Which lottery is really to win, which one is more likely? How are cash lotteries conducted, how fair are they? How to win the lottery or proven ways to get big winnings.

Kokorin Artem, student of MAOU secondary school No. 11

In the work, the winning situations of lotteries are studied:

· Lottery "5 out of 36".

Lottery "5 out of 40".

Lottery "6 out of 49».

The work received a diploma at the regional conference of research papers.

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Municipal educational institution

"Secondary school No. 11"

Probability of winning in number lotteries

Kokorin Artem,

10th grade student
MOU secondary school №11 Tchaikovsky

Batueva Lyubov Nikolaevna,

mathematics teacher higher category

MOU secondary school №11 Tchaikovsky

Tchaikovsky

1. Introduction.
2. Targets and goals.
3. History of lotteries.
4. Object of study.
5. Lottery "5 out of 36".
6. Lottery "5 out of 40".
7. Lottery "6 out of 49".
8. Analytical part.
9. Scope of the obtained results.
10. Conclusion and recommendations.

Introduction.

Lottery (from ital. lottery ) - an organized game of chance, in which the distribution of benefits and losses depends on the random extraction of a particular ticket or number

The urgency of the problem.

My topic is relevant, since mathematics is in contact with everyday life much more closely than it is traditionally taught at school. W. Weaver writes: “Probability theory and statistics are two important areas that are inextricably linked with our daily activities. The world of industry, insurance companies are more indebted to probabilistic laws. Physics itself has an essentially probabilistic nature; and so is biology at its core. Meanwhile, despite this importance, the universal character of probability theory and statistics has not yet become generally accepted. Lotteries, gambling, election companies, insurance companies, etc. How to predict the outcome?.. Which position to choose?.. To answer these questions, I decided to do this research.

Hypothesis : Most believe that it is impossible to predict the outcome of a chill lottery in which chance reigns. This is not true. The mathematical expectation of winning is a value that will help us determine whether this or that game is fair and whether it is profitable for us to play it. The object of my research is various gambling games, on the basis of which the basic concepts of probability theory are introduced.

Subject of study: number lotteries

1. "6" out of "49"
2. "5" out of "36"
3. "5" out of "40"
4. "6" out of "45"

Starting the study, I set for myself the main goal - to carry out a probabilistic analysis of numerical lotteries, which, using the formulas of the theory of probability, will help us determine whether this or that lottery is fair and whether it is profitable for us to play it. From this goal follow 4 main tasks, which I sought to fulfill in the course of the study:

1. To study the rules for conducting numerical lotteries and consider methods for their study, using the formulas of the theory of probability.
2. To conduct an experiment
3. Analyze the received data

4.Create a mini-guide containing useful information about number lotteries

To accomplish my goals, I used methods studies like comparison, induction, deduction, analogy, experiment and questioning.

History of occurrence.

Many fans of sports and numerical lotteries, including Sportloto, may not know that its prototype was a lottery with the numerical formula "5 out of 90", organized in 1530 in the Italian city of Genoa. The fact is that in the Republic of Genoa, elections to the main body of self-government - the Great Council - were held by lot. After a multi-stage selection, 90 candidates were allowed to the last round of voting, of which only five people had to be selected. The elections took place as follows: each candidate for membership in the Council was assigned a serial number from the first to the ninetieth. Then 90 numbered balls were placed in a special urn. After thorough mixing, only 5 balls were taken out of it. Chance made its choice. The numbers on the balls taken out were the names of the members of the Great Council of Genoa!
Such a lottery principle of choice was universally recognized in Italy and, having crossed state borders, began to spread to other European countries.
Currently, there are several varieties of number lotteries in different countries. I did not set out to describe here about each of them..

Mathematical justification of numerical lotteries

Each numerical lottery with any numerical formula has its own mathematical justification. It is necessary in order to know how many classes of winnings should be in the lottery, and what is the probability of winning each class.
The mathematical justification of the number lottery is calculated using the theory of probability and number theory . Intuitively, the probability of some event is perceived as a characteristic of the possibility of its occurrence. It turns out that when the experiment is repeated many times, the frequency of the event takes on values ​​close to a certain constant number. By calculating the probable number of wins for each class, you can find out what percentage of the total income should go to win each class and what should be the amount of each win.
The total number of combinations in the number lottery is calculated using the formula:

Lottery 6 out of 49

. To get a big win, you had to guess 6 numbers out of 49. Cards won with a match of 5 and even 4 numbers. And how many cards would you need to buy and fill in so that they have all combinations of 6 numbers out of 49 possible, that is, in order to win for sure? The number of cards is equal to the number of combinations of 49 elements by 6, i.e.

49! = 44∙45∙46∙47∙48∙49 = 13 983 816

6!∙43! 1∙2∙3∙4∙5∙6

To implement such an idea, you had to be a millionaire! And it would be difficult to get rich in this case, since the winnings were not fixed, and in each draw only a part of the amount collected from ticket sales was allocated to the prize fund. But after all someone same won! I did some experiments in my class. I asked to cross out 6 numbers out of 49 on the card.

Based on the results of the experiments, I compiled tables and diagrams..Absolute frequencyshows how many times in a series of experiments this event was observed.Relative frequency(sometimes called simply the frequency) shows what proportion of experiments ended with the occurrence of a given event.

1 experiment

Not a single win! Three numbers were guessed only 2 times! But this lottery does not provide a win if 3 numbers are guessed.

Then I decided to find the probability of winning using the classical definition of probability. Probability random event A is called a fraction, that is, where - the number of all possible outcomes of the experiment, m - the number of outcomes favorable for event A.

Designated with R 6, R 5, R 4, R 3, R 2, R 1, R 0 the probability that 6 , 5 , 4, 3, 2, 1 or 0 numbers marked by the player turned out to be winning.According to probability theory, the probability of guessing n (from 0 to 5) numbers out of 36 can be expressed by the formula: According to probability theory, the probability of guessing n out of m can be expressed by the formula:

43! = 38∙39∙40∙41∙42∙43 = 6 096 454

6!∙37! 1∙2∙3∙4∙5∙6

Р 0 ≈ 0.435965

· - the number of choices of 1 number out of 6 given numbers and 5 numbers that do not match the given 6 numbers

· =

Р 1 ≈ 0.413019

· - the number of choices of 2 numbers out of 6 given numbers and 4 numbers that do not match the given 6 numbers

· =

Р 2 ≈ 0.132378

· - the number of choices of 3 numbers out of 6 given numbers and 3 numbers that do not match the given 6 numbers

· =

Р 3 ≈ 0.0176504

- the number of choices of 4 numbers out of 6 given numbers and 2 numbers that do not match the given 6 numbers

· =

C 6 C 43 = 6! · 43! = 5 6 42 43 = 13545

four! · 2! · 2! · 41! 2 2

Р 4 ≈ 0.000969

- the number of choices of 5 numbers out of 6 given numbers and 1 number that does not match the given 6 numbers

C 6 C 43 = 6! · 43! = 6 43 = 258

5! · 42!

R 5 ≈ 0.000184

It follows that the probability of losing is

R 3 + R 2 + R 1 + R 0 ≈ 0.999012

The probability of the biggest win is P 6 ≈ 0.0000000715 = 0.7115 10 -7

Probability of the smallest win P 4 =0,000969

Experiment number	Relative frequency of outcome 0
	0,54
	0,75
	0,47
	0,72
	0,54

The average value of the relative frequency that the player does not guess a single number is 0.514757143

And according to the calculations, the probability that the player does not guess a single number is 0.413019.

The difference is not very large, 0.101738, and can be related to both the number of experiments and the number of participants in each experiment.

Experiment number
	0,31
	0,14
	0,35
	0,52
	0,18

The average value of the relative frequency that the player guesses 1number is 0,366342857 .And according to the calculations, the probability that the player guesses 1 number is 0.413019. The difference between the calculations and the data obtained using the experiment is 0,0466761 .

Experiment number
	0,13
	0,045
	0,045

The average value of the relative frequency that the player guesses 2 numbers is 0,114021 . And according to the calculations, the probability is 0.132378. The difference between the calculations and the data obtained, using the experiment, is 0,018357 .

Experiment number
	0,045
	0,045

The average value of the relative frequency that the player guesses 3 numbers is 0,01 . And according to the calculations, the probability is 0.0176504. The difference between calculations and data obtained by experiment is equal to 0,007654 . It turns out that the experimental data are not much different from the data obtained by calculations.

