stream of wins compared to playing with a random collection of tickets. I will expand a bit on that in the next section. Players also like the fact that playing with a system increases the chances of winning. This comes with a price, of course: The price of purchasing more than just one ticket. However, you might have already been playing with more than one ticket per draw, or, perhaps, you have considered doing so. Then this book is exactly the book you need.
Suppose for example, you want to play with 9 numbers instead of just 5. Naturally, you are willing to play more than one ticket and you want a certain guarantee. Let us say that you want a 3win whenever 3 of the numbers drawn are in your set of 9 numbers. This means you want a set of combinations (tickets) that covers every possible triple out of your 9 numbers. Such a set of combinations is an example of a lottery system. You can find a lottery system with this property under #26 in the book. In this example, the lottery system has the property that any triple out of your set of 9 numbers is contained in at least one of your combinations, so you get a guaranteed 3win whenever 3 of your 9 numbers are drawn.
In a sense, a lottery system expands the guarantee that you have on playing just 5 numbers (one ticket). If you just play one ticket and correctly guess 3 numbers, then you are guaranteed a 3win. The lottery system in our example has the same guarantee, a 3win if 3 numbers are guessed correctly, except that now you play a larger selection of numbers; 9 in this case. (In this book we also present systems with 3 if 3 guarantee for playing anywhere between 7 and 27 numbers.)
All of the lottery systems presented in this book have certain guarantees. In this section, I will explain what the advantages of using a lottery system are and what exactly a guarantee means when you play a lottery system. Using a lottery system assumes that you play with more than five numbers, and you want to organize your numbers in such a way that a certain minimum win is guaranteed. If you play with just one ticket and you correctly guess 3 numbers, then you are guaranteed exactly one 3win. A possible question was mentioned earlier, namely: How to build a system that will guarantee a 3win on 3 guessed numbers, if you play with not 5, but say, 9 numbers. Let us look at our previously mentioned example from the book, System #26. By using System #26, you are guaranteed a 3win whenever 3 of your 9 numbers are among the 5 numbers drawn. The system shows that you only need 12 combinations (or 12 tickets) to do so. Out of 9 numbers, one can form 126 distinct quintuples (5number combinations); the nonmathematicians can take my word for it; those with some mathematical preparation can apply the formula C(9,5)=126. Therefore, you only need to play 12 of these 126 combinations to achieve the 3 if 3 guarantee. What are the advantages of playing for such a guaranteed win? Let us compare playing with 12 random tickets against 12 tickets chosen according to our lottery system. We should mention that the probability of a 5win is the same for each ticket. However, if any 3 of the numbers drawn are among the 9 numbers chosen by you, then the 12 tickets of the lottery system guarantee at least one 3win, while 12 random tickets (on the same 9 numbers) guarantee nothing! This illustrates one of the main advantages of using a lotto system. Suppose you played your 9 numbers in the 12 combinations of System #26 for a long time and hit 3 of the numbers drawn, say, 10 times, over this period of time. Every time you hit 3 of the numbers drawn, you won at least one 3prize. Had you played your 9 numbers in 12 random combinations, you would have probably hit a 3win several times, but, most likely, not all 10 times, as with the system. In a worse case scenario, you could have missed the 3win in each of the 10 draws in which you hit 3 of the numbers drawn! The reason is quite simple: Random combinations do not come with a guarantee; a system does!
Lottery systems have been used by lottery players throughout the world. In fact, some European lottery corporations have integrated lottery systems in the automated processing of lottery tickets. Most of the existing implementations are based on outofdate systems. Lottery players have always been attracted to the most economical lottery systems, that is, systems achieving a certain guarantee in the minimum possible (or known) number of tickets. Recent advances in the research on coverings made it possible to reduce the number of combinations in many systems to the absolute minimum in the entire range of possible guarantees. These advances are reflected in my book.
Minimality is an important quality of all lottery systems in this book. The logic behind seeking minimal systems is simple: Let us assume you play with 9 numbers. If you could get a guaranteed 3win by using a system in 12 combinations (system #26 from this book) and a system in 20 combinations, then which one would you choose? The answer is obvious: You would most likely prefer to get the guaranteed 3win in the fewest number of tickets possible, in this case, in 12 tickets. Some players might argue here: OK, but if I play 20 tickets, I will have 20 shots at a 5win rather than just 12. True, but if you really want to play 20 tickets, perhaps, you can play for a higher guaranteed prize, or you can play more than 9 numbers for the same guarantee, thereby giving yourself a better chance to capture all of the drawn numbers in your larger set. For example, in 20 combinations, you could play system #28, which has 11 numbers and still guarantees a 3win if 3 of your numbers are drawn, or you could even go down to 18 combinations and play system #108, which has 9 numbers and guarantees not one, but two 3wins if 3 of your numbers are drawn! (Yes, you read it right, you do not have to double the number of combinations from 12 to 24 to get the double guarantee! More on that can be found in Part II of the book.) So, the minimality concerns the following question: How many tickets have to be played in order to have a certain guarantee? Clearly, you want to achieve this guarantee in the minimum number of tickets possible. Well, you are at the right place: All of the systems presented in this book use the minimum known number of tickets. The systems are combinatorial objects that have been extensively studied by mathematicians and computer scientists. The systems in this book are either impossible or very unlikely to ever be improved. Some of the systems represent classical results in combinatorics; others originate from recent research. Many of the systems have been obtained by the author and described in depth in a series of scientific papers. Others have been obtained via hundreds of hours of programming and computations. As a result, all of the systems are currently the best (in the minimum number of tickets) known. For most of the systems presented here, we can say even more: They are mathematically minimal, meaning that no further improvement (that is, reducing the number of tickets while preserving the guarantee) can ever be done.
Let us look one more time at our example, System #26. It has been proven that the minimum number of tickets is 12 for the given guarantee. In other words, if you want to play 9 numbers and you want a guaranteed 3win if 3 of your 9 numbers are drawn, then you need to play at least 12 tickets. System #26 achieves the 3 if 3 guarantee in exactly 12 tickets, and this is the minimum possible number of tickets for that guarantee. That is why we call such a system mathematically minimal.
A new feature and a very important quality of this book is the full table of possible wins for each presented system. The tables give the distribution of wins in all possible draws and are excellent tools for determining which system to choose and what could the expected win be once you hit some (usually at least two) of the numbers drawn. Let us take a look at the full table of possible wins for System #26. It is somewhat long. This explains why for some systems I present an abbreviated table of wins. Here is the full table first:
Guessed 
5 
4 
3 
2 
% 
5 
1 
 
