THE ULTIMATE BOOK ON PICK-6 LOTTO SYSTEMS

Lotbook Publishing are proud to present the best  book on lottery wheeling systems or lotto wheels for any pick-6 lottery in the world. If you are a PLAYER or a member of a GROUP OF PLAYERS and you plan to play with more than one ticket and more than 6 numbers, then this is the book for you! If you are interested in pick-5 lotto systems, then your best choice will be Dr. Bluskov's pick-5 book.

We continue with a presentation of Professor Bluskov's new pick-6 book. In this new, improved, and expanded edition, Professor Bluskov again delivers the best lottery systems to the attention of lotto players from around the world. A total of 128 current world record least expensive systems for a broad range of guarantees are presented.

We also offer a pocket version of the new edition, The Ultimate Guide to Lottery Systems, with 34 of the best  Bluskov's wheels for playing with up to 20 tickets, which is appropriate for individual players and small syndicates. All of the information presented at this site has relevance to both Combinatorial Lottery Systems and the Ultimate Guide. The pocket version can be ordered here.

 ORDERING INFORMATION A MUST FOR EVERY LOTTERY PLAYER! LOTTERIES LOTTERY SYSTEMS GUARANTEES MINIMALITY TABLES OF WINS PLAYING WITH THE SYSTEMS IS THIS BOOK THE BEST ONE IN THE MARKET? CAN YOU WIN THE JACKPOT BY PLAYING WITH A LOTTERY SYSTEM? BONUS NUMBER(S) THE ODDS OF WINNING ATTENTION! LARGER SYSTEMS A WORD FROM THE AUTHOR ACKNOWLEDGMENTS SYSTEMS WITH MULTIPLE GUARANTEES A DOUBLE GUARANTEE SYSTEM (EXAMPLE) LINKS

# A MUST FOR EVERY LOTTERY PLAYER!

Consider the following example: Suppose you play any pick-6 lottery and you buy just one ticket. A single ticket  guarantees you a 4-win if 4 of your numbers are in the draw. What would you do if you want to play not just a single ticket and 6 numbers, but, for example, 10 numbers, and you want the same guarantee, that is, you want a 4-win
whenever 4 of your 10 numbers are among the ones drawn? Then you will need to buy more tickets. How many? How would you arrange your numbers in the tickets? This book gives you the BEST ANSWERS to these and to MANY OTHER similar QUESTIONS.

In fact, if you want to play with 10 numbers, then you need to buy at least 20 tickets for a 4-win guaranteed if 4 of your numbers are drawn. However, just a set of 20 tickets, filled with random combinations of your 10 numbers, DOES NOT GUARANTEE YOU ANYTHING. This book tells you how to organize your numbers so that you ALWAYS GET A GUARANTEED SET OF PRIZES, and it shows you how to do so IN THE LEAST EXPENSIVE WAY.

It is a book for every lottery player (or a group of players) who wishes to play with more than one ticket. It provide strategies of playing for a desired guarantee using more than 6 numbers in the MOST ORGANIZED, WELL-BALANCED and ECONOMICAL WAY. The objects used for this purpose are the LOTTERY SYSTEMS (known also as WHEELS or COVERINGS). Each system is presented together with a TABLE OF ALL POSSIBLE WINS, so that the players can estimate the expected win before the draw. The complete tables of wins appear for the FIRST TIME IN A LOTTERY PUBLICATION. SYSTEMS WITH MULTIPLE GUARANTEES are also published for the FIRST TIME EVER.

The book provides an ENTERTAINING STRATEGY of playing the lottery. It is written by the RENOWN LOTTERY EXPERT, PROFESSOR in MATHEMATICS and COMBINATORICS, Dr. BLUSKOV, who is also the INVENTOR of many of the WORLD RECORD-BREAKING CONSTRUCTIONS of wheels (or coverings, as they are called in mathematics). The book offers, ready to use, the BEST LOTTERY SYSTEMS EVER CREATED, completely supplied with information on the WINNING POSSIBILITIES.