(6) (6)

(43) (0)

6 x 5 x 4 x 3 x 2 x 1 1 x 2 x 3 x 4 x 5 x 6

1 win

(6) (5)

(43) (1)

6 x 5 x 4 x 3 x 2 1 x 2 x 3 x 4 x 5

43 1

258 wins

(6) (4)

(43) (2)

6 x 5 x 4 x 3 1 x 2 x 3 x 4

43 x 42 1 x 2

13.545 wins

In total, the "6 out of 49" lottery thus contains 13.804 wins, i.e. 1 win falls on 1.013 combinations.

13.983.816 13.545

1 to 1.032 combinations

Lottery 5 out of 36

To win, you need to guess 5 numbers out of 35. I experimented with this lottery as well. Each student who participated in the experiment received a card.

5 out of 35

Calculate the probability that the player does not guess any number.

5!∙30! 1∙2∙3∙4∙5

5!∙25! 2∙3∙4∙5

Р 0 ≈ 0.438977.

Experiment number	Relative frequency of outcome 1
	0,34
	0,34
	0,375
	0,38

four! · four! · 26! 2 3 4

Р 1 ≈ 0.422093

Experiment number	Relative frequency of outcome 2
	0,13
	0,17
	0,13
	0,17
	0,125
	0,09

Р 2 ≈ 0.284900

Experiment number	Relative frequency of outcome 3
	0,04
	0,04

3! · 2! · 2! · 28! 2 2

Р 3 ≈ 0.030525

R 5 ≈ 0.00000308041

This is 5729.9 times less than the probability of getting the smallest win in the SPORTLOTO lottery, and 43.1 times more than the probability of the biggest win in the same lottery. But not a single win in the experiments turned out.

The probable number of wins of each class is determined taking into account the probability coefficient of each win as follows:

(5) (5)

(31) (0)

5 x 4 x 3 x 2 x 1 1 x 2 x 3 x 4 x 5

1 win

(5) (4)

(31) (1)

5 x 4 x 3 x 2 1 x 2 x 3 x 4

31 1

155 wins

(5) (3)

(31) (2)

5 x 4 x 3 1 x 2 x 3

31 x 30 1 x 2

4.650 wins

In total, the "5 out of 36" lottery thus contains 4,806 wins, i.e. 1 win per 78 combinations.
The probability of occurrence of a win of each class is determined by the ratio of the probable number of wins to the total number of cases of winning, equal to the total number of combinations in the lottery:

376 992 4.650

1 for 81 combinations

outcomes	Absolute frequency		Relative frequency
			12/23
			8/23
			3/23

outcomes	Absolute frequency		Relative frequency
			10/23
			7/23
			4/23
			1/23

outcomes	Absolute frequency		Relative frequency
			11/22
			9/22
			3/22

outcomes	Absolute frequency		Relative frequency
			10/23
			8/23
			4/23

outcomes	Absolute frequency		Relative frequency
			11/24
			9/24
			3/24
			1/24

outcomes	Absolute frequency		Relative frequency
			10/24
			8/21
			2/21
			1/21

Lottery 5 out of 40

5 out of 40

The average value of the relative frequency of the fact that the player does not guess a single number is 0.4865875.

C 35 = 35! = 31∙32∙33∙34∙35 = 324 632

5!∙30! 1∙2∙3∙4∙5

C 30 = 30! = 26∙27∙28∙29∙30 = 142 506

5!∙25! 2∙3∙4∙5

Р 0 ≈ 0.438977.

The difference in the value obtained through experiments and calculations turned out to be 0.0476105.

Experiment number	Relative frequency of outcome 1
	0,52
	0,47
	0,38
	0,23
	0,38
	0,23

The average value of the relative frequency that the player guesses 1 number is 0.3865875. Let's calculate the probability that the player guesses 1 number.

C 5 C 30 = 5! · thirty! = 5 27 28 29 30 = 137025

four! · four! · 26! 2 3 4

Р 1 ≈ 0.422093

The difference between the values ​​obtained through experiments and calculations turned out to be 0.0355055.

Experiment number	Relative frequency of outcome 2
	0,04
	0,14
	0,23
	0,14
	0,09

The average value of the relative frequency that the player guesses 2 numbers is 0.151475.

Calculate the probability that the player guesses 2 numbers. 2 3

C 5 C 30 = 5! · thirty! = 4 5 28 29 30 = 40600

2! · 3! · 3! · 27! 2 2 3

Р 2 ≈ 0.284900

The difference between the values ​​obtained through experiments and calculations turned out to be 0.133425.

Experiment number	Relative frequency of outcome 3
	0,04
	0,04
	0,04

The average value of the relative frequency that the player guesses 3 numbers is 0.0225.

Calculate the probability that the player guesses 3 of the same number.

C 5 C 30 = 5! · thirty! = 4 5 29 30 = 4350

3! · 2! · 2! · 28! 2 2

Р 3 ≈ 0.030525

The difference between the values ​​obtained through experiments and calculations turned out to be 0.008025. The probability of winning in this lottery is

R 5 ≈ 0.00000308041

The probable number of wins of each class is determined taking into account the probability coefficient of each win as follows:
Winnings of the 1st class (for 5 guessed numbers):

(5) (5)

(35) (0)

5 x 4 x 3 x 2 x 1 1 x 2 x 3 x 4 x 5

1 win

Winnings of the 2nd class (for 4 guessed numbers):

(5) (4)

(35) (1)

5 x 4 x 3 x 2 1 x 2 x 3 x 4

35 1

175 wins

Winnings of the 3rd class (for 3 guessed numbers):

(5) (3)

(35) (2)

5 x 4 x 3 1 x 2 x 3

35 x 34 1 x 2

5.950 wins

In total, the "5 out of 40" lottery thus contains 6.126 winnings, i.e. 1 win per 107 combinations.
The probability of occurrence of a win of each class is determined by the ratio of the probable number of wins to the total number of cases of winning, equal to the total number of combinations in the lottery:
Winning class 1 (for 5 guessed numbers):

Winning class 3 (for 3 guessed numbers):

658.008 5.950

1 for 110 combinations

outcomes	Absolute frequency		Relative frequency
			9/21
			11/21
			1/21

outcomes	Absolute frequency				Relative frequency
					8/21
					10/21
					3/21
outcomes	Absolute frequency				Relative frequency
					8/21
					8/21
					5/21
outcomes	Absolute frequency				Relative frequency
					12/21
					5/21
					3/21
					1/21

outcomes	Absolute frequency		Relative frequency
			10/21
			8/21
			2/21
			1/21
outcomes	Absolute frequency		Relative frequency
			15/21
			5/21
			1/21
outcomes	Absolute frequency		Relative frequency
			12/22
			7/22
			3/22
outcomes	Absolute frequency		Relative frequency
			15/20
			3/20
			2/20
			0
outcomes	Absolute frequency		Relative frequency
0	14		14/22
1	7		7/22
2	0		0
3	1		1/22
4	0		0
5	0		0
6	0		0
outcomes	Absolute frequency		Relative frequency
0	11		11/23
1	12		12/23
2	0		0
3	0		0
4	0		0
5	0		0
6	0		0

outcomes	Absolute frequency	Relative frequency
0	16	16/22
1	4	4/22
2	1	1/22
3	1	1/22
4	0	0
5	0	0
6	0	0

outcomes	Absolute frequency	Relative frequency
0	12	12/22
1	9	9/22
2	1	1/22
3	0	0
4	0	0
5	0	0
6	0	0

Lottery 6 out of 45

To win, you need to guess 5 numbers out of 40. I also experimented with this lottery. Each student who participated in the experiment received a card.

6 out of 45
1	6	11	16	21	26	31	36	41
2	7	12	17	22	27	32	37	42
3	8	13	18	23	28	33	38	43
4	9	14	19	24	29	34	39	44
5	10	15	20	25	30	35	40	45

The average value of the relative frequency of the fact that the player does not guess a single number is 0.4865875.

Calculate the probability that the player does not guess any number. 5

FROM35 = 35! = 31∙32∙33∙34∙35 = 324 632

5!∙30! 1∙2∙3∙4∙5

5

FROM30 = 30! = 26∙27∙28∙29∙30 = 142 506

5!∙25! 2∙3∙4∙5

R0 ≈ 0,438977.

The difference in the value obtained through experiments and calculations turned out to be 0.0476105.

Experiment number	Relative frequency of outcome 1
1	0,42
2	0,33
3	0,38
4	0,28
5	0,42
6	0,47

The average value of the relative frequency that the player guesses 1 number is 0.3865875. Let's calculate the probability that the player guesses 1 number.

