Incomplete systems for numerical lotteries. Proven to be the best lottery system! World lottery statistics

Hello!

My name is Ivan Melnikov! I am a graduate of the National Technical University “KhPI”, Faculty of Engineering and Physics, specialty “Applied Mathematics”, a happy family man and just a fan of games of chance. Since childhood, I have been interested in lotteries. I have always wondered by what laws certain balls fall out. Since I was 10 years old, I have been recording lottery results and then analyzing the data.

Sincerely,

Ivan Melnikov.

1. Mathematical odds of winning

   • Simple calculation with factorials

The most common lotteries in the world are games of luck such as “5 out of 36” and “6 out of 45”. Let's calculate the chance of winning the lottery using probability theory.

An example of calculating the possibility of receiving a jackpot in the “5 out of 36” lottery:

It is necessary to divide the number of free cells by the number of possible combinations. That is, the first digit can be selected from 36, the second from 35, the third from 34, and so on.

Therefore, here is the formula:

Number of possible combinations in a “5 out of 36” lottery = (36*35*34*33*32) / (1*2*3*4*5) = 376,992

The chance of winning is 1 in almost 400,000.

Let's do the same for a lottery like 6 in 45.

Number of possible combinations = “6 out of 45” = (45*44*43*42*41*40) / (1*2*3*4*5*6) = 9,774,072.

Accordingly, the chance of winning is almost 1 in 10 million.

• A little about probability theory

According to a long-known theory, each ball in each subsequent search has an absolutely equal chance of falling out compared to the others.

But not everything is so simple, even according to probability theory. Let's take a closer look at the example of tossing a coin. The first time we got heads, then the next time the probability of getting tails is much higher. If heads come up again, then next time we expect tails with even greater probability.

With the balls coming out of the lottery machines, it's about the same story, but a little more complicated and with a more significant number of variables. If one ball is drawn 3 times and the other is drawn 10 times, then the probability of the first ball being drawn will be higher than that of the second. It is worth noting that this law is diligently violated by the organizers of some lotteries, which change lottery machines from time to time. A new sequence appears in each new lottery machine.

Some organizers also use a separate lottery machine for each ball. Thus, it is necessary to calculate the probability of each ball falling out in each individual lottery machine. On the one hand, this makes the task a little easier, on the other hand, it complicates it.

But this is just a theory of probability, which, as it turns out, doesn’t really work. Let's see what secrets there are, based on dry science and statistical data accumulated over decades.

1. Why doesn't probability theory work?

   • Less than ideal conditions

The first thing worth talking about is the calibration of lottery machines. None of the lottery machines are perfectly calibrated.

The second caveat is that the diameters of lottery balls are also not the same. Even differences of the slightest fraction of millimeters play a role in the frequency of a particular ball falling out.

The third detail is the different weight of the balls. Again, the difference may not seem significant at all, but it also affects the statistics, and significantly.

• Sum of winning numbers

If we look at the statistics of winning numbers in a “6 out of 45” lottery, we will notice an interesting fact: the sum of the numbers that players bet on ranges between 126 and 167.

The sum of the winning lottery numbers for “5 out of 36” is a slightly different story. Here the winning numbers add up to 83-106.

• Even or odd?

What numbers do you think are most often found on winning tickets? Even? Odd? I can tell you with complete confidence that in the “6 out of 45” lotteries these numbers are equally divided.

But what about “5 out of 36”? After all, you need to choose only 5 balls; there cannot be an equal number of even and odd balls. So here it is. Having analyzed the results of lotteries of this type over the last four decades, I can say that slightly, but still more often, odd numbers appear in winning combinations. Especially those that contain the number 6 or 9. For example, 19, 29, 39, 69 and so on.

• Popular groups of numbers

For a lottery of the “6 to 45” type, we conditionally divide the numbers into 2 groups - from 1 to 22 and from 23 to 45. It should be noted that in winning tickets the ratio of numbers belonging to the group is 2 to 4. That is, either the ticket will contain 2 numbers from the group from 1 to 22 and 4 numbers from the group from 23 to 45 or vice versa (4 numbers from the first group and 2 from the second).

