How to win the lottery based on mathematical expectation. Start in science

How to win at Gosloto: 5 ways to buy a ticket + 3 options for checking results + 3 ways to get money + 5 reasons why you still haven't been able to win anything.

Winning the lottery is a great chance to get money, so to speak - "on the ball."

A big one is a chance to dramatically change your life for the better.

Of course, you will have to invest some amount in lottery tickets.

Of course, there is no guarantee that luck will smile on you.

But why not try?

For demand, as they say, do not hit in the nose. In addition, after analyzing the stories of the lucky ones, understanding the conditions of the game, it will be easier for you to understand how to win in Gosloto and thus increase your chances of winning.

Fortune usually smiles on those who are willing to take risks.

What is Gosloto and how to win it?

State lotteries can be treated differently.

Those who are unlucky call them names in every possible way, and the most harmless of these names is a scam.

But the lucky ones who managed to win thank the Universe for this chance to change their lives.

Which camp will you join?

1. Lottery called Gosloto.

Behind the simple abbreviation Gosloto lies an equally simple decoding - the All-Russian State Lottery.

This is one of the largest all-Russian lotteries, which positions itself as a state lottery.

Actually, it is precisely the fact that it is state-owned, and attracts the majority of those who want to try their luck.

National popularity came to this lottery at the end of 2013, when the President, by his decree, banned the distribution of any lottery tickets, except for state ones.

Since the initiator of the creation of Gosloto is the Ministry of Sports, this decree not only did not threaten her, but would also allow her to become even more popular among the people.

Today, you can use four types of Gosloto lottery tickets to win good money:

You can follow the draws on the website stoloto.ru.

2. Where can I buy a ticket to win at Gosloto?

There are plenty of ways to buy a Gosloto lottery ticket - both traditionalists and fans of new technologies will find the right one for themselves.

5 ways to buy a Gosloto ticket to win money:

3. Terms of winning in Gosloto.

The lottery ticket of each type of Gosloto looks quite standard, the differences are small. But the rules of the game are slightly different.

Well, for example, this is how the lottery ticket “6 out of 45” looks like:

What to do to win at Gosloto:

Mark the required number of digits.

How many numbers you need to mark depends on the name of the lottery.

For example, "6 out of 46" - we mark 6 numbers if we make the minimum bet, etc. If you play at higher stakes, then you can mark more numbers.

Enter your mobile phone number so that the organizers can contact you if you win.


The presence of a mobile phone indicates that you may not be able to follow the draw itself if you are unable to do so.

But it's still better to insure and see how your fate will be decided.

Give the completed part of the ticket to the seller.

If you bought a lottery ticket online, for example, on the website stoloto.ru, then do not forget to indicate your phone number and carefully read the rules posted on the site.

The same lottery ticket can participate in several draws at once. To do this, you need to indicate at the bottom of the form how many draws you want to participate in.

Naturally, the more chances you are given, the higher the cash rate.

4. How do you know if you managed to win at Gosloto or not?

Of course, the easiest way to find out if you managed to win or not is to follow the draw on the stoloto.ru website or on TV.

If for some reason you could not watch the broadcast of the draw, then you can make sure that you won at Gosloto in the following ways:

5. How to get money if you managed to win at Gosloto?

If you have become one of those lucky ones who managed to win, then you can only be happy for you.

Take your money, but spend it wisely so you don't regret doing stupid things later.

Rules for receiving money that you managed to win at Gosloto:

If luck smiled at you not for the whole mouth and the prize amount is small (up to 2,000 rubles), you can get it where you bought the ticket.

Another official point of sale for these purposes is also suitable.

If you are more fortunate and the amount of winnings is from 2,000 to 100,000 rubles, then you can receive it by transferring it to your personal account.

Send all your details to the address Volgogradsky prospect, 43, building 3, JSC "TD" Stoloto "in Moscow and after a while you will receive your money.

1. If you are super lucky that you managed to win more than 1 million rubles, then you will have to come personally to the central Moscow office at the address indicated above to settle all the formalities.

Do not forget that Gosloto winnings are taxed. You will have to pay 13% of the amount to the state if you are a citizen of the Russian Federation, 30% - to foreigners.