1 4

FROM5 · FROM30 = 5! · thirty!= 5 27 28 29 30= 137025

four! · four! · 26! 2 3 4

R1 ≈ 0,422093

The difference between the values ​​obtained through experiments and calculations turned out to be 0.0355055.

Experiment number	Relative frequency of outcome 2
1	0,14
2	0,23
3	0,14
4	0,33
5	0,19
6	0,14

The average value of the relative frequency that the player guesses 2 numbers is 0.151475.

Calculate the probability that the player guesses 2 numbers. 2 3

FROM5 · FROM30 = 5! · thirty!= 4 5 28 29 30= 40600

2! · 3! · 3! · 27! 2 2 3

R2 ≈ 0,284900

The difference between the values ​​obtained through experiments and calculations turned out to be 0.133425.

Experiment number	Relative frequency of outcome 3
1	0,04
2	0,04
3	0,04
4	0,04
5	0
6	0

The average value of the relative frequency that the player guesses 3 numbers is 0.0225.

Calculate the probability that the player guesses 3 of the same number.

3 2

FROM5 · FROM30 = 5! · thirty!= 4 5 29 30= 4350

3! · 2! · 2! · 28! 2 2

R3 ≈ 0,030525

The difference between the values ​​obtained through experiments and calculations turned out to be 0.008025. The probability of winning in this lottery is

R5 ≈ 0,00000308041

. Not a single win in the experiments turned out

outcomes	Absolute frequency	Relative frequency
		8/21
		9/21
		3/21
		1/21

outcomes	Absolute frequency	Relative frequency
		8/21
		7/21
		5/21
		1/21

outcomes	Absolute frequency	Relative frequency
		9/21
		8/21
		3/21
		1/21

outcomes	Absolute frequency	Relative frequency
		7/21
		6/21
		7/21
		1/21

outcomes	Absolute frequency	Relative frequency
		8/21
		9/21
		4/21

outcomes	Absolute frequency	Relative frequency
		8/21
		10/21
		3/21

The probable number of wins of each class is determined taking into account the probability coefficient of each win as follows:
Winnings of the 1st class (for 6 guessed numbers):

(6) (6)

(39) (0)

6 x 5 x 4 x 3 x 2 x 1 1 x 2 x 3 x 4 x 5 x 6

1 win

Winnings of the 2nd class (for 5 guessed numbers):

(6) (5)

(39) (1)

6 x 5 x 4 x 3 x 2 1 x 2 x 3 x 4 x 5

39 1

234 wins

Winnings of the 3rd class (for 4 guessed numbers):

(6) (4)

(39) (2)

=

6 x 5 x 4 x 3 1 x 2 x 3 x 4

39 x 38 1 x 2

11.115 wins

In total, the "6 out of 45" lottery thus contains 11,350 wins, i.e. 1 win per 718 combinations.
The probability of occurrence of a win of each class is determined by the ratio of the probable number of wins to the total number of cases of winning, equal to the total number of combinations in the lottery:
Winning class 1 (for 6 guessed numbers):

Winning class 3 (for 4 guessed numbers):

8.145.060 11.115

1 for 733 combinations

Conclusion:

All the tasks were completed, the hypothesis that with the help of the probability of winning in numerical lotteries was proved. I would like my work to help people not make the mistakes they make when playing various lotteries, and I hope that many people will take advantage of my work. To substantiate my hypothesis that many believe that the results of lotteries in which chance reigns cannot be predicted, I present the results of my survey among ninth graders on the topic “Is it possible to predict the outcome of a game in which chance reigns?”.

Here are his results presented in chart form:

As you can see, this confirms my hypothesis about students' misconceptions about the possibilities of probability theory.

Literature.

1. Encyclopedia for children. Maths. Volume 11. Moscow, Akvanta+ , 2001
2. I know the world. Maths. Moscow, Ast, 1998
3. M.F. Rushailo Elements of the theory of probability and mathematical statistics. Moscow, 2004
4. E.A. Bunimovich, V.A. Bulychev Probability and statistics 5 - 9 grades. Bustard, Moscow, 2002

Examples of lottery tickets.

Slides captions:

The probability of winning in numerical lotteries The work was completed by: student 10 "A" class MOU secondary school No. 11 Kokorin Artyom

Lottery. Lottery (from Italian lotteria) - an organized game of chance, in which the distribution of benefits and losses depends on the random extraction of a particular ticket or number

The urgency of the problem. Hypothesis. My topic is relevant, since mathematics is in contact with everyday life much more closely than it is traditionally taught in school. Most believe that it is impossible to predict the outcome of a numerical lottery in which chance reigns. This is not true. The probability of winning is a value that will help us determine whether this or that game is fair, and whether it is profitable for us to play it

Goals. To study the rules for conducting numerical lotteries and consider methods for their study, using the formulas of the theory of probability. Conduct an experiment Analyze the data obtained Create a mini-guide containing useful information about number lotteries

The history of the creation of lotteries. Many fans of sports and numerical lotteries, including Sportloto, may not know that its prototype was a lottery with the numerical formula “5 out of 90”, organized in 1530 in the Italian city of Genoa. The fact is that in the Republic of Genoa, elections to the main body of self-government - the Great Council - were held by lot. After a multi-stage selection, 90 candidates were allowed to the last round of voting, of which only five people had to be selected. The elections took place as follows: each candidate for membership in the Council was assigned a serial number from the first to the ninetieth. Then 90 numbered balls were placed in a special urn. After thorough mixing, only 5 balls were taken out of it. Chance made its choice. The numbers on the balls taken out were the names of the members of the Great Council of Genoa! Such a lottery principle of choice was universally recognized in Italy and, having crossed state borders, began to spread to other European countries. Currently, there are several varieties of number lotteries in different countries.

Subject of study. Numerical lotteries: "6 out of 49" "5 out of 36" "5 out of 40"

Numerical lottery "6 out of 49" Rules: To get a big win, you had to guess 6 numbers out of 49. Win cards with a match of 5 and even 4 numbers

References: Encyclopedia for children. Maths. Volume 11. Moscow, Aquanta +, 2001 I get to know the world. Maths. Moscow, Ast, 1998 M.F. Rushailo Elements of the theory of probability and mathematical statistics. Moscow, 2004 E.A. Bunimovich, V.A. Bulychev Probability and statistics 5 - 9 grades. Bustard, Moscow, 2002

Lotteries are popular entertainment all over the world. Many people want to try their luck by making minimal investments and getting huge winnings. There are many reasons for such a risk: the desire to get rich quickly and effortlessly, to believe in a miracle, to change life, to have fun, to get positive emotions. Fortune smiles on some, while others are still in search of answers to the question: "How to win the 6 out of 45 lottery."

General Lottery Rules

For more than eight years, gamblers have been buying tickets, hoping for a solid reward. To have a chance of winning, you need to know the basic information about Gosloto "6 out of 45". There are several options for getting the opportunity to place a bet:

1. On the official website, where after paying the receipt, you can choose the numbers you like.
2. On the mobile app.
3. In the branches of the Russian Post.
4. Via SMS, which is sent to the number 9999.
5. At points of sale of tickets.
6. With a QR code.

The probability of winning the lottery "6 out of 45" depends on the number of guessed numbers. For example, a match of six numbers occurs in one case in 8,145,060. Further, the odds are: 5 - 1 in 34808, 4 - 1 in 733, 3 - 1 in 45, 2 - 1 in 7. To get closer to victory, many produce more bets, while others firmly believe in luck.

Draws take place daily. First, the amount of the prize fund is calculated, and only then the "6 out of 45" lottery is drawn. Lottery equipment determines the lucky combinations that are obtained randomly. Participants will learn about the results by calling the number 84 992 702 727, which is indicated on the official website or at ticket sales points.

Ways to increase your chances of becoming a millionaire

In their interviews, joyful winners report different ways of achieving success. So how do you win the 6 out of 45 lottery? The most popular ways:

1. The use of conspiracies and mystical rituals to attract good luck.
2. Choice of favorite numbers.
3. A bet on those numbers that are happy, significant, carrying a certain meaning.
4. Blind faith in the fact that someday fortune will certainly show favor.
5. The usual positive attitude.
6. Deep analysis of the lottery "6 out of 45", the study of statistics.
7. Recourse to the help of self-made LFOs.
8. Development of personal strategies.
9. Using the same combination over and over again.
10. Help from loved ones who are distinguished by enviable luck.