8 
2 
0.79 

1 
 
7 
4 
6.35 

1 
 
6 
4 
0.79 

1 
 
5 
6 
1.59 

 
3 
6 
2 
4.76 

 
3 
5 
3 
1.59 

 
3 
4 
5 
12.70 

 
3 
3 
6 
6.35 

 
2 
7 
2 
4.76 

 
2 
6 
4 
9.52 

 
2 
6 
3 
17.47 

 
2 
5 
5 
9.52 

 
2 
5 
4 
6.35 

 
2 
4 
6 
3.17 

 
1 
8 
2 
9.53 

 
1 
7 
4 
3.17 

 
 
10 
1 
1.59 
4 
 
1 
4 
6 
0.79 

 
1 
4 
5 
6.35 

 
1 
3 
6 
17.46 

 
1 
3 
5 
1.59 

 
1 
2 
8 
10.32 

 
1 
2 
7 
4.76 

 
1 
2 
6 
4.76 

 
1 
1 
10 
1.59 

 
 
6 
5 
1.59 

 
 
6 
4 
3.17 

 
 
6 
3 
6.35 

 
 
5 
5 
9.52 

 
 
5 
4 
12.70 

 
 
4 
7 
9.52 

 
 
4 
6 
9.53 
3 
 
 
3 
3 
2.38 

 
 
3 
2 
1.19 

 
 
3 
 
1.19 

 
 
2 
6 
9.52 

 
 
2 
5 
7.14 

 
 
2 
4 
16.67 

 
 
1 
8 
4.76 

 
 
1 
7 
21.43 

 
 
1 
6 
35.72 
2 
 
 
 
5 
2.78 

 
 
 
4 
27.78 

 
 
 
3 
69.44 
Each line represents a
possible distribution of wins. The last column shows the probability of
the corresponding distribution of wins. If you play System # 26 and 3
of your 9 numbers are drawn, then the system guarantees you at least
one 3win. Note that you will actually win more than that: There are
nine possibilities that are clearly seen from the section of the table
corresponding to
Presenting individually every line in the full table is not always physically possible; in many cases the full table would contain several hundred entries. In such cases, and in order to keep the book compact, I present an abbreviated table. In fact, you will notice that the table of possible wins for System #26 looks a bit different from the full table presented earlier in this section; we give the abbreviated table here as well, for easy comparison.
Guessed 
5 
4 
3 
2 
% 
5 
1 
 
58 
26 
9.52 

 
3 
36 
26 
25.40 

 
2 
47 
26 
50.79 

 
1 
78 
24 
12.70 

 
 
10 
1 
1.59 
4 
 
1 
4 
56 
7.14 

 
1 
3 
56 
19.05 

 
1 
2 
68 
19.84 

 
1 
1 
10 
1.59 

 
 
6 
35 
11.11 

 
 
5 
45 
22.22 

 
 
4 
67 
19.05 
3 
 
 
3 
03 
4.76 

 
 
2 
46 
33.33 

 
 
1 
68 
61.91 
2 
 
 
 
5 
2.78 

 
 
 
4 
27.78 

 
 
 
3 
69.44 
Note that no essential information has been lost: An abbreviated table still comprises all possible distributions of wins, but most of the lines in such a table actually represent several lines from the full table. We can justify such abbreviations by observing that what matters most are the highestranked prizes. The number of such prizes is given by the first number of a line in the table. What one gets in lowerranked prizes is generally a small part of the entire win. In abbreviating the full tables I tried to keep distinction between the highest prizes. In other words, I tried to start every line in a table of possible wins by a single number rather than by an entry of the range type ab. For example, I could have further abbreviated the second section (corresponding to 4 of your 9 numbers drawn) of System #26 as
Guessed 
5 
4 
3 
2 
% 
4 
 
1 
4 
56 
7.14 

 
1 
3 
56 
19.05 

 
1 
2 
68 
19.84 

 
1 
1 
10 
1.59 

 
 
46 
37 
52.38 
but I did not, because the last line of the section would not have been quite informative. If that section was much longer, perhaps, an abbreviation like
Guessed 
5 
4 
3 
2 
% 
4 
 
1 
14 
510 
47.62 

 
 
6 
35 
11.11 

 
 
5 
45 
22.22 

 
 
4 
67 
19.05 
would have been justified, as every line still starts by a single number entry rather than one of the range type ab.
We include a further brief explanation for those readers who are not familiar with probabilities: Let us look again at the section of the table corresponding to hitting three of the numbers drawn. Suppose you have played long enough with the same system and hit 3 of the numbers many times. Then, in approximately 62 out of 100 cases (61.91, to be precise), you will have one 3win, in 33 (33.33, to be precise) out of 100 cases, you will have two 3wins, and in 5 (4.76, to be precise) out of 100 cases, you will get three 3wins.
Playing with the systems is very easy: In our example (System #26), where you play with 9 numbers, you will just have to perform the following simple operations:
(1) write the numbers from 1 to 9 in a line (these are the numbers in the original system);
(2) write your 9 numbers in a line below the first one;
(3) substitute each number in the original system with the corresponding number from the second line to obtain your set of tickets;
(4) fill your combinations in the playing slips.
For example, if your 9 numbers are 2,3,7,12,15,18,19,22 and 24, then you will have the following.
Numbers in the original system: 
1 
2 
3 
4 
5 
6 
7 
8 
9 
Your numbers: 
2 
3 
7 
12 
15 
18 
19 
22 
24 
Original system: 

Your set of tickets: 