All about how to win at Gosloto

I do not think that it will be a big surprise for you to learn that only lucky people can win in Gosloto. Those from whom luck flies away at great speed should look for other ways to improve their financial situation.

But still, there are ways to increase your chances of winning, if not by much, but still.

a) What are the chances of winning in Gosloto?

To begin with, let's turn to statistics to understand what are the general chances of winning at Gosloto. Let's omit the least promising option "4 out of 20" and turn to three others.

Statistics say that the chances of winning look like this:

Focusing on the size of the circulation, you can calculate which type of lottery will bring you the maximum winnings for the least spending.

We see that Gosloto "5 out of 36" gives us the most likely chances to win. In addition, you will have to spend the least money on its acquisition.

b) How to increase your chances of winning in Gosloto?

If you conduct a survey among people who buy lottery tickets in the hope of winning, you will find out the different ways they use to try to catch their luck by the tail.

Someone marks the numbers in a chaotic manner on the form, someone uses important dates and lucky numbers in their lives, someone is helped by the scheme he developed.

There are several strategies for choosing numbers in order to win at Gosloto:

Trust fate.

When choosing numbers, do not think at all, but mark the first numbers that appear in your head.

A couple of winners who managed to enrich themselves by several tens of millions of rubles acted just like that.

Repeat the same combination.

While preparing this material, I read on the Internet the story of one of the winners of Gosloto, Vitaly, who won almost 2 million rubles in 5 out of 36.

He encoded the name of his eldest daughter (Nastya) in numbers, acting according to the principle A - 1, B - 2, C - 3, etc. And every time I bought a ticket, I marked the same numbers.

After a while, his strategy worked.

Consider the time period.

Your task is to analyze the winning combinations over the past few months and mark in your ticket those numbers that have not fallen out for a long time.

Consider frequency.

The principle of analysis is the same - winning combinations for six months - a year. In your ticket, mark the numbers that fell out the least.

We focus on both the temporal principle and the frequency at the same time.

Experienced players claim that this helps to double the odds.

You can use one of the ready-made strategies, or you can develop your own.

There is no magic recipe on how to become a millionaire thanks to Gosloto. Here, as in war, all means are good.

Why can't you win at Gosloto?

Can everyone win at Gosloto?

Of course, not all!

You can see for yourself that the statistics are ruthless and a relatively small number of people managed to win large sums during the entire existence of the lottery.

The 5 most common reasons why you can’t get rich at the expense of Gosloto:

You are an unlucky person.

You yourself know perfectly well that you are not among the favorites of fortune. Everything that you have in life, you have earned by hard work and in spite of circumstances, and not because of them.

It is better for such people not to spend money on lottery tickets, but what can really make a profit.

You are not trying hard.

Buy a couple of lottery tickets from the last two years and still complain that you can't win? Come on, you can't be so impudent!

Make it a rule to buy one Gosloto ticket once a week. This will greatly increase your chances of winning.

You are using too banal strategies.

All sorts of strategies, for example, taking into account time or frequency, are known not only to you. They are also known to the organizers of Gosloto.

Of course, they are interested in no one winning the super prize, and therefore they minimize your chances.

How to deceive these greedy? Act against them, turning your strategy on its head.

You gave up early.

Let's say you bought Gosloto tickets for a whole year, hoped and believed, and then despaired and did not want to play anymore.

Should we have waited a little longer? What if fate has already prepared a gift for you in the form of several million?

In general: do not hang your nose and do not give up under any circumstances.

You do not believe that you will succeed.

For any task you need to take on with sincere confidence that you will succeed. In situations where fortune comes into play, skepticism and uncertainty are generally inappropriate.

Only a sincere message from the Universe: “Today I will be able to win at Gosloto!” bring good luck to your side.

Gosloto winners share their joy in this video!

Have you bought your lucky ticket yet?

There is no clear answer to the question How to win at Gosloto?". None of the lucky ones knows exactly why luck smiled at him.

Try, believe, don't give up and sooner or later you will rejoice at your winnings.

You need to play the lottery wisely. Before buying tickets, you should study the conditions, including what are the chances of winning. Obviously, it is easiest to win in the games with the highest probability of winning the lottery.

They usually use fewer balls. But the prizes rarely reach the values ​​that are typical for multiple lotteries. To understand what is the probability of winning the lottery, look at the signs below.