Determining the size of the bet

The question of how to win the "6 out of 45" lottery by varying the bet is still open. There are cases in history when a person bought a single ticket, spending minimal money, and as a result received a large reward. There are also people who have been investing for years, combining ways of playing, using expanded rates, but still only suffer losses.

With the increase in the cost of a receipt, the probability of winning increases, as evidenced by the repeated analysis of past draws. However, it is not very wise to invest the last savings in the illusory hope of becoming a millionaire. You always have to be mentally prepared for failure. Therefore, it is recommended to spend only the money that you do not mind losing forever.

Some winners used multi-circulation bets to win. They chose the number series they liked once, paying for participation in several future draws at once. One of the fans of such a strategy was able to receive more than 184 million rubles.

How to select winning combinations

How to win the "6 out of 45" lottery using the correct number guessing tactics? The main tips for beginners are as follows:

• You don't have to pick numbers in a row.
• Do not pay too much attention to dates, since there are only 31 days in a month, and even fewer months. A number from 32 to 45, as a rule, often remains unclaimed.
• It is worth trying to bet with a group of friends, increasing the number of combinations.
• From time to time, you should make detailed bets, getting the opportunity to choose up to 14 numbers.

Is there a secret to getting 100% winnings?

Now you can meet a large number of scammers who ask for solid money for providing those who wish with step-by-step instructions that can bring the jackpot. They assure that it is their "6 out of 45" lottery winning system that is the only correct, reliable and successful one. However, you do not need to believe in such fairy tales.

If there is a desire to try your luck, then it is better to do it yourself than to give your funds to dishonest citizens who are trying to get rich at the expense of gullible players. The secrets of victory are unique.

Someone is helped by mathematical charts, in which the analysis of the "6 out of 45" lottery plays a decisive role. Others invent formulas for calculating lucky combinations. Still others "poke a finger in the sky." There are people who claim that the cherished numbers appeared to them in a dream. Therefore, you should rely on personal intuition.

It is not recommended to skip distribution draws, because if you guess the correct numbers, the jackpot will be many times larger in them. An indispensable guarantee of success is a good mood, self-confidence and lack of fanaticism. If you are unlucky once, do not give up your hobby. Regularity is an essential condition for achieving what you want.

Thus, each participant has the same chances of getting the coveted jackpot. Experienced lottery fans are constantly inventing new ways to get closer to the big prize. However, there are no 100% successful algorithms. You can try each of them in turn, combine, combine, come up with personal theories. The result will still be individual and random.

Is it possible to win the lottery and how to do it? What are the best lotteries to play? As life practice shows, winning the lottery is an event that can happen to anyone.

Good day, dear readers of HiterBober.ru business magazine. Alexander Berezhnov and Vitaly Tsyganok are with you.

Winning in some local lotteries and "intellectual casinos" ourselves, we summarized the topic of winning the lottery, talked with friends who regularly raise good money in this business and presented our vision of this issue.

You don't have to have a college degree, be the son of wealthy parents, or finish school with a gold medal to win. To win, you need only luck and faith in your own luck. It is faith that makes a person buy a lottery ticket.

Some lucky people need to buy a lottery ticket only once to win, others buy lotteries regularly (sometimes for several years in a row), until they finally receive a reward for patience and perseverance.

These questions are of interest to many - not only avid players and gamblers - read our article about working methods and profitable technologies for playing the lottery, as well as about the biggest wins in history.

1. Is it possible to win the lottery and what you need to know for this

Skeptics believe that only lottery organizers remain the winners, optimists believe that Sportloto, Gosloto and other popular lotteries are a real way to gain real financial well-being.

Let's say right away that, of course, it is possible to win the lottery, and each player has the chance of taking the jackpot. Probability theory and mathematics with basic statistics allow for the possibility of winning any lottery ticket at any time.

However, in game theory there is also such a thing as distance, and it is the distance that is the main obstacle on the way of ordinary players to the desired wealth. In other words, a fair amount of time can pass from the moment you expect a win to the moment you win. You can play the lottery for a day, a month, a year, ten years - and the probability of winning will always be about the same.

In the article we will try not to touch on the "mystical" aspect of the game, but it should still be mentioned.

There are players who believe in spells for good luck, in a series of victories, in lucky days and numbers, in rabbit feet and rituals. There are many films, books and TV shows devoted to examples of incredible luck. However, in reality, everything is more prosaic: when playing the lottery, we are dealing with the mathematical theory of the game and nothing more.

Of course, faith in one's own strengths and healthy optimism are conditions that work more as a plus than a minus. A person who believes in luck is more likely to be right than a hopeless pessimist.

Currently, online lotteries have become very popular, which almost do not differ from the usual "paper" and offline lotteries.

EuroMillions is a Friday lottery for players across Europe. Players from nine countries take part in the game, including Austria, Belgium, France, Ireland, Luxembourg, Portugal, Spain, Switzerland and the USA.

The prize consists of bets placed in each of these nine countries, and the top prize starts at 15 million euros. If the jackpot is not won within a week, the prize rolls over to the next week.

The biggest recorded win per person was 115 million euros and the biggest jackpot was 183 million euros. These huge jackpots have made the EuroMillions lottery one of the most successful and exciting lotteries in the world.

5. Examples of the Biggest Winners in Lottery History

There are a lot of examples of people who have received the biggest and biggest lottery winnings. If there are jackpots, then there are people who win them periodically.

Meet: the biggest winnings in the history of world and domestic lotteries.

Among domestic lotteries, the podium is occupied by Albert Begrakyan, who hit the Gosloto jackpot in the amount of 100 million rubles in 2009.

Lucky lottery tickets bought regularly. Before winning, Albert worked as a security guard in a store.

The most successful "foreign" lottery players today are the Messners from New Jersey and Georgia truck driver Ed Neighbors.

It was these people who equally split the $390 million jackpot of the Mega Millions lottery in 2007.

In Europe, the biggest win is 185 million euros in the EuroMillions lottery: another married couple (Kristen and Colin) received the prize in 2011.

In connection with the entry yesterday, 06/30/2009, into force of Clause 1 of Article 17, Clause 1 of Article 18 and Article 19
OF THE FEDERAL LAW N 244-FZ of December 29, 2006 "ON STATE REGULATION OF ACTIVITIES IN ORGANIZING AND CARRYING OUT GAMBLING AND ON AMENDING SOME LEGISLATIVE ACTS OF THE RUSSIAN FEDERATION" (adopted by the State Duma of the Federal Assembly of the Russian Federation on December 20, 2006), http://nalog.contant.contant. en/doc64924.html

THE PARADOX OF THE LOTTERY AND THE LAW OF LARGE NUMBERS BERNULLI

Opportunity is an opportunity to be disappointed

("Aphorisms, quotations, and winged words",
http://aphorism-list.com/t.php?page=vozmojnost)

Your chances of winning the lottery will increase
if you buy a ticket

Winston Groom (from The Rules of Forrest Gump)
("Aphorisms about games",
http://letter.com.ua/aphorism/game1.php)

"The paradox of the lottery

It is quite expected (and philosophically verifiable [English]) that this particular ticket will not win, but one cannot expect that any ticket will not win” (“Akademika”, List of Paradoxes, http://dic.academic.ru/dic.nsf /enwiki/165304).

“The paradox of the lottery (such as sports lotto)

Most participants in lotteries (in which the prize is distributed among all the winners, as in the sports lotto) usually do not bet on "too symmetrical" combinations, although all combinations are equally possible. The reason is simple. Players know from experience that, as a rule, non-symmetrical combinations win. In fact, it is more profitable to bet on the most symmetrical combinations precisely because…. Why?" (excerpts from the book: G. Sekey. Paradoxes in probability theory and mathematical statistics. M.: Mir. - 1990, http://arbuz.uz/t_paradox.html).

SOLUTION

Everyone in their life has played some kind of game, not necessarily gambling, which, one way or another, is associated with probability. And if someone didn’t play, then he probably tossed a coin a couple of times in his life. Just like that, for fun or solving some issue, on which it turned out to be overwhelming or impossible to make a choice on your own. And I did the same as a child. But even then, some doubt crept into my head about the correctness of justifying my choice of solving even trifling questions by tossing a coin. Apparently, even then they did not want to entrust their own right of choice to blind chance. But not so much because I myself can choose the best option right now and just for myself, but more because such a choice will not be fair. So fair that without any further thought and internal hesitation I could accept it and act in accordance with this choice. And then I completely stopped trying to make decisions in such a simple way, when my fears were confirmed while watching one of the popular Indian films that took place with us in the 80s. If I'm not mistaken, it was the film "Revenge and the Law." In it, one of the main characters, making a choice of something, tossed a coin with a serious look. And everything would be fine, but only when he was shot after all, and he presented his “lucky coin”, it turned out that it was with two identical sides. Apparently, this hero has learned the first rule of success well: if you want to win at a casino, become its owner.