I came to a similar conclusion when analyzing the statistics of lotteries like “5 out of 36”. Only in this case the groups are split up a little differently. Let's designate the first group that includes the numbers from 1 to 17, and the second the one that contains the remaining numbers from 18 to 35. The ratio of numbers from the first group to the second in winning combinations in 48% of cases is 3 to 2, and in 52 % of cases – on the contrary, 2 to 3.

• Is it worth betting on numbers from past draws?

It has been proven that in 86% of cases, a new drawing repeats a number that has already appeared in previous drawings. Therefore, you just need to follow the draws of the lottery you are interested in.

• Consecutive numbers. To choose or not to choose?

The chance that 3 consecutive numbers will appear at once is very low, less than 0.09%. And if you want to bet on 5 or 6 consecutive numbers at once, there is practically no chance. Therefore, choose different numbers.

• Numbers with a single step: win or lose?

You should not bet on numbers that appear in the same sequence. For example, you definitely don’t need to choose step 2 and place a bet with this step. 10, 13, 16, 19, 22 are definitely a losing combination.

• More than one ticket: yes or no?

It’s better to play once every 10 weeks with 10 tickets than once a week with one. And also play in groups. You can win a big cash prize and split it between several people.

1. World lottery statistics

   • Mega millions

One of the most popular lotteries in the world was carried out according to the following principle: you need to choose 5 numbers out of 56, as well as 1 out of 46 for the so-called golden ball.

For 5 matched balls and 1 correctly named golden ball, the lucky winner receives the jackpot.

The remaining dependencies are shown in the table:

Statistics of dropped regular balls for the entire duration of the above lottery draws.

Statistics of golden balls drawn throughout the Mega Millions drawings.

The most frequently drawn combinations in the lottery are shown in the table below:

• Powerball lottery where more than a dozen lucky people have managed to hit the jackpot. You must select 7 main game numbers and two Powerballs.

1. Winners' stories

   • Lucky compatriots

Evgeny Sidorov from Moscow received 35 million in 2009, before that Nadezhda Mekhametzyanova from Ufa hit the jackpot of 30 million. “Russian Lotto” sent another 29.5 million to Omsk to the winner, who did not want to identify himself. In general, winning jackpots is a good habit of Russian people

• 390 million US dollars in one hand

In the lottery we already talked about, Mega Millions, a lucky winner who wished to remain anonymous won $390 million. And this is far from a rare case. In the same lottery in 2011, two people managed to hit the jackpot, which at that time consisted of an amount of 380 million. The cash prize was divided into two parts and awarded to people who guessed the winning numbers.

A pensioner from South Carolina decided to participate in the Powerball lottery and won 260 million, which he decided to spend on the education of his children, and also bought a house, several cars for the family, and then went traveling.

1. conclusions

So, here is a summary of the most effective rules, following which you are sure to win:

1. The sum of all the numbers you bet on on a lottery ticket must be calculated using the following formula:

Amount = ((1 + n)/2)*z + 2 +/- 12%

n – maximum bet number, for example, 36 in a “5 out of 36” lottery

z – the number of balls you bet on, for example 5 for the “5 out of 36” lottery

That is, for “5 out of 36” the amount will be like this:

((1+36)/2)*5 + 2 +/-12% = 18,5*5+2 +/-12% = 94,5 +/-12%

In this case, from 94.5 + 12% to 94.5 – 12%, that is, from 83 to 106.

1. Bet equally on even and odd numbers.
2. Divide all the numbers into two large groups in half. The ratio of the number of numbers on a winning ticket is 1 to 2 or 2 to 1.
3. Follow the statistics and bet on the numbers that came out in previous draws.
4. Don't bet on numbers with one step.
5. It’s better to play less often, but buy several tickets at once, and also get together with friends and relatives.

In general, be brave! Follow my rules, place bets, analyze statistics and win!