Probability of winning 5 out of 36

In order to get the jackpot, playing the lottery according to the 5 out of 36 gaming system, you need to guess one combination out of 376,992. This is the probability of winning the Gosloto 5 out of 36 lottery or the like.

Probability of winning 6 out of 45

1 of 8 145 060

In order to win the jackpot, you need to guess one combination out of 8 million. Despite such a low probability of winning the lottery 6 out of 45, there are lucky ones who guess it.

Probability of winning the lottery 7 out of 49

1 out of 85 900 584

The chances of winning the 7 out of 49 lottery are 1 in 85.9 million - winning the jackpot is usually low, but here they are completely outrageous. Other than luck, there is hardly anything that will help to achieve real success ...

Probability of winning in KENO

As you can see from the table, the probability of winning the jackpot in KENO is 1 in 8.9 million. In this lottery, the winnings are fixed, to increase the size of the prize, you can apply multipliers or buy several identically filled tickets.

The probability of winning the jackpot in the Rapido lottery is 1:503,880. In it, you need to guess 8 numbers out of 20, and also choose one additional number out of four correctly.

The probability of winning in Russian Lotto, Golden Key, State Housing Lottery (GZhL)

These lotteries are very similar and differ only in the form of the draw. In the first round, the jackpot wins a ticket in which one horizontal line is crossed out in 5 moves. If the jackpot is not drawn, the first round continues until the appearance of such a player. In the second round, you need to cross out 15 numbers in one of the two cards before the others, and in the third - all the numbers in both cards. The sooner the entire field is closed, the larger the prize will be.

The probability of winning the main prize (jackpot) in Russian Lotto, GZhL, Golden Key is approximately equal and is 1: 7 324 878.

Probability of winning in Gosloto TOP-3

The probability of winning in the first round depends on the number of the purchased ticket and is equal to: 1 in 1,000,000,000.
The probability of winning in the second round depends on the chosen numbers and the chosen way of playing:

Hello!

My name is Ivan Melnikov! I am a graduate of the NTU "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 fond of lotteries. I've always been interested in what laws fall out certain balls. Since the age of 10, 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 luck games like "5 out of 36" and "6 out of 45". Calculate the chance of winning the lottery trite according to probability theory.

An example of calculating the possibility of obtaining 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 chosen 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 the 6 to 45 lottery.

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 bit about probability theory

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

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

With the balls coming out of the lottery machines, the story is approximately the same, but somewhat more complicated and with a more significant number of variables. If one ball fell out 3 times, and the other - 10, then the probability of the first ball falling out will be higher than that of the second. It is worth noting that this law is diligently violated by the organizers of some lotteries, who change the lottery drums from time to time. In each new lottery drum, a new sequence appears.

Some other organizers use a separate lottery drum for each ball. Thus, it is necessary to calculate the probability of falling out of each ball 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 turned out, does not really work. Let's see what are the secrets based on dry science and statistics accumulated over decades.

1. Why doesn't probability theory work?

   • Non-ideal conditions

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

The second caveat is that the diameters of the lottery balls are also not the same. Even the slightest difference of millimeters plays a role in the frequency of falling out of one or another ball.

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, moreover, significantly.

• Sum of winning numbers

If we look at the statistics of the numbers that won the lottery like “6 out of 45”, then we can notice an interesting fact: the sum of the numbers on which the players bet fluctuates between 126 and 167.

The sum of 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 do you think are the most common numbers in winning tickets? Even? Odd? I will tell you with full confidence that in the lotteries "6 out of 45" these numbers are equally divided.

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

• Popular number groups

For a lottery like "6 to 45", we conditionally divide the numbers into 2 groups - from 1 to 22 and from 23 to 45. It should be noted that in the winning tickets the ratio of numbers belonging to the group is 2 to 4. That is, either the ticket will have 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 by analyzing lottery statistics like "5 out of 36". Only in this case, the groups are split up a little differently. Let's designate the first group, which includes numbers from 1 to 17, and the second - the one where the remaining numbers from 18 to 35 are placed. 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.

• Should I bet on numbers from past draws?

It has been proven that in 86% of cases, the number that was already in previous draws is repeated in the new draw. Therefore, it is simply necessary to follow the draws of the lottery you are interested in.