The lottery systems are explained in PLAIN LANGUAGE and are VERY EASY TO USE. NO MATHEMATICAL KNOWLEDGE IS ASSUMED to either play or understand the systems and the tables of possible wins, in spite of the fact that these objects were created by using  quite ADVANCED MATHEMATICS.

LOTTERIES

"Life is finite. Time is infinite. The probability that I am alive today is zero. In spite of this, I am now alive. Now, how is that?"

Albert Einstein

Unlike the time in the curious example of Einstein, the number of possible draws in the lottery is finite and the probability of winning the jackpot is greater than zero. For example, the probability of winning the jackpot in a 6/49 lottery is 1/13,983,816. The chances of winning smaller prizes are much better. That is why, in the quest for the elusive Jackpot, many players prefer to play with a well-organized group of tickets, so that they can win guaranteed smaller prizes. 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,  you will find an explanation on what constitutes a lottery system and how to use it, and you will also be provided with a number of excellent lotto systems to diversify your lotto experience. You can go directly to the explanation of lottery systems (wheels) here.

However, you might find it useful to start with the following brief description of lotteries. In this book we focus on 6-numbers-drawn lotteries, but most of the existing lotteries operate on the same principles as the 6-numbers-drawn lotteries. If the main draw consists of 6 numbers, the lottery is usually referred to as a pick-6 lottery. If the main draw consists of 5 numbers, the lottery is called a pick-5 lottery. There are also pick-3, pick-4, pick-7 and even pick-more lotteries (Keno, for example). So, a pick-6 lottery is a game where one has to correctly guess several (usually 3 or more) of the numbers (6, in the case of a pick-6 lottery) drawn from a larger set, of, say, 49 numbers, for example, in order to win a prize. In various places of the world, there are  lotteries with 25,26,27, etc., up to 90 numbers. The size of a lottery often depends on the size of the country (or state) where the lottery is played. This book concerns lotteries where the main draw consists of 6 numbers drawn out of a larger set of numbers (anywhere between 25 and 90). One can use the systems in the 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 25-90. You can even use the systems for playing 7-numbers-drawn lotteries, by adding a power number (a number which is present in all of your tickets).

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 6/49 lottery, each table has all 49 numbers, and the player fills 6 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 6 numbers filled in a particular table. When the draw comes, 6 numbers are drawn arbitrarily from the set of all numbers in the lottery. Players win whenever they correctly guess 3 or more of the numbers drawn in one of their tickets. The number of tables on a slip is irrelevant to the application of our lottery systems.

# 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, have not you? 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 a lottery system is and how it can help you diversify your lottery playing experience? In this book, 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 well-organized way of playing the lottery. This book introduces the best-known systems (also called trapping systems, or wheeling systems, or wheels in short; mathematicians call these objects coverings). I talk more about what "best" means in here. 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 (7,8,9,10,… etc.). I believe that using a lottery system from my 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 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. You can find more on that in the Guarantees 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 10 numbers instead of just 6. Naturally, you are willing to play more than one ticket and you want a certain guarantee. Let us say that you want a 4-win whenever 4 of the numbers drawn are in your set of 10 numbers. This means you want a set of combinations (tickets) that covers every possible quadruple out of your 10 numbers. Such a set of combinations is an example of a lottery system. You can find a lottery system with this property under #20 in the book. In this example, the lottery system has the property that any quadruple out of your set of 10 numbers is contained in at least one of your combinations, so you get a guaranteed 4-win whenever 4 of your 10 numbers are drawn.

In a sense, a lottery system expands the guarantee that you have on playing just 6 numbers (one ticket). If you just play one ticket and correctly guess 4 numbers, then you are guaranteed a 4-win. The lottery system in our example has the same guarantee, a 4-win if 4 numbers are guessed correctly, except that now you play a larger selection of numbers; 10 in this case. (In this book we also present systems with 4 if 4 guarantee for playing anywhere between 7 and 19 numbers.)