1. 
1 
2 
3 
7 
8 

1. 
2 
3 
7 
19 
22 
2. 
1 
2 
4 
7 
9 

2. 
2 
3 
12 
19 
24 
3. 
1 
2 
5 
6 
7 

3. 
2 
3 
15 
18 
19 
4. 
1 
3 
4 
5 
6 

4. 
2 
7 
12 
15 
18 
5. 
1 
3 
4 
8 
9 

5. 
2 
7 
12 
22 
24 
6. 
1 
5 
6 
8 
9 

6. 
2 
15 
18 
22 
24 
7. 
2 
3 
4 
5 
8 

7. 
3 
7 
12 
15 
22 
8. 
2 
3 
5 
7 
9 

8. 
3 
7 
15 
19 
24 
9. 
2 
3 
6 
8 
9 

9. 
3 
7 
18 
22 
24 
10. 
2 
4 
6 
7 
8 

10. 
3 
12 
18 
19 
22 
11. 
3 
4 
6 
7 
9 

11. 
7 
12 
18 
19 
24 
12. 
4 
5 
7 
8 
9 

12. 
12 
15 
19 
22 
24 
You can write your numbers in any order in the second line, not just in increasing order; still the guarantee of the system will be the same; moreover, the table of possible wins will be the same (however, you might hit a different line of the corresponding section of the table of wins). Usually the systems are balanced, in the sense that all numbers are almost equally represented. That is why I recommend arranging your numbers in increasing order; then the substitution can be made in the easiest possible way. Of course, if the system is not completely balanced, then you might choose to put your favorite numbers under the system numbers with the highest number of occurrences.
Let us illustrate one more time the guarantee of the system from our example (a 3win if 3 of your numbers are drawn): Suppose the numbers 7,12 and 24 are drawn, then the system must bring you at least one 3win. Indeed, it is easy to check that this is so. In fact, you will get two 3wins (in tickets 5 and 11).
The book also contains systems with different types of guarantees, for example, a guaranteed 3win if 4 of the numbers drawn are guessed correctly; or a guaranteed 4win if 5 of the numbers drawn are in your chosen set of numbers. The use of such systems is the same as in the example above. We also introduce systems that have never appeared in the lottery literature or software: Systems where the main guarantee is multiple prizes, for example, a guarantee of two 3wins if 3 of the numbers drawn are in your set of chosen numbers, or a guarantee of three 4wins if 5 of the numbers drawn are in it. Again, these systems can be used in the same way as explained at the beginning of this section.
Finally, I want to bring to your attention a question that players ask sometimes: I have used a system and won, but my set of prizes can be found nowhere in the table of wins. What is wrong? There are two possible explanations: You have either produced your set of tickets incorrectly, or you have made a mistake while filling your playing slips. So, do the substitution carefully, avoid any distraction while filling the playing slips. A single mistake can cost you a huge prize...
In order to get your guaranteed wins you still have to guess correctly some of the numbers drawn. A natural question is then how to choose the right numbers. Lottery officials tell us that any draw is totally random and unbiased. Mathematicians and statisticians are consulted to make sure that any particular draw represents a completely random selection of numbers. I agree that lottery officials make any effort to secure a fair game for all players. I trust that and I trust that my fellow mathematicians and statisticians do their best to make the lotteries as unbiased as possible. Still, any draw is a physical process; even generating random numbers by a computer is a physical process, and the numbers generated are as random as the skills of whoever programmed and patented the random generator. There are not many types of physical machines that draw the numbers. Perhaps the most popular mechanical solution is a machine that mixes and draws the numbers by using compressed air. The numbers are painted or imprinted on balls. The balls are usually made of light plastic; often they use table tennis balls. Let us assume, for the purpose of this discussion, that the lottery has 39 numbers. Initially, the balls are arranged in some random manner in a container. When the draw starts, the balls get pushed by the compressed air into a transparent sphere where they bounce on the inside surface of the sphere under the action of the compressed air and get mixed well, until one of them is captured in a pipe, through which it rolls into a display. The process continues until all five numbers are drawn (6 or 7, if there are bonus numbers in the lottery). Now, this is a physical process all throughout. There are so many factors that affect the draw that one might easily be tempted to question the integrity of the entire process: The initial arrangement of the balls, the weight and shape of the balls, the air pressure provided by the compressor, etc. One question which is frequently discussed at lottery forums, and which I do not have to answer for you here is the following: You paint the numbers 1 and 34 on two identical balls; are they still identical? I know lottery officials do their best to ensure the lotteries are unbiased. They are happy if the public believes their lottery is unbiased. The reality is: The public chooses what to believe in. Some people do not trust random generators, for example. Random generators were proven to be not that random in the past. You might have heard stories about lottery corporations that decided to draw the numbers by computer and got flooded by letters from players questioning the integrity of the draw. Mechanical ways to draw the numbers are more trusted: One sees what is going on; testing looks easier, etc. Now, we have to very well realize that lottery officials do as they say; they are truly interested in the complete randomness of their lotteries. After all, why would they need to cheat the public if the lottery usually takes approximately 50% of all money that goes in the game? Of this 50%, probably about 510% goes to expenses associated with running the lottery, the rest goes to various charities, so money spent on the lottery actually serves good causes, if this makes you feel good. Lottery is a game of chance, it is a gambling game and as such it is no different than any other gambling game. The house (the lottery officials in this case) is truly interested to provide a fair game.
Still, gamers have exploited `random' processes to the tune of making millions by tracing bias in such processes. They have exploited pretty much everything: From gaming terminals in pubs and casinos, to roulette tables in the big gambling cities, to poker and other gaming sites on the Internet. They have exploited bias in physical devices such as roulette tables, but they have also exploited computer games, such as online poker where the cards are dealt based on numbers between 1 and 52 generated by a random number generator (RNG). Stories like that are all over the Internet and the available literature. So, you decide for yourself what you believe or not believe in when you play the lottery.
... … … … … … … … … … … … … … … … … … … … … … … … … … … … … …
(read the full text of this section in the book)
Can You Win The Top Prize in Your Lottery by
Playing With a System?