• consecutive numbers. To choose or not to choose?

The chance of getting 3 consecutive numbers 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. So choose different numbers.

• Numbers with a single step: win or lose?

You should not bet on numbers that go in the same sequence. For example, it is definitely not necessary to choose step 2 and make a bet with this step. 10, 13, 16, 19, 22 is definitely a losing hand.

• More than one ticket: yes or no?

It is better to play once every 10 weeks for 10 tickets than once a week for one. Also play in groups. You can win a big cash prize and share it among 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 must choose 5 numbers out of 56, as well as 1 out of 46 for the so-called golden ball.

For 5 guessed balls and 1 correctly named golden lucky one gets the jackpot.

Other dependencies are shown in the table:

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

Statistics of dropped golden balls for the entire duration of the Mega Millions draws.

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

• Powerball Lottery, where more than a dozen lucky ones have managed to hit the jackpot. It is necessary to choose 7 main game numbers and two Powerballs.

1. Winner 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 name himself. In general, hitting jackpots is a good habit of Russian people

• 390 million US dollars in one hand

In the Mega Millions lottery, which we have already talked about, a lucky winner, who wished to remain anonymous, won 390 million US dollars. And this is far from rare. In the same lottery in 2011, two people managed to hit the jackpot at once, 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 retiree 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 on a trip.

1. conclusions

So, here is a summary of the most effective rules, following which you will definitely win:

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

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

n is the maximum bet number, for example, 36 in a 5 out of 36 lottery

z is the number of balls you are betting on, e.g. 5 for the 5 out of 36 lottery

That is, for "5 out of 36" the sum will be:

((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 hit numbers in the winning ticket is 1 to 2 or 2 to 1.
3. Follow the statistics and bet on those numbers that fell out in previous draws.
4. Don't bet on numbers with one step.
5. It is better to play less often, but buy several tickets at once, and also get together with friends and relatives.

In general, bolder! Follow my rules, bet, analyze statistics and win!

Have you ever dreamed of suddenly getting a million dollars? Do you run to the nearest postal kiosk to purchase a lottery ticket when the jackpot hits a certain mark? If yes, then you are not alone. In 2014 alone, the desire of Americans to suddenly become millionaires was so strong that they collectively spent about $70 billion on lottery tickets. However, as much fun as it is to participate in the lottery, you should be aware of your chances. After all, the probability of being struck by lightning is twenty times higher than the probability of winning the jackpot in the lottery, and no amount of calculation will help you.

Does victory depend on luck or mathematics?

The lottery is a game of chance. The probability of your winning is determined by a certain set of factors, including the number of winning numbers or combinations that you must get in order to win, as well as the number of people participating in the lottery at the same time as you. The more people who buy lottery tickets, the less likely you are to walk away with a prize. If we consider the most popular lotteries, then the probability of winning them is 175 million to one. As you can see, victory depends on both mathematics and luck, but at the same time, mathematics indicates that you most likely will not see luck.

Why is it important to know the odds of winning?

Many people spend large sums on lottery tickets without realizing their chances. Moreover, in some low-income communities, buying a lottery ticket is seen as an investment, a form of entertainment, and a possible ticket to a better life. There is a complex pattern of socio-economic factors that contribute to the lottery being perceived as an investment. If you are denying yourself something to buy a lottery ticket or saving money to buy it, chances are that you will be very disappointed.

How can you increase your chances of winning?

Here are a few methods that will help you improve your chances of winning if you do decide to play the lottery:

• Play the right games. When it comes to national lotteries with huge jackpots, your chances of winning will be minimal. If you participate in the district or even in the city lottery, then you can increase your chances of winning. Scratch tickets for small lotteries usually have small prizes, but your chances of winning will be quite high.
• Participate in second chance games. If your numbers were not chosen initially, you will have a second chance. Save your ticket until the next draw to increase your chances of winning.
• While playing the lottery doesn't require the same skills as playing poker, for example, you still need to have some strategy in choosing your numbers. Seven-time lottery winner Richard Lustig recommends using the same numbers over and over instead of changing them. He also recommends not choosing numbers randomly, and also not using birthdays or other dates, as they greatly reduce the choice of numbers.
• You cannot win if you don't play. Richard Lustig also recommends that you keep playing the lottery you've taken on. Pay attention to what numbers fall out each time, and play over and over again, increasing your chances of winning. Every year, a huge number of people do not receive their prizes because they stop following the developments.