To the question of the problem given by Szekei in his book, about why it is MORE PROFITABLE to choose exactly symmetrical options for the geometric arrangement of numbers on the card field, the answer is not so complicated. The conclusion follows from three conditions:

1) all options: both symmetrical and asymmetric are equally probable;

2) most players choose non-symmetrical options;

3) the amount of winnings received depends on the number of: a) participants, b) winners (by categories of winnings, of course);

Hence, from the point of view of profit, that is, the increase in the possible profit when guessing, symmetrical options will be guessed by a much smaller number of players with the same number of participants in the lottery, and the winnings will be divided among a much smaller number of winners.

But on the other hand, if everything were so simple, then there would be no difficulties in determining the probability of certain events. And paradoxes and various paradoxical problems in probability theory exist no less, if not much more, than in other branches of science (in the same mathematics, logic, physics). For example, such a task.

"The Paradox of Dice

A correct dice, when thrown with equal chances, falls on any of the faces 1,2,3,4,5 or 6. (The sum of points on opposite faces is 7, i.e. a fall on 1 means a loss of 6, etc.) .

In the case of throwing 2 dice, the sum of the numbers drawn is between 2 and 12. Both 9 and 10 can be obtained in two different ways: 9 = 3 + 6 = 4 + 5 and 10 = 4 + 6 = 5 + 5. In the problem with three dice and 9 and 10 are obtained in six ways. Why then does 9 appear more often when two dice are rolled, and 10 when three dice are rolled? (excerpts from the book: G. Sekey. Paradoxes in probability theory and mathematical statistics. M.: Mir. - 1990, http://arbuz.uz/t_paradox.html)”.

There is no paradox in this problem. The paradox, or rather the trick, is hidden in incomplete information: the number of possible combinations is greater than indicated. Because only the types of options are indicated, the methods of compilation that need to be distributed by the number of bones.

The answer is simple: 9 appears more often when two dice are rolled, and 10 when three dice are rolled, because the probability of rolling a sum of 9 with two dice is greater than the probability of rolling a sum of 10 with three dice, which reflects the ratio of the number of options compiling these amounts.

Number of summing options:

A. 9 on two dice: 3 + 6 (2 possible options, that is, on the first 3 on the second 6 and vice versa) and 4 + 5 (2 options). Total: 4 options

10 on two dice: 4+6 (var. 2) and 5+5 (var. 1). Total: 3 options

Probability ratio in favor of the sum 9.

B. 9 on three dice: 1+2+6 (var. 6), 1+3+5 (var. 6), 1+4+4 (var. 3), 2+2+5 (var. 3) , 2+3+4 (6 variant), 3+3+3 (1 variant). Total: 25 options

10 on three dice: 1+3+6 (var. 6), 1+4+5 (var. 6), 2+2+6 (var. 3), 2+3+5 (var. 6), 2 +4+4 (variant 3), 3+3+4 (variant 3), 4+4+2 (variant 3) Total: 30 variants

Probability ratio in favor of the sum 10.

Why does the probability of events give rise to so many contradictions?

I may be wrong, but in my opinion, even mathematicians, not to mention those who are not at all familiar with probability theory, are captivated by one false assumption about the probability distribution. This is the idea that events occur only depending on their probability, without taking into account the distribution of probability over time. Life does not always go according to calculated schemes and exactly as it is described mathematically. The reflection of this duality: mathematical calculation and at the same time not coincidence with it - is given in the following paradox.

PARADOX OF THE LAW OF LARGE BERNULLI NUMBERS

“The ratio of the loss of a coat of arms or tails to the total number of attempts with a large number of throws tends to 1/2. Some players believe that with a series of heads, the probability of getting tails increases. And at the same time, coins have no memory, they do not know the previous throws, and each time the probability of getting heads or tails is 1/2. Even if before that 1000 coats of arms fell out in a row. Doesn't this contradict Bernoulli's law? (excerpts from the book: G. Sekey. Paradoxes in probability theory and mathematical statistics. M.: Mir. - 1990, http://arbuz.uz/t_paradox.html).

Bernoulli's law of large numbers

“Let a sequence of independent trials be carried out, as a result of each of which event A may or may not occur, and the probability of this event occurring is the same for each trial and is equal to p. If event A actually happened m times in n trials, then the ratio m / n is called, as we know, the frequency of occurrence of event A. Frequency is a random variable, and the probability that the frequency takes the value m / n is expressed by the Bernoulli formula ...

The law of large numbers in the form of Bernoulli is as follows: with a probability arbitrarily close to one, it can be argued that for a sufficiently large number of experiments, the frequency of occurrence of the event A differs arbitrarily little from its probability, i.e. ...

... in other words, with an unlimited increase in the number n of experiments, the frequency m / n of event A converges in probability to P (A) "(Probability theory, § 5. 3. Bernoulli's law of large numbers. , http://www.toehelp.ru/ theory/ter_ver/5_3)

Thus, from the contradictions contained in these paradoxes, one can formulate a general problem.

Contradictions:

1. The paradox of the lottery - the probability of winning a particular ticket is negligible, but the probability of winning any ticket is 1, that is, 100 percent;

2. The paradox of the law of large Bernoulli numbers - the probability of any option falling out is equivalent, but in reality it should change with a larger loss of some options to bring the probability to balance.

The problem, in my opinion, lies in the misunderstanding of the uneven distribution of probability over the number of options, or, in other words, the dependence of the probability of one event option on another in a time context.

No one will argue that the sum of the probabilities of the variants of an event is equal to one. But why does everyone think that the distribution of options is even? This approach completely ignores the variability of the world over time. And the same falling sides of the coin should then strictly alternate in turn: heads, tails, heads, tails. Then the probability distribution calculated by the formula will completely coincide with the actual one FOR ANY SPECIFIC TIME PERIOD. Because within this time period, the number of drop-down different options will be the same. But in reality this is not so. Within individual periods, the probability of each event variant varies from 0 to 1 (from zero to one hundred percent). For example, when out of ten times all ten times an eagle falls out (or red, if it is a roulette in a casino). I know of a case where black came up 15 times in a row in a roulette wheel. From the point of view of calculating the probability, this is generally impossible, if taken as a unit, that is, the sum of all possible options, for example, 20 occurrences, which include these fifteen. And this, by the way, continuing the thought, for some reason did not lead to the next fifteen fallouts of red. Players call such falling out in a row a series. Series are observed in sports, but in general everywhere.

You will say that Bernoulli's law describes periods with large, "unlimited number of experiments" and within these limits it is correct? Then why shouldn't the same coin come up 1000 times on one side in a row, and then a thousand times on the other side? After all, the law in this case is not violated in the least bit? In reality, this does not happen. In fact, any long series of occurrences of two possible events (A and B, which can be replaced, for example, with “heads” and “tails”) will closely correspond to the pattern of occurrences:

A, B, A, B, AAA, B, AA, BB, AA, BBBBBBB, AA, BBB, A, BBBBBBB, AAA, B, AA, BB, A, B, AAAA, B, AA, BBB, AAAA, B, A, B, A ... (30 A and B each, 60 in total).

As you can see, within each specific segment (periods of precipitation or periods of time), unevenness is observed. And the duration of the “series” of falling out of one option a) in a row and b) within a period (for example, 10 falling out) can fluctuate. Theoretically, the amplitude of such oscillations is not limited by anything, but there are no practically unlimited series. That is, there is a certain limit to which the duration of the "series" increases, its "length". These two restrictions govern the balance of probability of event variants: firstly, by the variability of variants within an arbitrary period (time), in other words, by changing the “length” of series from 1 to several repetitions in a row, and secondly, by limiting the length and frequency of series in within an arbitrary period (time). This achieves a variety of events, variability.