Of course, you can! In fact, every ticket of your system can win the top prize. Here we assume that the top prize in your lottery is a 5win. This is not exactly the case in the Mega Lotteries such as Powerball, Mega Millions Thunderball, and Euro Millions, although you still have to hit all 5 of the main numbers drawn; there you also have to hit one or two bonus numbers; these are essentially twopick lotteries and will be discussed separately. The advantage of using a lottery system is that even if you do not win the top prize, you will still get your guaranteed wins provided the draw hits your numbers. That is one of the reasons why lottery players and groups of players prefer to use systems. A lottery system gives you the opportunity to chase the top prize in an organized and entertaining way, and also guarantees some smaller prizes if less than 5 of your numbers are drawn. Of course, if you hit the top prize by using a lottery system, then you will also win a number of smaller prizes.
A system that guarantees the top prize (that is, a 5win if 5
of your numbers are drawn) is expensive. Below is a table that gives
you the number of combinations you need to play in order to get every
possible combination out of your numbers.
Numbers played 
Number of combinations 
6 
6 
7 
21 
8 
56 
9 
126 
10 
252 
11 
462 
12 
792 
13 
1,287 
14 
2,002 
15 
3,003 
16 
4,368 
17 
6,188 
18 
8,568 
19 
11,628 
20 
15,504 
21 
20,349 
22 
26,334 
23 
33,649 
24 
42,504 
25 
53,130 
26 
65,780 
27 
80,730 
28 
98,280 
29 
118,755 
30 
142,506 
The
number of tickets increases very fast. A system that contains all
possible combinations is called a complete system. If you play
with
Now, how difficult is to be a big
winner? The Jackpots vary considerably in type and size. There are
lotteries with a fixed Jackpot, which can be any sum starting as low as
$20,000. In this type of lottery, there is usually a restriction on the
number of Jackpots that can be given at the fixed value in any given
draw. For example, if the fixed value of a Jackpot is $100,000, the
lottery might stipulate that they pay up to three such Jackpots (up to
$300,000 designated for first tier prizes) in any particular draw. If
there are five Jackpot winners, the value of the Jackpots will be
reduced to $60,000. There are lotteries where the designated Jackpot
sum rolls over to the next draw, essentially making the Jackpot bigger
and bigger until a player or several players win it. This is the case
with the big lotteries such as Powerball, Mega Millions and
EuroMillions, as well as some big state lotteries such as California
SuperLOTTO Plus. There are also lotteries where the designated Jackpot
sum goes to lower tier prizes (rolls down) if no one hits the Jackpot.
These lotteries are particularly well suited for system players,
because the expected value of the lower tier prizes is higher than in
other lotteries. Some of the roll over lotteries have restrictions on
the number of roll overs (or the size of the Jackpot, as in
EuroMillions, where the current limit is 185,000,000 euros) before the
entire sum rolls down to lower tier prizes, or stays at a fixed limit
and the extra money goes to lower tier prizes if there is no jackpot
winner. Winning a Jackpot is the ultimate goal of any player and it is
always good if it happens, but, it might not even make you a really big
winner, while in some cases it might make you insanely rich. Some
lotteries are so big that even winning a nonJackpot prize could make
you a big winner. So it is difficult to evaluate the chances of a big
win over a lifetime of playing. In what follows, I will just give a
simplified argument, an approximation to the reality to illustrate how
difficult it is to win a lifechanging sum in a lottery. I am now
thinking how difficult it is to actually precisely define the meaning
of a "lifechanging sum''; obviously it depends on the individual
player and his/her financial status.
Let us assume that the lottery is a fair game of chance. Let us assume that a ticket costs a dollar and you (or your syndicate) play 10 tickets 100 times per year (this will approximately be the case if your lottery has two draws per week). This means you (or your group) spend about a $1,000 per year on lotto tickets. Now, to win a $1,000,000 jackpot, you have to be ready to wait some period of time in the range of 2,000 years (recall that the lottery returns just about 50% of the money that goes into it). The reality is: It might not happen to you (or your syndicate). Now, let us say, you play with the same sum for 40 years. The chance that you will win the one million jackpot during that time will be 40/2,000=1/50 or just about 2%. In other words, for one big win over a lifetime of playing, there must be 49 small losers who will pay for it. When I say "small" I mean it relatively; there will be many small wins that will partially cover the cost of playing for the small losers; one could end up being a winner even without winning big jackpots along the way, hitting, say a top prize in a small pick5 lottery, or several 4wins over the years, or hitting a 5win or several (1+4)wins in one of the Mega Lotteries. As I mentioned before, the above computation is quite an approximation to what could happen in reality. There are several factors that will have to be taken into account if we want to precisely evaluate how difficult it is to win a jackpot and how long the "waiting period" will be for it to happen on average, given that you play a fixed amount each draw. A precise computation is impossible, due to these additional factors. First of all, we did not factor the small wins which will come along the way and which you will probably put in the play to partially finance your game. The precise computations will also depend on how your lottery distributes the money for the different tier prizes. Another, very important factor will be the size of the jackpot. In fact, much larger than $1,000,000 jackpots happen on a regular basis, and although this does not significantly affect the "waiting period", it certainly affects the reward if it does happen. In any case, the point to keep in mind is: It is difficult to be a Jackpot winner. Well, why do we play the lottery then? First of all, there are supposedly factors that can change the numbers in favor of a smart player, or so we believe; I spoke about these in the section Choosing Your Numbers. Also, it is the "one never knows" factor, or the "it could be me" factor; the same factors that motivate people in any form of gambling. This is a good place for the usual warning, which is valid for all forms of gambling: Do not play with money that you cannot afford to lose! Playing the lottery is often compared to a high risk investment: The risk to lose is high indeed, but the return is immense if you beat the odds.
The odds (or probability, or chance) of hitting the top prize of your lottery are the same for any particular ticket. A system contains several tickets, so the chance of winning the top prize increases with the number of tickets played, but so do the expenses. What a system really does is that it guarantees smaller wins, while just a random selection of tickets usually guarantees nothing, even if all of the 5 numbers drawn are in your set of numbers (assuming that you play with more than 8 numbers). The chance of winning any particular set of prizes is clearly seen from the tables of wins.
Some lotteries introduce one or more additional numbers (we will call them bonus numbers) drawn either from the same set as the main 5 numbers, or from a different set, and pay prizes if you hit some of the main numbers plus one or two of the bonus numbers. For example, if you hit, say, 4 of the main numbers and the bonus number (or one of the bonus numbers in EuroMillions) then you will have a 4+1win. Other winning combinations are also possible. All of our systems are valid for these lotteries. Due to the diversity in using bonus numbers, and in order to keep the book compact, I have chosen not to include information on bonus number prizes in the tables of wins, however, I will discuss a couple of additional strategies on using systems in some of these lotteries in the next two sections. If your lottery has a bonus number (or two bonus numbers, as in EuroMillions), you only need to doublecheck each winning ticket containing a bonus number (or two bonus numbers).