Lotteries of this type are held in many countries around the world, mainly according to the “3 out of 10” formula: in Ukraine - “Loto Troika”, in New Zealand - “Play 3”, in the USA - “Daily 3” (California), “Pick 3” "(Florida), "CA$H 3" (Georgia), etc. Typically, to win these lotteries you must match three numbers from 0 to 9, and depending on the type of game you choose, the sequence may be important. Therefore, we present here one complete system and several incomplete ones for clarity. After substituting the numbers, do not forget to reduce all numbers of the resulting system by 1. In addition, the systems published in this category can serve as the basis for systems with fixed numbers for playing lotto using the formulas 5 out of N, 6 out of N, etc.

Partial or drum systems
or how do they play according to the system?

There are a huge number of templates of incomplete systems that differ only in the number of combinations they can offer, as well as the guaranteed number of guessed numbers in any combination... - provided that in your row, for example, of twenty numbers - there will be all the prize money or the necessary number of partial matches (depends on the selected system). The choice of system is usually based on the willingness to sacrifice some amount for the game. An incomplete system is a concept from the field of applied combinatorics, denoting a reduced matrix of combinations calculated based on the formula for the number of combinations of n-elements by m. A complete system is all possible combinations from a given set of numbers. The systems are mainly used when playing lotteries.

Many players who are fond of number lotteries, sooner or later begin to use incomplete systems, and show special interest in system play. Basically, systems are resorted to when it is necessary to use more numbers in a draw, and the budget is limited. It is important to note that no lottery system can guarantee effective winnings in every draw. The system can guarantee a win if certain conditions are met. In addition, no system can guarantee a jackpot if not all numbers (all possible combinations) are used in the system. However, if in the selected group of numbers the required number of prize balls coincides, the incomplete system will play effectively, accordingly, bet more combinations on the next game, therefore, there will be a greater chance of winning a super prize, or a prize of the second category, which in some lotteries is quite decent in amount .

The more combinations the system can generate and the guaranteed addition of a combination from a series of numbers, by some coincidence, the more expensive it is and the greater the chance of a super prize, or a second category prize. Let’s imagine this situation: you somehow know exactly 18 numbers for the 5 out of 36 lottery, in which there are guaranteed to be 5 prizes - in fact, even in 18 numbers, it is not at all easy to “drive” all the prizes. If you expand these 18 numbers into a full system, you get 8568 combinations. Of course, they can be added theoretically if the budget and capabilities allow. But if there is no budget and opportunities, then an incomplete system will come to our aid, which will at least provide guarantees of the second, third,... categories of winnings. The warranty depends on the specific system. What about the first category prize? More on this below.

What is an incomplete system pattern?

I will give a specific example that simply clearly shows the very principle of composing systems. Let's say we want to play in the next draw of a lottery like 6 out of 49, not with 6 numbers, but with 20 numbers. And the budget is enough for 10 bets...

Our choice in this case: System “20 numbers - 10 combinations”
Guarantees at least a “three” with 6 guesses out of 20.

01 01-02-07-08-16-20
02 01-05-09-11-12-20
03 01-07-10-16-19-20
04 02-03-04-08-10-19
05 02-08-10-14-18-19
06 03-04-06-13-14-18
07 03-04-14-15-17-18
08 05-06-12-13-15-17
09 05-07-09-11-12-16
10 06-09-11-13-15-17

We choose any 20 numbers out of 49 at our discretion.

For example:

2, 5, 7, 9, 10, 12, 14, 16, 24, 25, 28, 32, 34, 36, 37, 39, 42, 43, 45, 49.

We assign the selected numbers their own serial number (from 1 to 20). You can number the selected numbers in any random order, in this case we will do it in ascending order.

Then we substitute our numbers instead of the system numbers (according to their serial numbers)
and as a result we get ready-made combinations for the game.