Don't fall into the trap!

As with any other form of gambling, you can develop an addiction to the lottery. Participants may mistakenly think that because the lottery is government sanctioned, it is not as harmful as other forms of gambling. However, in reality, the risks remain exactly the same. If you have a history of gambling addiction, then you may develop unhealthy habits if you start playing the lottery. The hope of a big win, occasional small wins, and the idea that your big win is around the corner are the main drivers of any lottery. The most important thing you need to know about lotteries is that you need to set a specific budget that you are willing to spend before you start playing and always stick to it. The lottery can be fun and safe, but if you start using finances that you would otherwise spend on food or bills to get yourself a better chance of winning, you need to think again, as you have strayed into dangerous territory.

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Introduction

At the lessons of mathematics, we got acquainted with the initial concepts of probability theory. I was interested in the practical application of this branch of mathematics. I noticed that on television lately they are talking more and more about drawing large sums of money, and I decided to find out how popular participation in lotteries is in various age groups. To do this, I conducted a survey of students from my school, school employees, relatives and friends of my family. The survey data are presented in the table and on the histogram (Appendix 1 and Appendix 2). Convinced of the popularity of lotteries, I prepared a research paper “The Probability of Winning the Lottery”.

Hypothesis: The results of the survey show that the majority of people believe that there is a significant amount of winnings in the number lottery.

object my research are various lotteries, the history of their occurrence, the mathematical justification of the stated hypothesis.

Subject of study: probability of winning in number lotteries

Primary goal- to carry out a probabilistic analysis of numerical lotteries, using the formulas of the theory of probability, which will help determine whether this or that lottery is fair, and whether it is profitable for us to play it.

Tasks- study the mathematical formulas of probability theory, use them to calculate the probability of winning in numerical lotteries, consider the economic feasibility and psychological aspects of participating in lotteries.

To complete the tasks I used the following research methods like comparison, survey, mathematical justification.

My research work is devoted to the study of the probability of winning in lotteries. The theoretical part of the work includes consideration of the issue of the origin of the lottery, the rules for conducting and drawing in America, Europe, England, the USSR and Russia. The main attention is paid to the study of the probability of an event, as well as the mathematical laws associated with this concept. The theoretical part includes definitions and formulas of elements of combinatorics, such as permutations, combinations, factorial, as well as examples of using combinations in problems of calculating probability.

The practical part includes calculating the probability of winning in the lotteries "7 out of 49", "5 out of 36" and "6 out of 49", "6 out of 45", as well as a comparative analysis of the probabilities of winning in lotteries. In addition, one of the tasks is to calculate the number of all combinations, as well as their cost, taking into account the data of one of the lottery sites. Conclusion about the economic feasibility of buying the entire circulation of tickets.

In conclusion, the psychological aspect of the lottery and dependence on it is described.

Theoretical part

1. History of lotteries

All lotteries are similar to each other. By paying a small amount for a ticket, you are in the queue of potential millionaires. The biggest prizes are offered by the lottery, in which the player must independently choose the winning combination of numbers, thereby predicting the outcome of the drawing. A complete match of the result gives the so-called "Jackpot", the maximum win, which amounts to tens of millions. Lotteries with a fixed combination of numbers can bring the winner a little less. In instant lotteries, the cheapest and least profitable. But the meaning of the game, with all the differences, in each lottery remains the same: without making an effort, once and for all change your destiny, catching the elusive smile of Fortune. On one of the Gosloto sites on the Internet, I read the following information:

“New Year's broadcast of 2017 of one of the federal TV channels brought good luck to 7,649,624 participants of the state lotteries - they all won various prizes in Gosloto. And 12 people even received prizes of several million! In total, 1,388,771,199 rubles were raffled off in this festive draw - “a truly historic event”, as Zoya Gafarova, director of marketing and sales of the Stoloto Trading House Joint-Stock Company, put it: “Grand Prix” of 54,462,613 rubles , received during the drawing of the Gosloto 6 out of 45 draw, its lucky owner took it to his place in the Nizhny Novgorod region. 8 residents of various regions of Russia received 6,842,262 rubles each, sharing the winnings of 54,738,096 rubles in Gosloto 5 out of 36, and three more lucky winners became owners of 4,184,276 rubles in the Gosloto 7 out of 49 draw. However, this note does not say what is the probability of a lottery participant winning.