# GUARANTEES

All of the lottery systems presented in this book have certain guarantees. Here I 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 six 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 4 numbers, then you are guaranteed exactly one 4-win. A possible question was mentioned earlier, namely:  How to build a system that guarantees a 4-win on 4 guessed numbers, if you play with not 6, but say, 10 numbers. Let us look at our previously mentioned example from the, System. By using System, you are guaranteed a 4-win whenever 4 of your 10 numbers are among the 6 numbers drawn. The system shows that you only need 20 combinations (or 20 tickets) to do so. Out of 10 numbers, one can form 210 distinct sextuples (the non-mathematicians can take my word for it; those with some mathematical preparation can apply the formula C(10,6)=210).  Therefore, you only need to play 20 of these 210 combinations to achieve the 4 if 4 guarantee. What are the advantages of playing for such a guaranteed win? Let us compare playing with 20 random tickets against 20 tickets chosen according to our lottery system. We should mention that the probability of a 6-win ("hitting the jackpot") is the same for each ticket. However, if any 4 of the numbers  drawn are among the 10 numbers chosen by you, then the 20 tickets of  the lottery system guarantee at least one 4-win, while 20 random tickets (on the same 10 numbers) guarantee nothing!  This illustrates one of the main advantages of using a lotto system. Suppose you played your 10 numbers in the 20 combinations of System #20 for a long time and hit 4 of the numbers drawn, say, 15 times, over this period of time. Every time you hit 4 of the numbers drawn, you won at least one 4-prize. Had you played your 10 numbers in 20 random combinations, you would have probably hit a 4-win several times, but, most likely, not all 15 times, as with the system. In a worse case scenario, you could have missed the 4-win in each of the 15 draws in which you hit 4 of the numbers drawn! The reason is quite natural: Random combinations do not come with a guarantee; a system does!

# MINIMALITY

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 out-of-date systems. Lottery players have always been attracted to the most economical lottery systems, that is, systems achieving 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 the book.

Minimality is an important quality of all lottery systems in my books. The logic behind seeking minimal systems is simple: Let us assume you play with 10 numbers. If you could get a guaranteed 4-win by using a system in 20 combinations (system #20 from this book) and a system in 30 combinations, then which one would you choose? The answer is obvious: You would most likely prefer to get the guaranteed 4-win in the fewest number of tickets possible, in this case, in 20 tickets. Some players might argue here: OK, but if I play 30 tickets, I will have 30 shots at the jackpot rather than just 20. True, but if you really want to play 30 tickets, perhaps, you can play for a higher guaranteed prize, or you can play more than 10 numbers for the same guarantee, thereby giving yourself a better chance to capture all of the jackpot numbers in your larger set. 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, then 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 some of the systems 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 #20. It has been proven that the minimum number of tickets is 20 for the given guarantee. In other words, if you want to play 10 numbers and you want a guaranteed 4-win if 4 of your 10 numbers are drawn, then you need to play at least 20 tickets. System #20 achieves this guarantee in exactly 20 tickets, and this is the minimum possible number of tickets. That is why we call such a system mathematically minimal.

Tables of Wins

A new feature and a very important quality of our book is the full table of possible wins for each of the presented systems. 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 three) of the numbers drawn. Let us take a look at the table of possible wins for System #20. Each lines represents a possible distribution of wins. The last column shows the probability of the corresponding distribution of wins.

 Guessed 6 5 4 3 % 6 1 - 12 4 2.38 1 - 10 8 7.14 - 3 8 7 28.57 - 3 7 9 28.57 - 2 9 8 28.57 - - 15 2 4.77 5 - 1 4 10 23.81 - 1 3 11 23.81 - - 7 6 23.81 - - 5 11 23.81 - - 5 10 4.76 4 - - 3 4 2.38 - - 3 2 4.76 - - 2 7 28.57 - - 1 9 28.57 - - 1 8 35.72 3 - - - 5 8.33 - - - 4 16.67 - - - 3 75.00