01 02-05-14-16-39-49
02 02-10-24-28-32-49
03 02-14-25-39-45-49
04 05-07-09-16-25-45
05 05-16-25-36-43-45
06 07-09-12-34-36-43
07 07-09-36-37-42-43
08 10-12-32-34-37-42
09 10-14-24-28-32-39
10 12-24-28-34-37-42

The above system guarantees that if in the selected row of 20 numbers (2, 5, 7, 9, 10, 12, 14, 16, 24, 25, 28, 32, 34, 36, 37, 39, 42, 43, 45 , 49) if we guess 6 numbers, then 100% we will have at least one winning ticket with a “three”. The advantage of the systems is (if we successfully expand the series) that in most cases, not one, but several lottery tickets win. Quite often, incomplete systems “catch” partial matches, even if not all the prizes are in the selected group of numbers.

What can you say about Jack Pot?

Remember, in incomplete systems, combinations are optimized for maximum partial match coverage. The chances of winning Jack Pot increase significantly only if you accurately guess the group of numbers (all prizes in the group must match), which is extremely rare. Without a special program and strategy, you are unlikely to be able to collect all the prize money even in a row of 20 numbers!

Let's see what is the probability of matching all the prize money in a group of 20 numbers
To know the probability of a selected group of numbers (full and partial match)
use the HYPERGEOMET statistical function that comes with Excel
or watch

The probability of “hooking” all the prize money with 20 numbers out of 49 is 1:361.
If you use one group of 20 numbers, then it will play 1 time per 361 draws (average) (6 matches). This is a very low probability. If we still managed to “drive” all the prize money into a row of 20 numbers, then the chance of Jack Pot (in the system above) will be approximately equal to 13,983,816/361/10 = 1: 3,873
(13,983,816 total number of combinations in 6x49).

How to correctly compose a group of numbers for systems?

There is a lot of all kinds of information on the Internet about incomplete systems, but there is very little information about methods and strategies for selecting numbers, one might say there is none at all... This issue, as a rule, is avoided, since the group is subject to probabilities and chance (unlike the a system that obeys combinatorics and clear algorithms). The main problem of incomplete systems is to create a group of numbers that can “probably” in a certain period of time (or a cycle of games) “catch” all the prize money, significantly increasing the chances of a super prize. In this case, it is desirable that such a group of numbers contains as few numbers as possible. If we manage to assemble a group for all matches, consisting of an adequate number of numbers, plus an incomplete system for an adequate number of combinations works, we can consider that a super prize is in our pocket!

The program is ideal for incomplete systems STALKER LOTTO PRO . The program implements tools for generating the most likely groups of numbers (for a cycle of games) - using special methods and strategies for selecting numbers (more precisely, groups, not individual numbers - frequency is used). Additionally, this program implements a combinatorial generator with an “advisor” function (aka STALKER LOTTO ), which works with the complete system, highlighting the most likely part with special algorithms - for the game cycle. If a probable area from the complete system coincides, the “accuracy of fire” is very high, and the chance of Jack Pot increases tens and even hundreds of times. You don't need to make groups or look for templates. The resulting combinations will be the most likely - both for partial matches and for prizes of the 1st and 2nd categories.

lottery system templates for lotteries
5 out of 36, 6 out of 45, 7 out of 49, 6 out of 49, and others

La Jolla Covering Repository Tables is the largest repository site on the Internet, containing a huge number of systems that provide the best coverage. Contains coverage tables C (v, k, t)

http://ljcr.dmgordon.org/cover/table.html

Incomplete systems, for any lotteries, with any guarantees, and for any budget - you can upload to the program STALKER LOTTO PRO, which has built-in search strategies for the most likely groups of numbers, for any length - for incomplete systems and more. We copy the template and save it as .txt - then the prepared template can be opened in the program.

In this program, you can load a very large system, say 30,000 combinations, then filter it further to the desired number of combinations. Why such a huge system? It's simple, the larger it is, the more likely it is to contain a super prize.

There are eight tables in total t = 2, 3, 4, 5, 6, 7, 8. In this case, t = N means the minimum number of numbers that must match. It is worth noting that many lottery programs use systems from La Jolla, as they have the best parameters. The systems may seem overly large, but they guarantee partial group matches - in the system above you need to guess a minimum of 3 numbers - in a group of 8 numbers. The resulting combinations may contain a pair of triplets and several pairs. If 4 numbers in a group are guessed, then 4 matches are possible. You can filter (reduce) systems in the program, for example, by the number that plays 3 draws in a row and other characteristics.