A massive game with cash prizes was invented in the West. While our ancestors were just getting ready to conquer Siberia, the temperamental inhabitants of Central Europe were already praying to the Lord for a “lucky ticket”.

Today, Italy and France are arguing for the right to be called the birthplace of public lotteries. It is known that one of the first public drawings of cash prizes was held in Florence in 1530. The lottery bearing the proud name "La Lotto de Fiarenze" enjoyed a resounding success, uniting the scattered Italian cities and principalities in a common pursuit of winnings. Soon, lotteries, in addition to eating pizza and afternoons, became a popular Italian tradition. It is not surprising that one of the first steps of the king of reunited Italy was the holding in 1863 of the first all-Italian lottery.

In England, lotteries were implanted by the inexorable will of the monarchs. Appreciating the Italian lotteries, in 1566 Queen Elizabeth I announced a general drawing of cash prizes. The profits were enough to rebuild the sea harbors, so the main gain for Britain was the subsequently won unofficial title of "mistress of the seas." Subsequent English lotteries were also timed to coincide with important national economic projects. Thus, the 1627 lottery was designed to solve the problem of financing the construction of the London aqueduct. Profits from subsequent drawings went to the establishment of the British Museum, the arrangement of water supply and the construction of bridges. In 1826, the empire, growing rich at the expense of the colonies, decided to abandon lotteries, considering them an ungodly occupation.

But the lottery has taken root in America. As early as 1776, the Continental Congress proposed holding a lottery, the proceeds of which could be used to organize an uprising against the British authorities. George Washington himself became the head of one of the first American lotteries. Profits from the draw were used to build a road through the Cumberland Hills. Money from other lotteries was spent wisely, and in the fullest sense of the word: the proceeds from ticket sales allowed the US government to fund the establishment of universities such as Harvard, Yale and Columbia.

The founding father of the first French lottery was King Francis I. Desperate to deal with the cash shortages common to monarchs, he allowed private and public lotteries from 1520 to 1539. The idea did not take root: unlike the eccentric Italians, prudent Gauls did not believe in chance, and therefore kept their savings in straw mattresses. Only the ardent Giacomo Casanova could break the ice of distrust of Fortune. Through cunning intrigue, he won the right to become the manager of the first state lottery, the purpose of which was to raise money for the famous "Ecole Militer", the Royal Military School.

As expected, the first lotteries appeared in Russia under Tsar Peter I. The Russians learned about the advent of a new era from posters pasted on the walls of Moscow houses in 1700.

According to historians, the first drawing took place under the vigilant attention of the royal people. Muscovites were satisfied with the results. The novelty took hold. As in the West, in Russia lotteries were held in the case of a “state order”, such as tax collection, or the construction of a hospital. For example, the main prizes of the 1745 lottery were the goods and things of one of the merchants described for arrears. Sometimes villages and estates were played. The largest lottery took place in 1764, and the Senate acted as its organizer. After it was held, Empress Catherine ordered "from now on not to accept such lotteries", calling the idea a "harmful invention." The reason for the monarch's wrath was given by the lottery, which took place four years earlier. Then, in 1760, the main prize was an astronomical sum of 25 thousand rubles, a lot of players went bankrupt, and the treasury received nothing.

It was economic expediency that forced the Communists to reintroduce the game. In 1921, the government held the first lottery, the proceeds of which went to help the famine.

After the Great Patriotic Lottery, the countries of the Soviets took on a completely commercial character. True, until 1970 in the USSR they were carried out only by the republican Ministries of Finance. Circulations were held rarely - once a quarter. Then came the famous "Sportloto" "6 out of 49", and "5 out of 36".

The fact that lotteries are a profitable business was only understood by Russians after perestroika. In 1994, the lottery movement was enshrined in the Civil Code. From now on, practically everyone in Russia was allowed to establish and conduct lotteries.