If you play System #20 and 4 of your 10 numbers are drawn, then the system guarantees you at least one 4-win. Note that you will actually win more than that: There are five possibilities that are clearly seen from the table; these are given in the five lines of the section corresponding to 4 guessed numbers: You can either get one 4-win and either 8 or 9 3-wins with probabilities 35.72% or 28.57%, correspondingly, or you can get two 4-wins and seven 3-wins (probability 28.57%), or three 4-wins and either two or four 3-wins with probabilities 4.76% or 2.38% correspondingly. Similarly, if you correctly guess only three numbers, you get at least three 3-wins, or more precisely, three 3-wins with probability 75%, four 3-wins with probability 16.67%, or five 3-wins (probability 8.33%). The percentages add up to 100% in each of the four sections of the table. We include a further brief explanation for those readers who are not familiar with probabilities: Suppose you have played long enough with the same system and hit 3 of the numbers many times. Then, in approximately 75 out of 100 cases, you will have three 3-wins; in 17 (16.67, to be precise) out of 100 cases, you will have four 3-wins, and in 8 (8.33, to be precise) out of 100 cases, you will get five 3-wins.

Presenting individually every line in the full table is not always physically possible; in many cases, the full table would contain up to several thousands entries. In such cases, we present an abbreviated  table. 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 have chosen to keep distinction between the highest prizes. For example, had the table for System #20 been much longer, we could have written the 6-wins section abbreviated form as

 Guessed 6 5 4 3 % 6 1 - 10-12 4-8 9.52 - 3 7-8 7-9 57.14 - 2 9 8 28.57 - - 15 2 4.77

 Guessed 6 5 4 3 % 6 1 - 12 4 2.38 1 - 10 8 7.14 - 3 8 7 28.57 - 3 7 9 28.57 - 2 9 8 28.57 - - 15 2 4.77

We can justify such abbreviations by observing that what matters most are the highest-ranked prizes (those in the leftmost non-empty column of the corresponding part of the table). I tried to keep distinction between the highest prizes. What one gets in lower-ranked prizes is usually just a small percentage of the entire win.

PLAYING WITH THE SYSTEMS

Playing with the systems is very easy: The operations are the same for any system in the book. In our example, System # 20, where you play with 10 numbers, you just (1) write the numbers from 1 to 10 in a line (these are the numbers in the original system), then (2) write your 10 numbers in a line below the first one, and finally, (3) substitute each number in the original system by the corresponding number from the second line to obtain your set of tickets. Now, it only remains to (4) fill your combinations in the playing slips. For example, if you choose your 10 numbers to be 3,7,12,14,18,22,29,33,40, and 46, then you will write

 Numbers in the original system: 1 2 3 4 5 6 7 8 9 10 Your numbers: 3 7 12 14 18 22 29 33 40 46

 Original system: Your set of tickets: 1. 1 2 3 4 8 9 1. 3 7 12 14 33 40 2. 1 2 3 5 6 7 2. 3 7 12 18 22 29 3. 1 2 3 5 9 10 3. 3 7 12 18 40 46 4. 1 2 4 5 8 10 4. 3 7 14 18 33 46 5. 1 2 4 6 7 8 5. 3 7 14 22 29 33 6. 1 2 6 7 9 10 6. 3 7 22 29 40 46 7. 1 3 4 5 6 10 7. 3 12 14 18 22 46 8. 1 3 4 5 7 8 8. 3 12 14 18 29 33 9. 1 3 5 6 8 9 9. 3 12 18 22 33 40 10. 1 3 7 8 9 10 10. 3 12 29 33 40 46 11. 1 4 5 7 9 10 11. 3 14 18 29 40 46 12. 1 4 6 8 9 10 12. 3 14 22 33 40 46 13. 2 3 4 5 7 9 13. 7 12 14 18 29 40 14. 2 3 4 6 9 10 14. 7 12 14 22 40 46 15. 2 3 5 7 8 10 15. 7 12 18 29 33 46 16. 2 3 6 7 8 9 16. 7 12 22 29 33 40 17. 2 4 5 6 7 10 17. 7 14 18 22 29 46 18. 2 5 6 8 9 10 18. 7 18 22 33 40 46 19. 3 4 6 7 8 10 19. 12 14 22 29 33 46 20. 4 5 6 7 8 9 20. 14 18 22 29 33 40