Such a probability distribution is noted by players who choose asymmetric options for the arrangement of numbers on a lottery card. They do not proceed from an equal distribution of probability over the number of numbers, that is, their equally possible loss, but, just from an uneven distribution of probability over numbers. For some reason, the same numbers have not yet fallen out, not only in two draws in a row, but also in the mass of all draws. I can say this with confidence based on the study of the "Sportloto 5 out of 36" lottery, which has been carried out for decades. In a row, two draws will drop a maximum of 1 number of the previous draw (quite often - about a quarter of the draws), 2 (in isolated cases), 3 (in more rare cases). According to the theory of probability, someday all five numbers would fall out the same two runs in a row. But this would take thousands of years, even if the draws were held every day, and not once a week. This follows if we proceed from the fact that the total number of possible options in the Sportloto 5 out of 36 lottery (36 * 35 * 34 * 33 * 32 / 1 * 2 * 3 * 4 * 5) = 376.992, and the repetition of five numbers of the previous draw will happen no earlier than all possible options fall out at least once, which will happen when holding 1 draw per day, taking into account leap years for: 376.992 / (365 * 4 + 1) * 4 = 1032.1478 ~ 1032 of the year. But even after a complete enumeration of all possible options in a row, two identical runs may not fall out for several thousand more years, and possibly never.

Therefore, I absolutely agree with the players who choose the most frequently dropped, asymmetrical options. Because waiting for an option to drop out, for example, from the film “Sportloto - 82” with M. Pugovkin and M. Kokshenov - 1,2,3,4,5,6 is simply not-re-al-but. You might as well wait for rain on Mars.
I will add that, having fixed the probability distribution in a certain way, I saw that the types of options, similar to the one given from the film, make up an insignificant fraction of a percent of all other types that fall out, classes of options, and according to probability theory they are equally possible.

The paradox of the lottery arises from the fact that the probability of winning each specific ticket individually, that is, any one, is negligible, tends to zero, but the probability of winning any one specific ticket is one hundred percent. Because the probability of falling out of specific numbers in a particular draw is not distributed among all options equally. Roughly speaking, one hundred percent of the probability is divided not into the entire mass of tickets, but into two parts - all the winners (that is, one, for simplicity) and all the losers (all the rest). Thus, everyone has a chance to win, and no one. Because it is impossible to know WHICH ticket will win, but that SO ONE ticket will win, we know in advance (without going into details of the number of winners and winning conditions).
At this point, however ridiculous it may seem, the correctness of the “female logic” becomes obvious, which claims that the probability of a meteorite falling on Red Square is not one in several million, but fifty to fifty - either it will fall or not.
Apparently, such a well-known mathematician as Poincaré also adhered to an opinion similar to mine. “Poincare once noted with sarcasm that everyone believes in the universality of the normal distribution: physicists believe because they think that mathematicians have proved its logical necessity, and mathematicians believe because they believe that physicists have verified this with laboratory experiments” (De Moivre’s Paradox , excerpts from the book: G. Sekei, Paradoxes in Probability Theory and Mathematical Statistics, Moscow: Mir, 1990, http://arbuz.uz/t_paradox.html).

That is, the lottery paradox arises due to an incorrect initial premise - the probability distribution is not uniform within a separate period, but is changeable. And if we take one draw for a separate period, then ALL possible options CANNOT fall out in it, but only ONE will fall out. Therefore, the contradictory understanding of probability disappears: the probability of the absolute majority of options falling out will be equal to zero, and only the probability of one option will be equal to one.

There are no conflicting conditions in the lottery paradox:

1) only one option falls out of all possible ones in a particular draw (one ticket wins);

2) there are many more possible options.

Consequently, the probability of expecting a win for only ONE of all possible options (tickets) tends to one, and the probability of expecting a win for ALL options (tickets) remaining from ONE tends to zero.

There is no contradiction in the paradox of large Bernoulli numbers either:

1) the probability of falling out of one of the possible options is equal to half - 0.5;

2) the expectation of a change in the probability of falling out of the second of the possible options after a series of falling out of the first one changes.

Consequently, the probability of an event as a whole does not change, that is, the sum of the probabilities of the options remains the same, but within a separate period, especially if it is incomparably small in relation to the sum of all possible periods of occurrences, the probability changes, which is reflected in the expectations of the players.

Try to prove to the winner of a large sum that the probability of this was infinitely small. Moreover, try to prove it to several or thousands of such people. The probability of even being born for some was absolutely miserable, but, nevertheless, it happened.
Many compare the impossibility of winning with the possibility of a meteorite falling on the head or a lightning strike. Try to prove that this is impossible, because the probability of this is infinitely small, affected by them. Like, for example, a woman who was healed from a lightning strike: “A unique case was recorded in the Serbian city of Slivovitsa, according to the DELFI portal. Lightning hit 51-year-old Nada Akimovich, who previously suffered from arrhythmia. However, as a result of exposure to a powerful discharge of electric current, the disease disappeared ”(Lightning strike healed a woman / Days.ru, 23:23 / 10.07.2009, http://www.dni.ru/incidents/2009/7/10/170321.html ) - or to a boy from Germany: "... The chance of getting hit by a meteorite is 1 in a hundred million ... "First I saw a large fireball, and then suddenly I felt pain in my arm." (A meteorite hit a German boy / MIGnews.com, 06/14/2009, 02:42,

Thus, THERE IS NO CONTRADICTION IN THE LOTTERY PARADOX, AS IS THERE IN THE PARADOX OF LARGE BERNULLI NUMBERS.

01.07.2009 03:00 – 6.30

Photo - Gosloto, http://www.gosloto.ru/index.php?id=93

PS: The probability of another article appearing instead of this one was close to 100 percent, today or in the coming days. However, this did not happen. And the appearance of this article in the coming weeks was generally close to zero. However, it happened.

Reviews

"The chance of being hit by a meteorite is 1 in a hundred million... A German boy was hit by a meteorite." The example is not identical to winning the lottery, since it is not at all clear where the ratio "1 to one hundred million" comes from.

If we talk about the lottery, then, let's say for Israel to win the first prize is 1 to 18 million. The person who won knows that his chance was negligible, but he sees that people win at least once a month or two, and therefore, even "knowing", he does not realize the "smallness" of his chance. The catch is that the chance is small only for a specific person, but for a country as a whole, with a population of 6 million, it is very logical to win one of 10-20 games (not everyone plays, but each player can fill out more than one form).
The classic alignment, as in the paradox of birthdays.

As for the numbers - not for me, I took a quote. And it’s not so important, in theory, that the numbers may not be entirely accurate, the main thing that illustrates the idea is that even very rare events have happened, are happening and will always happen. Therefore, the example is still identical, I think.

Yes, you yourself pleased with the numbers, Dmitry. Speaking about Israel, in purely Jewish terms, they reduced the population of the country a little, by a couple of million :) And then why did you decide that the main prize is won "once or twice a month." It's from the ceiling, sorry. And do not think that people are all stupid, that they do not understand the insignificance of the chance. Understand! But the cost compared to the profit is as small as the chance of winning. So there is a balance here. And some people generally win all their lives! Recently I read about a woman who, after a misfortune with her health, began to play all available quizzes and lotteries. So her whole apartment is littered with various prizes. Uncle often won the Russian Lotto with 1-2 tickets, when others did not receive anything even from a pack or two. He himself participated in the lottery at the presentation, where the 1st main prize - a computer - was won by a woman who bought a computer, then she had only 1 ticket-check. And the second prize - the monitor - was won by the guy who bought the monitor, also with 1 ticket-check. There were a hundred or two people. However, fraud is also possible here, which is not uncommon in our country.

Well, there is no paradox. For one person, the probability of winning tends to zero, and for the country - to one hundred percent. This is my conclusion. I ran through about birthdays, but it is completely inadequate to this one, as far as I remember. Suffice it to recall how they are recruited into training classes.

"somehow they reduced the size of the country by a couple of millions ... why did you decide that the main prize is won "once or twice a month". 2000, but on the account "from the ceiling" - you are in vain. It just so happened that for almost 5 years I worked as the head of the computer department of the Israeli lottery and all the statistics went through the database I managed. The number of known users is updated every 10 years (so the data is for 2000), but the winnings and the number of winners with their amounts (even if it's only NIS 10) are recorded twice a week. So this is not an assumption, but a statement.

“And don’t think that people are all stupid, that they don’t understand the insignificance of a chance,” I didn’t say that. My quote: "Even "knowing", he does not realize the "smallness" of his chance. A person is not able to realize very large or very small numbers; it is important for him to go 10 km or 20 km, but the distance to the moon 380 thousand or 400 thousand does not matter - he is simply not able to realize this, since he personally does not operate with such distances.
The chance is easily reduced from 18 million to 1 to 9 million to 1 by just buying two tickets. One imagines this as an incredible advancement. And it's not stupidity, but awareness. In my memory, rarely ... VERY RARE a person buys ONLY ONE column in the loto, for this very reason: double-triple-...- 10 times the chance. Although it doesn't really matter.