Playing Systems in the Big DoublePick
Lotteries: Wheeling the Bonus Number(s)
If you play one of the big doublepick lotteries and you want to use a system with just one bonus number chosen for all of the combinations of the system, then you can skip both this section and the next one. These are for players who want to play a system and want to include more than one bonus number, thereby creating a bigger system (a multiple of the chosen one) with guarantees such as a 3+1win, 3+2win, 4+1win, etc.
Can we really wheel the bonus numbers? In some cases, we can. I will start with recalling that there are three types of pick5 lotteries, ordered in terms of increasing complexity:
1. Simple pick5 lotteries (such as 5/32, 5/39, etc.)
2. Pick5 lotteries where the 5 main numbers and the bonus number are drawn from the same set (such as MD Bonus Match 5, RI Wild Money, NM Roadrunner Cash, etc.)
3. Doublepick lotteries, where the 5 main numbers are drawn from one set and the bonus number(s) from another set (such as Powerball, Mega Millions, EuroMillions, Thunderball, Loto, California SuperLOTTO Plus, Hot Lotto, Megabucks Plus, Wild Card2, Kansas Cash Lottery, Tennessee Cash, etc.)
As I mentioned earlier, all of the systems from this book can be used in each of the three
types of lotteries. For the lotteries of type 2, we cannot do much
about the bonus number: It is drawn after the 5 numbers of the main
draw from the same set, so we do not have a way to distinguish it from
the other numbers or indicate it in the playing slips; therefore, we
can only doublecheck the tickets where we have 2, 3, 4, or 5wins
to see if we actually have 2+1, 3+1, 4+1, or 5+1wins. However, we
can do more in all of the lotteries of type 3: We can actually wheel
several bonus numbers, because the bonus numbers are chosen from a
different set. The bonus numbers have different names in different
lotteries: Mega Ball or Megaball (in CA SuperLOTTO Plus, Megabucks Plus
and Mega Millions), Powerball number or Red Ball (in Powerball), Lucky
Star Numbers (in EuroMillions), Thunderball (in UK's Thunderball),
Chance Ball (in France's Loto), Hot Number (in Hot Lotto), Wild Card
(in Wild Card2), Cash Ball (in Kanzas Cash), etc. In all of the type 3
lotteries (except for EuroMillions), 5 numbers are drawn from one set
and the bonus number is drawn from another set. The difference in
EuroMillions is that two bonus numbers (the Lucky Star Numbers) are
drawn from the second set, rather than just one. Therefore, I will
discuss EuroMillions separately from the rest of type 3 lotteries. This
will be done in the next section.
... … … … … … … … … … … … … … … … … … … … … … … … … … … … … …
(read the full text of this section in the book)
Wheeling Bonus Numbers in Euro Millions
... … … … … … … … … … … … … … … … … … … … … … … … … … … … … …
(read the full text of this section in the book)
Finding Your Way Through the Book
The two tables presented at the end of this section give you a quick and easy way to compare the systems in the book and choose the most appropriate one in terms of either how many numbers or how many combinations you want to play. The systems are listed by guarantees in the Contents and numbered consecutively. The first table here lists the systems by the number of combinations in increasing order. It can be used to find a system in a preferred price range. The second table can help if you already have a clear idea on how many numbers you want to play.
The contents and both tables can be used to compare the systems in the book by various characteristics. More facts about the properties of the systems can be found by comparison of the tables of wins. Each system is presented as a separate article. The title shows the main guarantee of the system. Many systems have additional guarantees that are explained in the presentation. I have also included some comments featuring particular strengths of the systems, information on the balance of the system (number of appearances of each number in all combinations of the system), and information on minimality.
Many systems in this book have the maximum
coverage property. I use it as a synonym of combinations being maximally apart, or as apart as possible, or combinations being maximally different.
What does this property mean and why is it good for a system to have
it? In order to explain it without using too much mathematics, I will
just continue with an example. Let us focus on a particular system,
say, the last system in the book, #126. It
has 11 numbers, 11 combinations and in my comments I say that the
combinations of the system are maximally `apart': Every two
combinations differ in at least three numbers. This also means that
every two combinations have at most two numbers in common. It also
means that if we take any two combinations of the system, they only
cover distinct triples (or distinct 3wins, if we use the usual
terminology). Each combination covers exactly 10 triples, so the entire
system covers 11(10)=110 distinct triples. Any other system with 11
combinations (or just a set of 11 random combinations) which does not
have the maximum coverage property will actually cover a total of less
than 110 distinct triples (3wins). Just for simplicity, let us assume
that the system has only two combinations; take the first two
combinations of System #126,
1 
2 
5 
6 
8 
1 
2 
9 
10 
11 
The triples covered by these
two combinations are all distinct, for a total of 20 triples. Compare
to the following two combinations
1 
2 
5 
6 
8 
1 
2 
5 
9 
10 
They
do have a triple in common (1 2 5), so the total number of triples
covered is 19. If we allow combinations which are even less apart, we
will get more repeated coverage of triples and the total number of
triples will further go down. For example, the next two combinations
have four numbers in common
1 
2 
5 
6 
8 
1 
2 
5 
6 
9 
and the total number of triples covered goes down to 16 (because all of the four triples contained in the common part 1 2 5 6 are repeated in both combinations). The same type of argument can be applied when we consider the coverage of pairs or quadruples. There is a formula which tells us how apart the combinations of a system can be (depending on the numbers played and the number of combinations), but the complexity prevents me from discussing it here. I will just say that whenever I claim good covering properties, it is based on strict mathematics.
Finally, in my comments to each system, I also discuss
balance. My ranking of possible balance is as follows: A system is well balanced if each of its numbers
appears in either
One of the advantages of playing a highly balanced system is convenience: You do not have to rank your numbers according to how likely you think each number is to be drawn and then place numbers with higher expectation to be drawn under the numbers with higher occurrences in the system. A highly balanced system usually has other nice properties (symmetries) such as the maximum coverage property discussed above and also a shorter table of wins.
Navigation Table by Number of Combinations
# of 
Num