1. Random events and probability

The world around us is full of accidents. These are earthquakes, hurricanes, economic ups and downs, wars, illnesses, chance encounters, and so on. The theory of probability as a science began to take shape in the 17th century. Gambling served as a source of tasks for her. We call an event accidental if it cannot be said that this event will certainly occur under the given circumstances.

About a random event, we cannot say in advance whether it will happen or not. But we can talk about the chances of this event occurring. In probability theory, the chances that a random event will occur are expressed as a number. This number is called the probability of a random event. The main properties of probability are set out in Appendix 3.

1. Elements of combinatorics.

For our further practical work, we will need some more formulas and concepts from combinatorics.

Combinatorics is a branch of mathematics that studies discrete objects, sets (combinations, permutations, arrangements and enumerations of elements) and relations on them (for example, partial order).

The basic concepts are set out in Appendix 4.

Practical part

So, we got acquainted with the theoretical concepts, as well as with the formulas for calculating the probability of winning the lottery. In this chapter, we will try in practice to calculate the probability of winning in the following lotteries "7 out of 49", "5 out of 36", "6 out of 49" and "6 out of 45". We will conduct a comparative analysis, calculate the economic feasibility of buying all tickets to achieve a win. To do this, he will use the previously discussed probability calculation formulas, as well as data from the site http://www.stoloto.ru.

Let's turn to calculating the probability of winning the 6 out of 45 lottery.

What is the probability that exactly 6 winning numbers will be matched?

Number of combinations (tickets) = 8145060

What is the probability of guessing at least 1 winning number?

What is the probability of guessing 2 winning numbers?

Of course, the probability of guessing at least 2 winning numbers is almost a million times greater than guessing all 6 numbers, but the winning amount in this case is only 70 rubles. Therefore, we will not consider the probabilities of winning 2 numbers. Let's analyze the probabilities for the rest of the lotteries.

Similarly, we will calculate the probability of guessing all the winning numbers in the lotteries "5 out of 36", "7 out of 49", "6 out of 49". We will draw up the results in a table, in which we will also present the data on the ticket price, the maximum winnings at the moment (this parameter may vary depending on the date). As well as the cost of tickets that we would have to pay if we wanted to redeem all tickets (combinations)

After analyzing the value of the probability, we can say that this number is negligible. The highest probability of guessing in the lottery is “5 out of 36”, but this value also matters, the winnings in this lottery are also the smallest, usually it is several million rubles.

If we wanted to “tame luck” and buy all the tickets by teaming up with “millionaire friends”, then we would have to invest at least 30 million rubles in the purchase price, as can be seen from the 6th column of the table. The maximum gain is much less. In addition, it must be taken into account that the winner is obliged to pay 13% of the winnings tax. Accordingly, the maximum gain becomes even smaller.

In addition to the economic inexpediency of buying all the tickets, there may be a practical difficulty in sorting through all the combinations, in other words, it is difficult to have time to redeem at least a million tickets, with the right combinations. To begin with, one would have to write a program that would allow one to go through all the combinations and print an array with at least a million combinations, then this set of combinations would have to be divided among the participants, and each would redeem their own set of tickets. The time spent on buying tickets can be calculated as follows.

If 20 participants redeem tickets in the 5 out of 36 lottery, then the time taken to purchase tickets for each participant will be approximately 26 hours.

All these mathematical calculations serve as another proof that it is economically and practically inexpedient to buy out all combinations.

From this we can draw a sad conclusion: "Buying a bird - happiness will not succeed, you will have to earn a living by physical or mental labor."

Psychological aspects of participation in lotteries

Lucky people rarely gamble. According to the apt remark of Western psychologists, "a rich man buys insurance, and a poor man buys a lottery ticket." Scientists believe that unjustified belief in one's luck has purely biological roots. At the same time, only in chronic losers does it become the main life guide.

The hope of winning each player gives a sense of their own exclusivity, which every person has, regardless of their place in society, the thickness of the wallet and physical data.

And this, according to scientists, is precisely the root of gambling. Numerous studies have shown that a normal level of self-esteem is diagnosed in a person when he evaluates himself not much, but higher than those around him. Genetic experience and plots of popular films suggest that this requires very little, for example, to swallow, like Neo from The Matrix, the right pill. Give God a chance to mark you with his mercy. At least buy a lottery ticket.