Ahh .. so it's you Systemism and someone else there, then, sir? ok:) By the way, you didn't answer one of my old reviews, and God be damned. I already forgot.

AS: having read to the words “I worked for almost 5 years as the head of the Israeli computer department ...”, the reader automatically added “intelligence” and, either hiccuping or giggling, swallowed convulsively ... # :-0))

As for increasing the chances: if you take 1-2 tickets, then the increase is considered zero. If you start to really increase, then the game will be at a loss, because there is no guarantee that everything will pay off in the end.

The daily audience of the Proza.ru portal is about 100 thousand visitors, who in total view more than half a million pages according to the traffic counter, which is located to the right of this text. Each column contains two numbers: the number of views and the number of visitors.

Hi all! The business expert of the Papa Pomog portal Denis Kuderin is with you! I will tell you whether it is worth participating in the lottery in terms of mathematics, and how game theory relates to practice.

Everyone who purchases a ticket has the chance to take a big jackpot in the lottery. Another thing is that the mathematical expectation of this probability can exceed all conceivable limits.

Are there ways to increase the chances of success? Is it possible to win the lottery regularly? What are the biggest winnings in the history of Russian and foreign lotteries? You will find detailed answers to these and other questions in a new article on our website!

In this article, 5 real ways to increase your chance of winning any lottery!

Is it possible to win the lottery - the opinion of mathematicians and experts

You don't have to go to college, be a wealthy heir, or have superpowers to win the lottery. You just need to buy a ticket and believe in your luck. All lottery winners are not celestials at all, but ordinary citizens whom we meet on the way to work or see at the next table in a cafe.

That is why the lottery is charming because it gives everyone a chance - regardless of education, intelligence, bank account, place of work. Some even manage to hit the jackpot by buying a ticket for the only time in their lives. However, more often than not, winning becomes a reward for months and years of patience - regular participation in circulation.

Skeptics believe that the lottery is profitable only for those who arrange it. But optimists are sure that Gosloto, Sportloto and other popular draws are the real way to wealth.

What does science say? Mathematics allows for the probability of winning any lottery ticket at any given time. Another thing is how high this probability is. Another point: in the lottery, the random factor plays a decisive role. If, say, strategy is important in many card games or sports betting, then here the ways of playing and the intellectual preparation of the participant have little effect on the results.

The opinions of mathematicians are similar: your chances are small ...

Another important concept from game theory is distance. It is the distance that is the main obstacle on the way of ordinary participants in the circulation to the main win. In practice, this means that the expectation of a win does not have a certain duration. Unsuccessful runs in no way increase the chances of winning.

In other words, even if you play the lottery for six months, a year, 15 years, the probability of winning from this will not increase, but will always be approximately equal.

All lotteries are divided into two types - instant and circulation.

Instant lotteries

In the first case, you will find out the result immediately, as they say, without leaving the cash register. The standard drawing method is extremely simple: the player just needs to remove the scratch layer or unfold the hidden part of the ticket.

The beauty of this method is that you do not have to wait until the weekend for the draw, and you get most of the prizes right on the spot. True, if you hit the jackpot, you will have to get in touch with the organizers of the event and receive your winnings at the company's office.

Instant lotteries have the right to arrange any supermarkets and commercial organizations. As a rule, the winnings here are modest, but their probability (if the draw is carried out fairly) is not difficult to calculate.

Circulation

This is a more common type of lottery with a solid prize pool.

Such lotteries are also divided into two types:

1. The participant himself chooses numbers from a certain range - for example, 5 out of 36.
2. Player cards initially have numbers.

The first type is more popular because it leaves the participant complete “creative freedom”. The ability to cross out numbers on its own gives rise to entire strategic systems and mathematical theories.

There are hundreds of "winning" strategies, but the truth is that this does not affect the total number of winners. No matter how difficult the mathematical method of guessing is, even if it increases your chances of winning by hundredths of a percent, the probability indicator still remains in an unattainable range.

One day I asked my university math teacher: How do you visualize the probability of winning the lottery?

He answered like this:

“Imagine a huge railroad container with small copper coins. One of these coins is gold. You have one or more attempts to pull out of the container, without looking, exactly the gold one. Do you think you have a good chance?" Maybe that's why people with mathematical education rarely play the lottery?

However, the above example does not negate the fact that regularly one of our compatriots or inhabitants of the planet becomes a millionaire by taking a jackpot or a big win.

If you are interested in specific probability indicators, then this table is at your service:

Number	Lottery	Probability of winning a super prize or jackpot
1	Mega Millions (USA)	1 to 175 711 536
2	Power Ball (USA)	1 to 175 223 510
3	EuroMillions (Europe)	1 to 116 531 800
4	Eurojackpot (Europe)	1 to 59 325 280
5	SuperEnalotto (Italy)	1 to 139 838 160
6	Gosloto 6 out of 45 (Russia)	1 to 8 145 060
7	Gosloto 5 of 36 (Russia)	1 to 376 992

These are current indicators: the probability varies depending on the number of participants and tickets purchased. And don't be confused by the presence of foreign companies on the list - many Russians regularly buy tickets from foreign companies and win.

How to win the lottery - TOP 5 working ways

So, there are about as many methods of play as there are players. Thousands of participants are sure that they are following the only true winning strategy, it's just that "their time has not yet come." And this, from a mathematical point of view, is an absolute truth: all strategies have approximately equal chances of winning.

However, there are several methods that make these chances more real. And if at least a few players can use these tips to improve their well-being, then the selection was not in vain.

The methods described below do not guarantee a win, but they can bring you closer to it.

I’ll warn you right away: people who are gambling and not capable of self-control should not engage in lotteries, sports betting, online games, etc. at all. The desire to recoup will override a reasonable approach. And no strategies will help to return the money spent.

Method 1. Lottery Syndicate

This method is especially popular with foreign lottery players. A group of people buys the tickets, and then distributes the winnings according to the shares contributed.

Without a special mathematical education, it is clear that the more tickets you buy, the higher the chances of winning. Syndicates use this elementary principle for their own purposes. The easiest way to organize a syndicate is to suggest it to your friends.

Conditional example

Lottery ticket costs 100 rubles. Do you want to close immediately 200 digital combinations. For this you will need 20 000 rubles. Until you are ready to risk that kind of money alone. You organize a syndicate from 10 people and each invests in the circulation of 2 000 rubles. Monetary losses in case of failure are reduced, and the probability of winning is vice versa.

There are well-known and long-term lottery syndicates not only abroad, but also in Russia. Not so long ago, such an association won about half a million in Russian Lotto. And one syndicate of bus drivers from the UK "raised" about 38 000 000 pounds ( 1.7 billion rubles).

practical advice

Never play in a syndicate by borrowing money from other members, and do not lend yourself to play either. It is noticed that such actions lead to negative results or conflicts in case of winning.

An example of a foreign lottery syndicate in which people won $420 million per group

Method 2. High-Circulation Approach

Another simple method to increase your chances with minimal effort. Choose the most optimal combination of numbers in your opinion and bet several draws ahead at once. Many lottery organizers have this option. No need to "warm your head" and invent strategies - bet on your favorite numbers until the combination plays out.

There are cases when people put such combinations for years, and what is most remarkable, in the end they won.

Method 3. Playing with a deployed bet

This option drastically increases the number of combinations. The strategy is suitable for games in which the player chooses the winning numbers on his own. For example, in “5 out of 36” you choose not 5, but 6 numbers or 7. And although such a ticket will cost you more, all combinations of the numbers you proposed will play, and the winning amount will increase significantly if you win.

Method 4. Participation in distribution draws

First, let's define the term.

Distribution runs– drawings of large super prizes accumulated over past games are divided between the winners of the current draw.

The regularity of such an event is regulated by the rules of the company, but at least once a year the organizer is obliged to distribute financial surpluses.

The big jackpot really increases the size of the played bet. Particularly large winnings are most often found in distribution draws. Sometimes the accumulated amount reaches fantastic proportions, while the cost of the ticket does not change. Simply put, you get more for the same money.

Method 5. Psychological analysis

In any game, questions of psychology are important. Loto is no exception. Let's call this technique "Down with stereotypes!" It is based on the simple truth that most participants, when choosing numbers, stop at the first 60-70% of options.