Syst.

#
of 
Num

Syst.

#
of 
Num

Syst. 
comb.

bers 
#

comb. 
bers 
#

comb. 
bers 
# 
3

7

11

36 
11

110

132 
12

123 
5

6

1

37 
17

53

132 
16

20 
5

7

24

37 
21

74

133 
20

37 
5

8

12

40 
22

75

133 
33

86 
5

9

45

43 
14

31

136 
17

116 
5

11

64

43 
18

54

136 
34

87 
6

12

65

48 
12

111

137 
26

62 
7

10

46

48 
13

17

151 
21

38 
8

8

25

49 
23

76

151 
27

63 
8

13

66

51 
10

5

157 
13

8 
9

7

2

52 
19

55

162 
35

88 
9

9

13

54 
24

77

169 
14

125 
9

11

47

56 
15

32

172 
22

39 
10

14

67

61 
20

56

175 
17

21 
11

11

126

63 
25

78

176 
36

89 
12

9

26

65 
13

112

180 
18

117 
12

12

48

65 
16

33

187 
23

40 
13

15

68

66 
11

6

201 
37

90 
14

8

107

68 
17

34

214 
18

22 
14

10

14

68 
26

79

216 
38

91 
14

16

69

69 
14

18

230 
14

9 
16

8

118

72 
10

121

231 
24

41 
16

13

49

72 
21

57

240 
39

92 
17

10

27

77 
27

80

255 
40

93 
18

9

108

78 
14

113

256 
25

42 
18

17

70

83 
22

58

260 
26

43 
19

14

50

86 
28

81

280 
41

94 
20

8

3

94 
18

35

284 
19

23 
20

11

28

95 
15

19

295 
15

10 
22

11

15

95 
23

59

295 
42

95 
22

18

71

97 
29

82

319 
27

44 
24

15

51

101 
15

114

320 
43

96 
26

19

72

102 
30

83

338 
44

97 
28

10

109

107 
24

60

359 
45

98 
29

12

29

108 
19

36

374 
46

99 
30

9

4

111 
31

84

411 
47

100 
31

16

52

113 
12

7

432 
48

101 
32

20

73

117 
13

124

447 
49

102 
34

13

30

121 
25

61

491 
50

103 
35

12

16

124 
32

85

516 
51

104 
36

9

119

125 
16

115

520 
52

105 
36

10

120

132 
11

122

579 
53

106 
Navigation Table by Quantity of Numbers
Num 
# of 
Syst. 
Num 
# of 
Syst. 
Num 
# of 
Syst. 
bers 
comb. 
# 
bers 
comb. 
# 
bers 
comb. 
# 
6 
5 
1 
13 
117 
124 
22 
172 
39 
7 
3 
11 
13 
157 
8 
23 
49 
76 
7 
5 
24 
14 
10 
67 
23 
95 
59 
7 
9 
2 
14 
19 
50 
23 
187 
40 
8 
5 
12 
14 
43 
31 
24 
54 
77 
8 
8 
25 
14 
69 
18 
24 
107 
60 
8 
14 
107 
14 
78 
113 
24 
231 
41 
8 
16 
118 
14 
169 
125 
25 
63 
78 
8 
20 
3 
14 
230 
9 
25 
121 
61 
9 
5 
45 
15 
13 
68 
25 
256 
42 
9 
9 
13 
15 
24 
51 
26 
68 
79 
9 
12 
26 
15 
56 
32 
26 
137 
62 
9 
18 
108 
15 
95 
19 
26 
260 
43 
9 
30 
4 
15 
101 
114 
27 
77 
80 
9 
36 
119 
15 
295 
10 
27 
151 
63 
10 
7 
46 
16 
14 
69 
27 
319 
44 
10 
14 
14 
16 
31 
52 
28 
86 
81 
10 
17 
27 
16 
65 
33 
29 
97 
82 
10 
28 
109 
16 
125 
115 
30 
102 
83 
10 
36 
120 
16 
132 
20 
31 
111 
84 
10 
51 
5 
17 
18 
70 
32 
124 
85 
10 
72 
121 
17 
37 
53 
33 
133

86 
11 
5 
64 
17 
68 
34 
34 
136 
87 
11 
9 
47 
17 
136 
116 
35 
162 
88 
11 
11 
126 
17 
175 
21 
36 
176 
89 
11 
20 
28 
18 
22 
71 
37 
201 
90 
11 
22 
15 
18 
43 
54 
38 
216 
91 
11 
36 
110 
18 
94 
35 
39 
240 
92 
11 
66 
6 
18 
180 
117 
40 
255 
93 
11 
132 
122 
18 
214 
22 
41 
280 
94 
12 
6 
65 
19 
26 
72 
42 
295 
95 
12 
12 
48 
19 
52 
55 
43 
320 
96 
12 
29 
29 
19 
108 
36 
44 
338 
97 
12 
35 
16 
19 
284 
23 
45 
359 
98 
12 
48 
111 
20 
32 
73 
46 
374 
99 
12 
113 
7 
20 
61 
56 
47 
411 
100 
12 
132 
123 
20 
133 
37 
48 
432 
101 
13 
8 
66 
21 
37 
74 
49 
447 
102 
13 
16 
49 
21 
72 
57 
50 
491 
103 
13 
34 
30 
21 
151 
38 
51 
516 
104 
13 
48 
17 
22 
40 
75 
52 
520 
105 
13 
65 
112 
22 
83 
58 
53 
579 
106 
Lottery systems with a
single guarantee
System
# 26 : Guaranteed 3win if 3 of the numbers
drawn are in your set of 9 numbers
Winning possibilities 

Guessed 
5

4

3

2

% 
5

1 
 
58 
26 
9.52 

 
3 
36 
26 
25.40 

 
2 
47 
26 
50.79 

 
1 
78 
24 
12.70 

 
 
10 
1 
1.59 
4

 
1 
4 
56 
7.14 

 
1 
3 
56 
19.05 

 
1 
2 
68 
19.84 

 
1 
1 
10 
1.59 

 
 
6 
35 
11.11 

 
 
5 
45 
22.22 

 
 
4 
67 
19.05 
3

 
 
3 
03 
4.76 

 
 
2 
46 
33.33 

 
 
1 
68 
61.91 
2

 
 
 
5 
2.78 

 
 
 
4 
27.78 

 
 
 
3 
69.44 
This system is MATHEMATICALLY MINIMAL with respect to the main guarantee. It also guarantees at least four 3wins if 4 of your numbers are drawn. If all five drawn numbers are within your selected 9 numbers, then you will either hit a 5win or up to three 4wins and additional prizes, or ten 3wins; the chance of getting at least a 4win plus a number of smaller prizes is 98.41%. The system is well balanced: Each number is in either 6 or 7 combinations as seen from the table below. It also has an additional nice property: The combinations are as `apart' as possible; in this case, every two combinations differ in at least two numbers, which also provides maximum coverage of quadruples. The complete system would require 126 combinations.
Number(s) 
Occurrences 
2, 3, 4, 7, 8, 9 
7 
1, 5, 6 
6 
1. 
1 
2 
3 
7 
8 