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 a 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 4-win if four of your numbers are drawn): Suppose the numbers 7,12,29, and 40 are drawn, then the system must bring you at least one 4-win. Indeed, it is easy to check that this is so. In fact, you will get two 4-wins (in tickets 13 and 16), and according to the table of wins, you will also get seven 3-wins (in tickets 1,2,3,6,10,14, and 15). You can also take a look at the complete table of possible wins for System #20.

The book also contains systems with different types of guarantees, for example, a guaranteed 4-win if 5 of the numbers drawn are guessed correctly. 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 4-wins if 4 (see an example) of the numbers drawn are guessed correctly. Again, these systems can be used in the same way as explained above.

Is This The Best Pick-6 Lotto Book On The Market?

We believe the answer is: Yes, it is. Let us elaborate a bit more on why we 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 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 you systems which, in fewer combinations, give the same guarantee as systems published elsewhere, meaning that we save you money while you  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 popular book, Gail Howard's Lotto: How To Wheel A Fortune. The table refers to both the third edition (three digit wheel numbers) and the fourth edition of the same title (five digit wheel numbers); the reason being that the third edition is still in circulation as of the time of publishing this book, plus the fact that there are systems included in the third edition, but not included in the fourth. We have listed systems for which we offer the same guarantee in fewer tickets, and we 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 our 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 Bluskov's systems and those found elsewhere. For example, Howard's 20 numbers wheel #513 gives a 4 if 5 guarantee in 216 combinations, while in this book you will find a 20 numbers system which gives the same guarantee in just 142 combinations. Not only will you find a system which gives the same guarantee with much less combinations, but you will also find two other systems with the same guarantee and more than twenty numbers, 21 and 22, respectively (systems numbers 42 and 43 in this book), both having much less combinations than Howard's 20 number wheel. You can observe a similar phenomenon with Howard's wheel 615 and systems 61 and 62 from our book.

Guarantee Numbers played Gail Howard’s book: Iliya’s Book:
System (wheel) # Number of tickets System (wheel) # Number of tickets
5 if 6 11 65111 23 11 22
5 if 6 12 65112 39 12 38
5 if 6 13 406 77 13 61
5 if 6 14 407 123 14 98
5 if 6 15 408 190 15 142
5 if 6 16 409 280 16 224
4 if 5 11 504 12 32 10
4 if 5 12 505 18 33 14
4 if 5 13 64113 22 34 21
4 if 5 14 64114 32 35 29
4 if 5 15 64115 44 36 40
4 if 5 16 64116 60 37 52
4 if 5 17 510 88 38 66
4 if 5 18 511 118 39 81
4 if 5 19 512 164 40 113
4 if 5 20 513 216 41 142
4 if 5 21 42 169
4 if 5 22 43 189
4 if 6 15 64215 20 51 19
4 if 6 16 64216 28 52 25
4 if 6 17 64217 36 53 33
4 if 6 19 64219 58 55 54
4 if 6 20 64220 80 56 66
4 if 6 21 611 124 57 80
4 if 6 22 612 140 58 101
4 if 6 23 613 153 59 119
4 if 6 24 64224 158 60 143
4 if 6 25 615 238 61 166
4 if 6 27 62 222

We should mention though that this table shows just a fraction of the advantages of our book in comparison with Gail Howard's book and any other book on the market. Other improvements and unique features are the presentation of the material, the newly introduced complete table of possible wins, considered by many readers to be one of the best features of the book, and the systems with double and multiple guarantees. Both the complete tables and the systems with double and multiple guarantees appear for the first time in a lottery publication.

Can You Win The Jackpot By Playing With A Lottery System?