The lottery, like any other game, gives an instant answer to the question of one's own viability. Luck communicates with the player directly, almost without intermediaries. And every time it gives a chance to start all over again. Over time, addiction to a regular test of fate can become a disease.

How many people on the planet will agree with the statement “happiness is not in money”, or at least with the fact that happiness is not only in them? Most likely, if you do not take into account the exotic tribes, who have an extremely vague idea of ​​\u200b\u200bthis achievement of civilization, most earthlings will answer that untold wealth may not make them absolutely happy, but it will definitely save them from unnecessary worries. And only a few sane people are aware that millions (billions, trillions - depending on the national currency) that suddenly fell on their heads can bring not happiness at all, but a complete collapse of life. But there are few of them.

A few years ago, the San Francisco Chronicle published an article about the mistakes big money prize winners make. As the journalists managed to find out, the first million dollars is usually spent on travel, and a significant part of the millionaires squander the rest of their fortune in the next five years.

When Juan Rodriguez, a Colombian New Yorker who worked in a parking lot store, won the lottery's top prize in November 2004, he was absolutely happy for the first time in his life. With only 78 cents in his account and $44,000 in debt, he won a $149 million jackpot. But ten days after winning, his family broke up. and he was left without a livelihood.

The victory of the American Jack Whittaker, by his own admission, the lucky one, brought him nothing but trouble. In 2002, Whittaker won a record prize of $315 million. In his winning interview, he said that he dreams of becoming a positive example for people and managing money in such a way that fellow citizens can later be proud of him. Then his character completely deteriorated and disagreements with the law began. He blamed money for his depression. Or rather, too many of them.

Unfortunately, the story of one of the big Russian wins ended no better. In May 2006, at the age of 52, Nadezhda Mukhametzyanova, who received the biggest prize in the history of Russia at that time, died from diseases caused by excessive alcohol consumption.

The lottery is a dangerous business. Of course, by collecting money through the game, the state can solve a couple of pressing problems. But in general, such experiments have a corrupting effect on the economy.

Undeserved wealth makes people dizzy, causing real inflation of the soul.

Conclusion

My hypothesis did not find mathematical confirmation. The probability of winning the lottery is negligible. The organizers of the lottery take the main profit, ruining a lot of people along the way.

Therefore, the advice to “lucky catchers”: “In order not to become an avid “gamer”, I advise you to read my work again!”

Literature and sources.

http://www.stoloto.ru/

http://svpressa.ru/post/article/118511/

Tyurin Yu. N. et al. Theory of Probability and Statistics. 2nd ed. revised MCNMO, 2008.

Shen A. Probability: examples and tasks. 4th ed., stereotypical. MCNMO, 2016.

Kolmogorov A. N., Zhurbenko I. G., Prokhorov A. V. Introduction to the theory of probability. 3rd ed., rev. MTsNMO, 2015 (Library "Kvant". Issue 135. Supplement to the journal "Kvant" No. 4 / 2015.)

Survey as part of the research work "Probability of winning in lotteries".

Bar chart.

Appendix 3

Main properties of probability

For each random event A, its probability P(A) is determined, and 0P1.

For a certain event U, the equality takes place

If events A and B are incompatible, then

P(AB) = P(A) + P(B).

For opposite events A and , we have the equality

P() = 1 - P(A).

For an impossible event, the equality P (= 0) holds. For incompatible events A and B, P (AB) = 0

For arbitrary events A and B

P(AB) = P(A) + P(B) - P(AB).

Appendix 4 Permutations, factorial

Factorial of a natural number n is the product of all natural numbers from 1 to n. The factorial is denoted n!

n!= 123…(n-1)n

permutation out of n objects, any way of numbering these objects is called (the way they are arranged in a row).

Permutations are denoted by the symbol Pn, where n is the number of elements in each permutation. (P is the first letter of the French word permutation - permutation).

The number of permutations of n items is n!

Combination

If there are n items, then the number of ways in which exactly k of them can be chosen is called the number of combinations from n to k and is denoted ("tse from en po ka"). It can be proved that

Thus, using the factorial, the number of combinations is expressed in terms of the numbers n and k.

We will use the formula to calculate the probabilities and the number of combinations in the further practical part.