7. 
2 
3 
4 
5 
8 
2. 
1 
2 
4 
7 
9 

8. 
2 
3 
5 
7 
9 
3. 
1 
2 
5 
6 
7 

9. 
2 
3 
6 
8 
9 
4. 
1 
3 
4 
5 
6 

10. 
2 
4 
6 
7 
8 
5. 
1 
3 
4 
8 
9 

11. 
3 
4 
6 
7 
9 
6. 
1 
5 
6 
8 
9 

12. 
4 
5 
7 
8 
9 
... … … … … … … … … … … … … … … … … … … … … … … … … … … … … …
(The full text of this part of the book contains 105 other systems)
Lottery systems with
double guarantees
In this part of the book, I introduce systems where the main guarantee is two identical prizes, two 3wins, in particular. Part III of the book presents systems where the main guarantee is more than two identical prizes. What is the point of playing with a double (or multiple) guarantee system? Let us focus on the double guarantee systems. The main advantage is that in some cases, due to the specifics of the combinatorial problem at hand, we are able to achieve the double guarantee in less than twice the number of combinations needed for the single guarantee.
For example, consider again System #26 (you play with 9 numbers in 12 tickets and you get a 3win whenever 3 of the numbers drawn are in your set of 9 numbers). Recall that 12 is the minimum number of tickets (check the section Minimality) that will guarantee you this prize. Now, suppose you want to play for two 3wins guaranteed whenever 3 of your numbers are drawn. The simplest way is to play twice System #26 (so you have to fill 24 tickets). This way you will have repeated tickets and repeated wins correspondingly. However, it is possible to have the same guarantee (two 3wins if 3 of your numbers are drawn) in just 18 tickets and no repetition! You can find a system with this property under #108 in the book (check it below). We should mention that 18 is again the minimum possible number of tickets, but now, it is the minimum for the double guarantee, so that you have another example of a mathematically minimal system. Indeed, almost all systems in this part of the book have the following nice property: They give you the double guarantee in a number of tickets which is less than twice the number of tickets needed for the single guarantee. (There is just one exception, System #116, which gives the double guarantee in exactly twice the number of tickets needed for the single guarantee, but there are good reasons to include it in this part; see my comments to that particular system in the book.)
System
# 108 : Guaranteed two 3wins if 3 of the
numbers drawn are in your set of 9 numbers
Winning possibilities 

Guessed 
5

4

3

2

% 
5

1 
 
12 
4 
14.29 

 
4 
6 
8 
28.57 

 
3 
9 
5 
57.14 
4

 
1 
5 
9 
57.14 

 
1 
4 
12 
14.29 

 
 
8 
6 
28.57 
3

 
 
3 
6 
14.29 

 
 
2 
9 
85.71 
2

 
 
 
5 
100.00 
This system presents a considerable improvement over the single guarantee system (#26, 12 combinations). Here you get the double guarantee in just 18 combinations, that is, in only 1.5 times the number of combinations needed for the best single guarantee system! This system is MATHEMATICALLY MINIMAL with respect to both the main guarantee and the guarantee of five 2wins if 2 of your numbers are drawn. It is also EXCEPTIONALLY HIGHLY BALANCED: Each number is in exactly 10 combinations and each pair of numbers is in exactly 5 combinations. The complete system would require 126 combinations. If all of the five drawn numbers are within your selection of 9 numbers, then you are guaranteed at least three 4wins (plus a number of smaller prizes). Note that the best single 4 if 5 guarantee system (#13) has 9 combinations. Here you get the triple 4 if 5 guarantee in just twice the number of combinations needed for the best single 4 if 5 guarantee, which is a considerable improvement over another single guarantee system! Note that both systems (#13 and #26) that we used for comparison were also mathematically minimal! Finally, the combinations of the system are maximally `apart': Every two combinations differ in at least two numbers, which provides the best possible coverage of quadruples.
1. 
1 
2 
3 
4 
5 

10. 
1 
5 
6 
7 
9 
2. 
1 
2 
3 
6 
9 

11. 
2 
3 
4 
6 
8 
3. 
1 
2 
4 
6 
7 

12. 
2 
3 
5 
6 
7 
4. 
1 
2 
4 
8 
9 

13. 
2 
3 
7 
8 
9 
5. 
1 
2 
5 
7 
8 

14. 
2 
4 
5 
7 
9 
6. 
1 
3 
4 
7 
9 

15. 
2 
5 
6 
8 
9 
7. 
1 
3 
5 
8 
9 

16. 
3 
4 
5 
6 
9 
8. 
1 
3 
6 
7 
8 

17. 
3 
4 
5 
7 
8 
9. 
1 
4 
5 
6 
8 

18. 
4 
6 
7 
8 
9 
... … … … … … … … … … … … … … … … … … … … … … … … … … … … … …
(The full text of this part of the book contains 10 other systems)
Lottery systems with
multiple guarantees
This part of the book contains systems with multiple guarantees. The systems here have the same nice properties as the double guarantee systems. I have chosen to present the best systems I know, that is, systems that give you the multiple guarantee in much less than the corresponding multiple number of tickets. I have included mostly highly balanced systems in this part: Not only every number appears the same number of times in the combinations of the system, but in many cases every pair of numbers appears the same number of times, and in some cases every triple and even every quadruple appears the same number of times! Information on the balance is provided with my comments to the systems.
Each system in this part (except the last one, #126) is titled as a multiple 4 if 5 guarantee system, although some of the systems possess other guarantees, which can also be considered as main guarantees. For example, each of the systems 119,120,121,122, and 123 has a multiple 3 if 3 guarantee: four, three, six, eight and six 3wins, respectively. In addition, each of these five systems is mathematically minimal with the corresponding 3 if 3 guarantee.
The systems in this part were designed with a focus on a main multiple guarantee and minimality, but you can find many systems with extra multiple guarantees in the first two parts of the book as well; the extra guarantees there come as a treat on top of the main single or double guarantee. For example, each of the systems 110 guarantees a 4win if 4 of your numbers are drawn, and that is the main guarantee. However, all of these systems also guarantee at least five 4wins if 5 of your numbers are drawn, and anywhere between at least two to at least six 3wins (depending on which particular system you play) if 3 of your numbers are drawn. You can easily check these features in the tables of possible wins.
Similarly, systems 107,108 and 109 have the main guarantee of two 3wins if 3 of your numbers are drawn, but they also guarantee three, three and two 4wins if 5 of your numbers are drawn, respectively. Likewise, systems 24 and 25 have the main guarantee of a 3win if 3 of your numbers are drawn, but they also have a guarantee of two 4wins if 5 of your numbers are drawn. Continuing through the book, you will notice that systems 111 and 112 have the main guarantee of two 3wins if 3 of your numbers are drawn, but each of them also guarantees a 4win if 5 of your numbers are drawn.
Finally, I should point out that there are some systems in this book which have a different type of "multiple guarantees". These are systems that have the main guarantee in the minimum known number of combinations, just like every other system in the book, but they also have a secondary single guarantee, in slightly more than the minimum known number of combinations. Examples are the eight systems 15 and 1723, where the main guarantee is a 4win if 5 of your numbers are drawn, and the secondary guarantee is a 3win if 3 of your numbers are drawn. Another example is system #27 where the main guarantee is a 3win if 3 of your numbers are drawn, and the secondary one is a 4win if 5 of your numbers are drawn.
System
# 126 : Guaranteed two 3wins if 4 of the
numbers drawn are in your set of 11 numbers
Winning possibilities 