Of course, you can! In fact, every ticket of your system can win the jackpot. The advantage of using a lottery system is that even if you do not win the jackpot,  you will still get your guaranteed wins. That is why lottery players and groups of players prefer to use systems.  The number of tickets purchased by individual players and groups increases with the increase of the jackpot. A lottery system gives you the opportunity to chase the jackpot in the most organized and entertaining way, and also guarantees some smaller prizes if less than 6 of your numbers are drawn. Of course, if you hit the jackpot, using a lottery system, then you will also win a number of smaller prizes.

A system that guarantees the jackpot (that is, a 6-win if 6 of your numbers have been 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 Number Of Played Combinations 7 7 8 28 9 84 10 210 11 462 12 924 13 1,716 14 3,003 15 5,005 16 8,008 17 12,376

The number of tickets increases very fast. A system that contains all possible combinations is called a complete system. Complete systems are not included in this book. Most of the existing lotteries allow using such systems automatically and supply the corresponding tables of wins.

# BONUS NUMBER(S)

Some lotteries introduce one or more additional (bonus) numbers and pay prizes if you hit, say, 5 of the "regular" numbers plus an additional number, which corresponds to a 5+1-win. 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, we have chosen not to include information on bonus number prizes in the tables of wins. If your lottery has bonus numbers, you only need to double-check the winning tickets containing these numbers.

# THE ODDS OF WINNING

The odds (or probability, or chance) of hitting the jackpot are the same for any particular ticket. A system contains several tickets, so the chance of winning the jackpot 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 6 numbers drawn are in your set of numbers (assuming that you play with more than 9 numbers). The chance of winning any particular set of prizes is clearly seen from the tables of wins.

# ATTENTION!

A frequently asked question is: 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...

# LARGER SYSTEMS

The systems in this book can be used to play any 6-numbers-drawn lottery in the world and are best suited for individual players or small syndicates. Most of the systems presented in this book have less than 300 combinations. There are only two exceptions, systems # 7 and # 29. Players who want to try larger systems, or larger syndicates who can afford larger systems, as well as all players who just like to have a bigger collection of systems of all sizes can contact the publisher or the author for information. We believe, and probably most of our readers will agree, that playing the lottery with systems with exceptionally large number of tickets contradicts the idea of lottery itself and is a risky investment. However, for larger and/or richer syndicates, bigger systems (up to many thousands of combinations) can be designed and delivered, if needed.

# A WORD FROM THE AUTHOR

I would like to start with making it perfectly clear that I do not promote any particular lottery and am not associated with any of the existing lotteries. This 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 a 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 my expert knowledge of the subject. That is why this book has no match among the publications and software in existence. I hope you will appreciate the qualities of this fine book and enjoy playing with the lottery systems. I wish you the best of luck! Finally, I would appreciate any feedback from my successful readers and users of lottery systems. Please write about your experience with the lottery systems, especially if you hit it big! Your stories could provide useful input for further improvements of this book. You can write to the publisher's address given below or send an e-mail to lotbook@telus.net.

Lotbook Publishing
P.O. Box 33031
West Vancouver, B.C.

# Acknowledgments

A book of this size and quality would not have been possible without using the knowledge created during centuries of mathematical research,  and without  the help and support of lottery enthusiasts, fascinated by the subject of creating and improving lottery coverings. During my long career as a professional mathematician and lottery contributor, I have had the opportunity to work with some of the greatest minds on the planet, lottery enthusiasts and researchers in the area of coverings, such as Ricardo Bertolo from Italy, Heikki Hammalainen from Finland and Jan de Heer from Holland. Special thanks to Jan de Heer for his permission to use a couple of his recent world record breaking covering constructions and also to Anastasios Tampakis (England), who recently broke a couple of records using his software Wheel Generator. In addition, I want to express my gratitude to unknown number of other researchers and lottery enthusiasts who have either contributed to the knowledge on coverings and the current table of records or have inspired the search for these beautiful objects.