For example, in "7 out of 49" people use numbers from 1 to 31 more often. This is logical - everyone likes memorable dates - wedding days, date and month of birth, etc. Picking numbers after 31 won't increase your chances, but if those numbers work, the amount you win will be much higher, since such combinations are used by a limited percentage of participants.

Conspiracies and prayers winning a large amount of money in the lottery

It is impossible not to mention the alternative ways and the "mystical" aspect of the game. Many players firmly believe in conspiracies, rituals, happy days, amulets, rabbit feet and other rituals.

Below I have listed the most famous:

Prayer for winning

Match numbers, numbers and bring me good luck,

Although I did not win yesterday, today everything will be different,

I'll take at least a million

I play a simple game...

Numerous films, books and TV shows form a kind of cult around lotteries and gambling. Incredible luck has become a kind of cultural phenomenon that the organizers of all kinds of games exploit.

Indeed, there have been cases of almost impossible happy coincidences in the history of lotteries.

This is still happening: for the first time in his life, a person buys a ticket for change, which he was given at the post office, and becomes a millionaire.

Conspiracy to win a large amount of money in the lottery

Coins jingle, banknotes rustle,

And the toad sat on the gold,

I'm dropping money

I'm sure of it

There will be no limit to wealth!

To believe or not to believe in rituals, prayers, conspiracies and cases is a personal matter for everyone. Let me just say that healthy optimism has never bothered anyone. Believing in your own luck works as a plus: at least such people calmly perceive failures.

A positive attitude and self-confidence help more than a pessimistic mood.

Scientific fact: optimists win the lottery much more often. Although it is likely that the reason for this distribution is simple: pessimists are less likely to buy lottery tickets.

People who have won large sums in the lottery in Russia and in the world

Since there are jackpots in nature, it means that someone wins them periodically. There are many examples of big, big, incredibly huge wins. Such examples are the best motivator for new participants in the draw, so the organizers of the games popularize such events in every possible way.

In the lottery you can win not only money, but also real estate

I won’t go far - just a few months ago, a resident of Novosibirsk won at Stoloto more than 300 million rubles . A person purchased a ticket through the site by paying 100 rubles. A resident of Voronezh won 506 million rubles in the same lottery. See how it happened in the video below:

And a resident of Sochi in 2017 won 371 million in Gosloto "7 out of 49". So far, this is the biggest win in Gosloto.

Sums from 100 to 200 million rubles citizens of the Russian Federation win every year.

Among the winners are people from various social groups - security guards, doctors, pensioners, entrepreneurs. The geography is also extensive: both megacities and settlements with an unknown name are represented.

As for foreign "lucky ones", their amounts are even more solid:

• 185 million euros went to the 2012 EuroMillions winner from Scotland;
• in 2007 in the US, a trucker and a New Jersey couple shared the top prize of $390 million in Mega Millions;
• in 2011 "big score" 185 euro in EuroMillions went to another married couple;
• on the ticket of the same lottery 168 million euros"raised" in 2016 by a cleaner from Belgium;
• in 2017 in PowerBall played the jackpot in 758 million dollars - a lucky ticket was purchased by a resident of Massachusetts.

Among the winners, those who have previously purchased tickets for many years in a row predominate. But there are those who bought the winning ticket quite by accident.

The lucky ones won $32 million in the lottery in 2016. Would you like to be in their place?

Technologies of winning in popular lotteries

Let's analyze the three most popular lotteries in the Russian Federation.

If you do not yet know the rules and nuances of Gosloto and other popular games, do not skip this section.

Russian loto

Perhaps every resident of Russia knows the host of this game by sight. The rules of the game are as simple as a day: you choose tickets with already indicated combinations of numbers from 1 to 90. Drawings are held on weekends.

How to improve your chances:

1. If you do not purchase several tickets, take those in which the numbers do not repeat.
2. On the site you have the right to choose tickets with your favorite numbers.
3. Do not miss the drawings of "Kubyshka" - draws with an accumulation fund.

In addition to cash prizes, apartments are raffled off here.

Gosloto 4 out of 20

It was in this game that the Novosibirsk recently won 300,000,000 rubles .

The point is clear from the title: player chooses 4 numbers from 20 possible. And if you guess the numbers in 2 fields at once, you will become a multimillionaire.

If you want to increase the probability of winning, make a detailed bet, that is, mark not 4 numbers, but 5 or more.

Gosloto 5 of 36

Similar to the previous lottery, only there are even more numbers, and therefore combinations. There are two super prizes at once. Statistics show that thanks to the game, a new millionaire appears in Russia every week.

The chances, as well as the amount of possible winnings, are increased by the deployed bet. In addition, you have the right to choose how many draws your ticket will take part in. The maximum number of draws is 20. The "multibet" option will allow you to fill in many tickets at once with automatic selection of numbers.

Where to play the lottery online

All of these lotteries, as well as most of the others, have online resources. It is much more convenient and faster to bet on the Internet: this way you save time, and in some cases you have a wider selection of combinations.

Making a bet online is as easy as shelling pears: go to the website of Gosloto or another lottery organizer and follow simple and understandable instructions.

As a rule, the first bet algorithm consists of 4 stages:

1. Registration on the website.
2. Selecting a lottery option.
3. Filling out a ticket.
4. Waiting for the draw and checking the winnings.

There are also mobile versions that make the process even easier and faster.

For example, you can play popular world lotteries online through this international lottery operator.

If you prefer Russian "producers", then welcome to the Gosloto website.

Frequently asked Questions

And now the answers to the most pressing questions of users.

Find a balance between passion, self-control and common sense

Question 1. Who is strictly contraindicated in playing the lottery? Svetlana, 26 years old, Murmansk

Partially, I have already answered this question above: to everyone who is not able to control emotions and financial spending. There are many such people, and gambling addiction is officially recognized as a disease. If you can't handle your emotions while gambling, it's best not to participate in lotteries.

Question 2. How to win a million in the lottery? Ilya, 22 years old, Penza

The easiest way is to use all our tips and play regularly.

Question 3. Is it true that beginners are lucky and if I play for the first time, then the chance of success is higher than that of the "experienced" ones? Dmitry, 24 years old, Naberezhnye Chelny

This is only partly true. In the event that a beginner uses a strategy that is free from the prejudices of inveterate players, his chances increase. But if he follows the beaten path and makes the same mistakes as ordinary players, the probability of winning will be average.

Question 4. How to win a large amount in the lottery on the first try? Marat, 22 years old, Makhachkala

The only possible option is to make a big bet with many combinations. But this advice is only suitable for those who have a large gaming bank (initial capital).

Question 5. Is there a win-win strategy for a 100% return on investment in lottery tickets? Zoya, 31 years old, Omsk

Unfortunately no. If such a strategy existed, the organizers of the draws would go bankrupt and take up other business projects.

Question 6. Are there free lotteries with real money winnings? Peter, 42 years old, Krasnodar

The trouble is that many of these projects are pure scams. How do they make money, you ask, if the tickets are free? Human psychology works for scammers, in which scammers are well versed.

Simple example

You are announced that you have won, but for this you need to enter and send the card details. Needless to say, you will no longer see any winnings or money on the card.

Question 7. How to win the Euromillions lottery, I heard that it is very popular? Vadim, 33 years old, Magnitogorsk

Everything is simple here. Everyone has the right to play the Eurolottery: go to the official resource, register and play. In the Russian Federation, it is not forbidden by law to play foreign online games, and even more so to win in them. The site has a Russian version, so there will be no problems with understanding the rules and conditions.

Instead of a conclusion

Friends, as you can see, everyone can win the lottery. Yes, chances are low. Below I have provided a brief summary of the article, facts that will help you better understand the lottery topic and succeed.

Who doesn't risk...

This must be remembered:

1. The mathematical probability of winning does not depend on the duration of the lottery game.
2. There are methods to increase both the probability and the size of the winnings.
3. In well-known foreign lotteries, jackpots are larger.
4. It is more convenient to buy and fill tickets online.
5. In the Russian Federation, winnings are subject to income tax in 13%, and when winning prizes in quizzes and promotions of companies are taxed at the rate 35%

And more about chances and probabilities: American Joan Ginter 4 times won over a million and enriched in total by $20 million . Forbes journalists calculated that the mathematical chances of winning big four times are 1 to 18 septillion (septillion - 10 to the 24th power). In other words, the chances are practically non-existent. And yet it happened!