Guessed 
5

4

3

2

% 
5

1 
 
 
10 
2.38 

 
1 
3 
5 
71.43 

 
 
6 
2 
11.90 

 
 
5 
5 
14.29 
4

 
1 
 
6 
16.67 

 
 
3 
3 
33.33 

 
 
2 
6 
50.00 
3

 
 
1 
3 
66.67 

 
 
 
6 
33.33 
2

 
 
 
2 
100.00 
This system could have been listed with the double guarantee systems, but it has a range of guarantees including multiple ones, and it happens to be MATHEMATICALLY MINIMAL with respect to each of them, namely: 1) five 3wins if 5 of your 11 numbers are drawn; 2) two 3wins if 4 of your numbers are drawn; 3) six 2wins if 3 of your numbers are drawn; and 4) two 2wins if 2 of your numbers are drawn; so that this part of the book is an appropriate place for it. The best single 3 if 4 guarantee system (#47) has 9 combinations (and it is mathematically minimal). The system presented here gives you the double 3 if 4 guarantee in just 11 combinations, that is, in only 1.22 times the number of combinations needed for the single guarantee! If all 5 of the numbers drawn are within your selected 11 numbers, then you have 73.81% chance of at least a 4win plus some smaller prizes, and, of course, you can get a 5win plus some extra cash. The system is EXCEPTIONALLY HIGHLY BALANCED: Each number is in exactly 5 combinations and each pair of numbers is in exactly 2 combinations. Also, the combinations of the system are maximally `apart': Every two combinations differ in at least three numbers, which provides maximum coverage of triples and quadruples. In fact, the system is quite symmetric, and has an additional nice property: Every two combinations of the system have exactly one pair of numbers in common. The complete system would require 462 combinations.
1. 
1 
2 
5 
6 
8 

7. 
2 
3 
6 
7 
9 
2. 
1 
2 
9 
10 
11 

8. 
2 
4 
5 
7 
11 
3. 
1 
3 
4 
5 
9 

9. 
3 
5 
6 
10 
11 
4. 
1 
3 
7 
8 
11 

10. 
4 
6 
8 
9 
11 
5. 
1 
4 
6 
7 
10 

11. 
5 
7 
8 
9 
10 
6. 
2 
3 
4 
8 
10 


... … … … … … … … … … … … … … … … … … … … … … … … … … … … … …
(The full text of this part of the book contains 8 other systems)
More about the book and
systems
Is This The Best Book On The Market?
I believe the answer is: Yes, it is. Let me elaborate a bit more on why I think this is the right answer. There are two types of people who are interested in creating and improving lottery systems. The first type is research mathematicians and computer scientists who study coverings (the scientific term for lottery systems) as a pure intellectual challenge, or, because of some practical applications of coverings, other than lottery systems. Then there is a second type of lotto systems chasers, again, people with strong mathematical or/and computer science background, who do not work in research, but had acquired an essential knowledge on the subject on their own, and have been interested in the challenge of creating a world record system. Also, there is a separate category, with few people in it: Those that actually bring the lottery systems to the attention of the players, the authors of books on the subject. Sadly, almost none of the people in the third category falls in the first two, except for the author of this book, who just happens to be both a research mathematician and a creator of lottery systems, and had been in the second category for quite some time before that.
A comparison of the wheels (systems) in this book with any other published book or software product shows that we offer systems which, in fewer combinations, give the same guarantee as systems published elsewhere, meaning that you save money and still play for the same guarantee. Naturally, no other author can make a true statement like that. For example, below is a table which gives a comparison with the last editions of the popular pick5 books, Gail Howard's Lotto Winning Wheels for Powerball and Mega Millions, and Lotto Wheel Five to Win. These two books have almost the same content and the numbering of the systems is pretty much the same (PB is added to the number of each system in Lotto Winning Wheels for Powerball and Mega Millions). In this partial comparison table I have listed systems for which I offer the same guarantee in fewer tickets, and I have also listed several systems with parameters that cannot be found in any of Howard's books; not only to just emphasize the fact that there are such systems in my book (actually, there are many more than those mentioned in the table), but also to demonstrate how big the gap could be in terms of performance between my systems and those found elsewhere. For example, Howard's 18 numbers wheel #54118 gives a 4 if 5 guarantee in 285 combinations, while in my book you will find an 18 numbers system which gives the same guarantee in just 214 combinations. Not only will you find an 18 numbers system which gives the same guarantee with much less combinations, but you will also find a system on 19 numbers, with the same guarantee and less combinations than Howard's 18 number wheel! You can observe similar phenomena with Howard's wheels 54117, 5311653122, 53124 and 53125.
Guarantee 
Numbers 
Gail Howard's
books: 


played 
System 
Number of 
System 
Number of 


(wheel)
# 
tickets 
(wheel)
# 
tickets 
4 if 5 
11 
54111 
26 
15 
22 
4 if 5 
12 
54112 
37 
16 
35 
4 if 5 
13 
54113 
58 
17 
48 
4 if 5 
14 
54114 
76 
18 
69 
4 if 5 
15 
54115 
118 
19 
95 
4 if 5 
16 
54116 
159 
20 
132 
4 if 5 
17 
54117 
217 
21 
175 
4 if 5 
18 
54118 
285 
22 
214 
4 if 5 
19 
 
 
23 
284 
3 if 5 
13 
53213 
9 
66 
8 
3 if 5 
16 
53216 
16 
69 
14 
3 if 5 
17 
53217 
20 
70 
18 
3 if 5 
18 
53218 
24 
71 
22 
3 if 5 
19 
53219 
28 
72 
26 
3 if 5 
23 
53223 
50 
76 
49 
3 if 5 
32 
53232 
125 
85 
124 
3 if 5 
39 
53239 
241 
92 
240 
3 if 4 
13 
53113 
18 
49 
16 
3 if 4 
14 
53114 
23 
50 
19 
3 if 4 
15 
53115 
28 
51 
24 
3 if 4 
16 
53116 
37 
52 
31 
3 if 4 
17 
53117 
46 
53 
37 
3 if 4 
18 
53118 
56 
54 