What is the difference between a complete system and an incomplete one? In both cases, the player chooses, for example, 12 numbers, among which there should be from 3 to 6 winning balls. However, in the full system you have to choose from an absolute range of combinations, sifting through more than 10,000 options. Incomplete - it is limited to a smaller range of combinations, which reduces the time spent on. So, incomplete lotto systems.

Incomplete lotto systems. Operating principle

You can calculate an incomplete system manually. However, Most often, this complex work is performed by lottery programs - online or without an Internet connection. To predict a sufficient number of options, you need to substitute the following into the system formula:

The number of winning numbers that allow you to earn a prize of a certain order;

The number of balls drawn during the draw;

Lottery machine capacity:

Number of options.

As a result, the player receives combinations with a guarantee of success from 70 to 99%. And the more tickets are filled, the higher the return on participation in a particular draw. At the same time, there is no point in taking less than 5 options, since the chances of winning will be too low.

What about the jackpot?

Yes, in theory, an incomplete system allows you to win several million. But in general, this technique sets a different goal, namely, to get the maximum number of second and third order prizes. AND if 70-80% of the options work for the user (which is quite realistic), then the resulting profit will more than pay for all costs.

The first lotteries appeared many years ago. And during this time, many different schemes, as well as game systems, have been developed, the use of which will allow you to obtain maximum results. When making some efforts to become the owner of an impressive lottery win, you should use existing systems. Their wide variety will certainly allow you to achieve excellent results.

Does it make sense to play according to the system?

It is worth noting that there is no specific scheme that would ensure a 100% win. This is due to the fact that in the modern world new lotteries appear almost every day. Moreover, each of them has its own characteristics that make it unique and original. That is why we can say with complete confidence that a universal scheme for playing the lottery not only does not exist today, but is also unlikely to appear in the future.

Complete systems and their features

The main feature of complete systems is that they are redundant. Accordingly, their constant use in practice is not always beneficial.

But we can also consider a situation in which it is the complete system that will allow you to become the owner of the winnings. Let’s say that in the process of participating in the “6 out of 45” lottery, a particular person’s choice fell on certain 10 numbers, among which there are guaranteed to be 6 numbers that can bring victory.

It is very important to remember that a complete lottery system will be most relevant when there are significant amounts of money at stake. Otherwise, the probability of becoming the owner of a large fortune due to guessing 5 or 4 numbers is extremely low. This means that this kind of system is losing its relevance.

So let's get back to what the complete system is. Its essence is to select all possible combinations that can be made from a specific number of pre-selected numbers.

In order to calculate the number of available combinations, you can use Newton's binomial. True, after making all the calculations, it will be possible to find out that the number of possible solutions is extremely large. Accordingly, playing the full system will be associated with huge material costs.

The essence of incomplete systems

It was in order to save the money needed to purchase lottery tickets that specialists created an impressive number of incomplete systems. They allow you to significantly increase the chance of getting a decent result, while ensuring minimal redundancy. This approach can justify itself even in a situation with lotteries, the jackpot of which is relatively small.

The principle of the incomplete system is based on the fact that it allows the player to become the owner of various winnings, except for the largest one. But to do this, you must ensure that all the winning numbers are in the system. In addition, using such a system does not mean that it will be impossible to win the jackpot

Competent creation of an incomplete system is based on comparison of a pair of complete systems. For example, if we are talking about the standard “6 out of 45” lottery and you want to get a system for 20 numbers with the probability of becoming the owner of a “three,” then you should compare such complete systems as 46/6 and 20/3.

Using the above-mentioned Newton binomial, it will be possible to find out that the number of suitable combinations for the 46/6 system is 8,145,060, but for the 20/3 system - only 1,140. Accordingly, the necessary combination will be discovered provided that the “three” of the 20/ system 30 will be in the “six” of the 46/6 system. There is a high probability that some of the resulting combinations will coincide. They will need to be excluded from the list by optimizing it.