# SYSTEMS WITH MULTIPLE GUARANTEES

The second part of the book presents systems where the main guarantee is two or more 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, we are able to achieve the double guarantee in less than twice the number of combinations needed for the single guarantee.

Let us consider our basic example, System # 20 (you play with 10 numbers in 20 tickets and you get a 4-win whenever 4 of the numbers drawn are in your set of 10 numbers). Recall that 20 is the minimum number of tickets that will guarantee you this prize. Now, suppose you want to play for two 4-wins guaranteed whenever 4 of your numbers are drawn. The simplest way is to play twice the System # 20 (so you have to fill 40 tickets). This way you will have repeated tickets and repeated wins correspondingly. However, it is possible to have the same guarantee (two 4-wins if 4 of your numbers are drawn) in just 30 tickets and no repetition! You can find the system with this property under # 88 in the book. We should mention that 30 is again the minimum possible number of tickets, but now, it is the minimum for the double guarantee, so that you have an example of another mathematically minimal system. Indeed, all of the systems in the second part of the book have the same 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.

Part III of the book contains systems with multiple guarantees. The systems in this part have the same nice properties as described for the double guarantees. We have chosen to present the most economical systems, that is, systems which give you the multiple guarantee in much less than the corresponding multiple number of tickets. In addition, we have selected only highly balanced systems for this section: 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 or even every quadruple appears the same number of times! Information on the balance is supplied in the author's comments on the qualities of each particular system.

An Example of a Double Guarantee System

Below is an example of a double guarantee system. It also shows how the systems are presented throughout the book. Each system is given as a separate article including
1) a table of all possible wins, 2) comments on various characteristics of the system such as minimality, balance and density, and 3) the system itself.

SYSTEM # 88: GUARANTEED TWO 4-WINS IF 4 OF THE NUMBERS DRAWN ARE IN YOUR SET OF 10 NUMBERS

1) Table of possible wins

 Guessed 6 5 4 3 % 6 1 - 18 8 14.29 - 4 12 12 85.71 5 - 1 6 16 71.43 - - 10 10 28.57 4 - - 3 8 14.29 - - 2 12 85.71 3 - - - 5 100.00

The best known single guarantee system (# 20) has 20 combinations. The system presented here gives you the double guarantee in just 30 combinations. It also guarantees ten 4-wins (plus ten 3-wins) if five of your numbers are drawn, five 3-wins if three of your numbers are in the draw, and four 5-wins plus a number of other prizes if all of the numbers drawn are guessed correctly. Of course, you can also win the jackpot plus some extra cash. The system is EXCEPTIONALLY HIGHLY BALANCED: Each number is in exactly 18 combinations, each pair of numbers is in exactly 10 combinations and each triple is in exactly 5 combinations. It is also MATHEMATICALLY MINIMAL for all of the above mentioned guarantees! This system even has an additional nice property: Every two combinations differ in at least two numbers, that is, the combinations are as 'apart' as possible. The complete system would require 210 combinations.

3) System

 1 1 2 3 4 5 10 16 1 4 5 6 8 10 2 1 2 3 4 7 8 17 1 4 5 7 8 9 3 1 2 3 5 6 8 18 1 5 6 7 9 10 4 1 2 3 5 7 9 19 2 3 4 5 8 9 5 1 2 3 6 9 10 20 2 3 4 6 7 9 6 1 2 4 5 6 9 21 2 3 4 6 8 10 7 1 2 4 6 7 10 22 2 3 5 6 7 10 8 1 2 4 8 9 10 23 2 3 7 8 9 10 9 1 2 5 7 8 10 24 2 4 5 6 7 8 10 1 2 6 7 8 9 25 2 4 5 7 9 10 11 1 3 4 5 6 7 26 2 5 6 8 9 10 12 1 3 4 6 8 9 27 3 4 5 6 9 10 13 1 3 4 7 9 10 28 3 4 5 7 8 10 14 1 3 5 8 9 10 29 3 5 6 7 8 9 15 1 3 6 7 8 10 30 4 6 7 8 9 10