To cope with the implementation of all these calculations on your own, you will need to make enormous efforts. It is quite easy to avoid such inconveniences today. It is enough to use special programs that carry out even very complex calculations efficiently and quickly. At the same time, you don’t have to worry about errors, which are extremely difficult to avoid in the case of manual data processing.

The basis of an incomplete system is probability theory

In order to become the owner of a win, it is very important to observe the principle of regularity. This indicates the need to constantly purchase lottery tickets, if not for all, then for many draws.

At the same time, we should not forget about the crucial role of chance. After all, if you analyze the dropped combinations over a long period of time, you can conclude that there is no ordered sequence.

With a systematic approach to purchasing tickets, the chances of getting a tidy sum increase significantly. Of course, there have been cases in history when a person who took part in the drawing for the first time managed to hit the jackpot. However, they are an exception to the rule. A person who buys lottery tickets not only regularly, but also in quantities of several pieces, has a much greater chance of improving their financial situation.

Main advantages of incomplete systems

Answering the question as to why exactly incomplete systems are needed, it should be noted that any accurate calculations significantly increase the chance of winning. A person who is serious about participating in the drawing is more likely to become the owner of a large sum of money than someone who does everything at random.

If 6 winning numbers are included in the selected 20, then the prize for the “three” will be guaranteed. And even if you managed to guess 5 numbers, the chance remains quite decent and is 80%.

In addition, we must not forget that incomplete systems do not require too large material investments, like complete systems. Accordingly, this method of playing will be available to almost everyone. And the wide variety of existing options guarantees that for any player there is a lottery system that fully meets all his individual preferences.

A good example

To understand in more detail how exactly these systems work, you can consider an available example. One of the simplest solutions was chosen for it, suitable for the “6 out of N” lottery and guaranteeing a “two” provided a pair of guessed numbers was chosen.

System “7 numbers – 3 options”

Initially, you need to select seven numbers and substitute them in certain places. In a situation with such a series 1=>3, 2=>7, 3=>11, 4=>29, 5=>33, 6=>40, 7=>43, the result will look like this:

The proposed system guarantees good results. For example, if you correctly guess only 4 numbers, you will be able to win for three “threes” at once, or from one to three “fours” and up to two more “threes”.

Playing according to the system: features and principles

People who organize lotteries take this issue very seriously and pay special attention to all kinds of calculations. Experts have found that in order to be guaranteed to guess a combination of 6 numbers, you need to purchase about 8 million lottery tickets. But in this case, even a very rich person is unlikely to agree to this kind of proposal.

Therefore, it is best to simply follow certain rules of the system that will help you achieve better results with minimal effort:

• if you have purchased a few tickets, you should try to fill out the maximum number of combinations, giving preference to different groups of numbers;
• You should not settle on one standard scheme, since it is best to use completely different combinations each time.

Competent game using the system

When purchasing lottery tickets, it is very important to immediately tune in to a positive wave. A good mood will allow you to get maximum pleasure from the process and enjoy the anticipation of winning.

One of the most popular systems that allows you to determine the optimal combinations is called the “7-7 scheme”. Its essence lies in the fact that numbers in ascending order from 1 to 7 are used to create combinations.

As a clearer example, consider using this scheme using random seven numbers. For example, a participant in the drawing chooses the numbers 45, 40, 37, 33, 21, 11, 4. In this case, the finished combinations will look like this:

Provided you choose the right numbers, such a scheme will allow you to become the owner of two to six winning tickets. The creators of this scheme classify it as a complete system.

If we consider incomplete options, then they include a solution involving the use of seven numbers in five combinations:

This approach does not guarantee winnings from the correct 6 numbers. However, with the right choice of numbers, it allows you to become the owner of a tidy sum for matching 4 numbers. And this is also very good.

Another popular solution is a permanent system. It involves long-term use of selected lucky numbers. As an example, we can consider this version of four combinations of seven constant numbers: