What is the chance to win the Europa lottery. Distribution circulation is a sure way to get more for the same money. What to do to win at Gosloto

Hi all! Denis Kuderin, business expert of the Papa Help portal, is with you! I will tell you whether it is worth participating in the lottery from a mathematical point of view, and how the theory of the game relates to practice.

Probability to take big jackpot The lottery is available to everyone who purchases a ticket. Another thing is that the mathematical expectation of this probability can exceed all conceivable limits.

Are there ways to increase your 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!

There are 5 in this article real ways, increasing your chance of winning any lottery!

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

To win the lottery, you do not need to study at a university, be a rich heir or a person with superpowers. You just need to buy a ticket and believe in your luck. All lottery winners are not celestial beings at all, but ordinary citizens whom we meet on the way to work or see at the next table in a cafe.

The beauty of the lottery is that 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 circulations.

Skeptics believe that the lottery brings profit only to those who arrange it. But optimists are confident that Gosloto, Sportloto and other popular draws are a real path to wealth.

What does science say? Mathematics allows for the probability of winning any lottery ticket at any given time. How high this probability is is another matter. One more point: in the lottery, the factor of chance plays a decisive role. If, say, in many card games or in sports betting, strategy is important, here the methods of play and the intellectual preparation of the participant have little influence on the results.

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

Another important concept from game theory is distance. It is distance that is the main obstacle on the way of ordinary circulation participants to the main winnings. In practice, this means that the expectation of winning does not have a specific duration. Unsuccessful draws do not increase the chances of winning in the slightest.

In other words, even if you play the lottery for six months, a year, 15 years, the probability of winning 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 find out the result immediately, as they say, without leaving the cash register. Standard method The draw 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 don’t have to wait until the weekend for the draw, and you get most of the prizes right on the spot. However, if you win the jackpot, you will have to contact 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 fair) is not difficult to calculate.

circulation

This is a more common type of lottery with a substantial prize fund.

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 are initially numbered.

The first type is more popular because it leaves the participant complete “freedom of creativity.” The ability to cross out numbers independently 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 overall number of winners. No matter how complex the mathematical guessing technique is, even if it increases your chances of winning by hundredths of a percent, the probability indicator still remains in an unattainable range.

I once asked my university mathematics teacher: how to visualize the probability of winning the lottery?

He answered like this:

“Imagine a huge railway container with small copper coins. One of these coins is gold. You have one or more attempts to pull out the gold one from the container without looking. Do you think your chances are good?” Maybe that's why people with a mathematical background rarely play the lottery?

However, the above example does not in any way negate the fact that regularly one of our compatriots or inhabitants of the planet becomes a millionaire by winning 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 in 175 711 536
2	PowerBall (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 out of 36 (Russia)	1 in 376,992

These are current indicators: the probability changes 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 purchase tickets foreign companies and win.

How to win the lottery - TOP 5 working methods

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

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

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

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

Method 1. Lottery syndicate

This method is especially popular among foreign lottery operators. A group of people buys tickets together, and then distributes winnings according to contributed shares.

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

Conditional example

Lottery ticket costs 100 rubles. Do you want to block it 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 of 10 people and everyone invests in the circulation 2,000 rubles. Monetary losses in case of failure are reduced, and the probability of winning is the opposite.

There are well-known and long-term lottery syndicates not only abroad, but also in Russia. Not 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, borrowing money from other participants, and don’t lend money to the game yourself either. It has been 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 for the group

Method 2. Multi-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. There is no need to “warm your head” and come up with strategies - bet on your favorite numbers until the combination plays out.

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

Method 3. Playing with an expanded bet

This option radically increases the number of combinations. The strategy is suitable for games in which the player chooses the winning numbers independently. 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 propose will be played, and the winning amount in case of victory will increase significantly.

Method 4. Participation in distribution circulations

First, let's define the term.

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

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

A large jackpot actually increases the size of the winning bet. Particularly large winnings most often occur in distribution runs. Sometimes the accumulated amount reaches fantastic proportions, but the cost of the ticket does not change. Simply put, you get more for the same money.

Method 5. Psychological analysis

In any game, psychological issues are important. Lotto 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 “6 out of 49” people more often use numbers from 1 to 31. This is logical - everyone likes memorable dates– wedding days, date and month of birth, etc. Choosing numbers after 31 will not increase your chances, but if these numbers are played, the winning amount will be significantly higher, since such combinations are used by a limited percentage of participants.

Spells and prayers for winning a large sum of money in the lottery

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

Below I have listed the most famous ones:

Prayer for winning

Match numbers, numbers and bring me luck,

Even though I didn’t win yesterday, today everything will be different,

I'll take at least a million

I'm playing a simple game...

Numerous films, books and television shows form a kind of cult around lotteries and gambling. Incredible luck has become a kind of cultural phenomenon, which is exploited by the organizers of all kinds of games.

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

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

Conspiracy to win the lottery large sum money

Coins jingle, bills rustle,

And the toad sat on the gold,

I'll get some money,

I'm sure of this

There will be no limit to wealth!

To believe or not to believe in rituals, prayers, conspiracies and cases is everyone’s personal choice. Let me just say that healthy optimism has never hurt anyone. Belief in one's own luck is a plus: at least such people calmly accept 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 purchase lottery tickets.

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

Since jackpots exist in nature, it means that someone wins them periodically. There are many examples of large, largest, incredibly huge winnings. Such examples best motivator for new participants in the drawing, which is why game organizers do their best to popularize such events.

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 Stoloto more than 300 million rubles . A person purchased a ticket through the website by paying 100 rubles. A resident of Voronezh won 506 million rubles into the same lottery. Watch how it happened in the video below:

And a resident of Sochi won in 2017 371 million V Gosloto “6 out of 49”. This is the biggest win in Gosloto so far.

Amounts from 100 to 200 million rubles Russian citizens win every year.

The winners include people from all walks of life social groups– security guards, doctors, pensioners, entrepreneurs. The geography is also extensive: both megacities and settlements with an unknown name.

As for the foreign “lucky” ones, their sums are even more substantial:

• 185 million euros went to the 2012 EuroMillions winner from Scotland;
• in 2007 in the USA truck driver and married couple from New Jersey shared the main winnings of $390 million in Mega Millions;
• in 2011 " big jackpot» 185 euros in EuroMillions went to another married couple;
• on a ticket of the same lottery 168 million euros“raised” in 2016 by a cleaner from Belgium;
• in 2017, a jackpot was drawn in PowerBall 758 million dollars – the lucky ticket was purchased by a resident of Massachusetts.

The winners are dominated by those who have previously purchased tickets for many years in a row. But there are also those who bought the winning ticket completely by accident.

Lucky people won $32 million in the lottery in 2016. Would you like to be in their place?

Technologies for winning popular lotteries

Let's look at 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 lotto

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

How to increase your chances:

1. If you purchase more than one ticket, take those in which the numbers are not repeated.
2. On the website you have the right to choose your own tickets with your favorite numbers.
3. Don't miss the "Kubyshka" draws - draws with a savings fund.

In addition to cash prizes, apartments are up for grabs.

Gosloto 4 out of 20

It was this game that a Novosibirsk resident recently won 300,000,000 rubles .

The essence is clear from the title: the 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 up for grabs here. 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 an expanded bet. In addition, you have the right to choose for yourself how many draws your ticket will participate in. The maximum number of draws is 20. The “multi-bet” option will allow you to fill out many tickets at once with automatic selection of numbers.

Where to play the lottery online

All specified lotteries, as well as most 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.

Placing a bet online couldn’t be easier: go to the website of Gosloto or another lottery organizer and follow simple and clear instructions.

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

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

There are also mobile versions, which make the process even simpler and faster.

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

FAQ

And now answers to the most pressing questions from users.

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

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

I have already partially answered this question above: to everyone who is not able to control emotions and financial spending. There are many such people, and gaming addiction is officially recognized as a disease. If you cannot cope with emotions when gambling, it is better 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”? Dmitry, 24 years old, Naberezhnye Chelny

This is only partly true. If a beginner uses a strategy that is free from the prejudices of seasoned 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 sum in the lottery on the first try? Marat, 22 years old, Makhachkala

The only one possible variant– make a large bet with many combinations. But this advice is only suitable for those who have large game bank(initial capital).

Question 5: Is there a win-win strategy to get a 100% return on your investment in lottery tickets? Zoya, 31 years old, Omsk

Unfortunately no. If such a strategy existed, the organizers of the sweepstakes would go bankrupt and move on to other business projects.

Question 6. Are there any free lotteries where you can win real money? Peter, 42 years old, Krasnodar

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

Simple example

They announce to you that you have won, but to do this you need to enter and send your 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. Anyone has the right to play the Euro lottery: go to the official resource, register and play. In the Russian Federation, it is not prohibited by law to play foreign online games, much less win in them. The site has a Russian-language version, so there will be no problems understanding the rules and conditions.

Instead of a conclusion

Friends, as you can see, anyone can win the lottery. Yes, the chances of this 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 take risks...

This is what you need to remember:

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 size of winnings.
3. Well-known foreign lotteries have larger jackpots.
4. It is more convenient to buy and fill tickets online.
5. In the Russian Federation, winnings are taxed income tax V 13%, and when winning prizes in quizzes and company promotions, they are taxed at the rate 35%

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

One way to earn a large sum of money quickly is to win the lottery. Although this activity is associated with great risk, however, if you analyze the rules of the game and identify the main trends, you can develop winning strategies. Also, to win you need faith in success and a little luck. According to mathematical statistics, winning the lottery is possible. Any ticket purchased anywhere can win. In gaming, there is a term “distance”, which shows how quickly a person can receive a reward. The point is that you can try your luck in the game for as long as you like (from several days to several months). It is impossible to predict exactly when the jackpot will occur, since all tickets have the same probability of winning. That is, both a beginner and a pro can get money. In addition, many players believe in special conspiracies, spells, lucky numbers, with which you can get into a winning streak. Stories of people associated with their successful use are demonstrated in literary works, TV series and films. Of course, the importance of faith in special signs and one’s own strengths is difficult to overestimate. But any player also counts on basic mathematical statistics and probability theory.

Which lottery has the best chance of winning?

Today there are a large number of lotteries on the market. For beginners, it is best to start with the most famous and largest domestic lotteries with simple and transparent rules. Namely:

The larger the draw, the easier it is to win. You can participate in Russian lotteries without intermediaries.

The player will know the result of instant lotteries immediately. To participate in the drawing, you need to erase the protective coating on the coupon, tear off part of the ticket and unfold it, etc. Most small prizes can be received right on the spot, but for the jackpot you will have to contact the organizers, and in a short time. In draw lotteries, prizes are distributed to players at a certain time. To participate in the game you need:

select certain numbers and write them down on the ticket or cross them off from the list; receive a branded card with the participant’s serial number.

TO draw lotteries also include quizzes and auction drawings (conducted by brands as advertising for their products). In such competitions, gifts are often given rather than a cash prize. Experienced players are advised to participate in such frivolous lotteries. Due to the small circulation of tickets and the limited number of players, winning the lottery is quite easy.

Secrets of Guaranteed Wins

There are a lot of strategies. They are all built on basic principles winning. First, you need to decide on a specific game. Secondly, you need to collect statistics on winning numbers in the lottery. Professionals advise indicating at least one of the winning numbers in the previous game on the new ticket. You need to play the lottery constantly. The likelihood of winning a large sum in a major lottery is small. In order not to miss your chance, you should buy tickets as often as possible. Try it different games. Even if you have developed a strategy for a specific game or simply prefer a particular game for some other reason, it is still worth testing your strategy in other lotteries from time to time.

How to guess the numbers in the lottery - 7 out of 49 winning probability theory

The domestic lottery “Gosloto 7 out of 49” attracts players with a large super prize. A person who guesses 7 numbers will receive 50 million rubles. To calculate the probability of winning in this and any other lottery, you can use a formula from combinatorics. To do this, you need to find a combination of k elements (in our case 7) from n data (out of 47): The probability of receiving a prize in Gosloto is:

Lotteries in which you can actually win a large sum

It is better for beginners to start training on domestic lotteries. It will be easier for the winners to claim their prize or cash reward. The most popular in Russia are:

Lotto “6 out of 49”; "Keno"; Gosloto; “Golden Key”; Russian Lotto; Housing Lottery.

A list of the most popular foreign lotteries and winning statistics for them are presented in the table below.

Russian Lotto - secrets of the game

Russian Lotto is the simplest and most exciting game that millions of Russians enjoy. During its existence, players managed to find out some secrets:

Potential winnings come from the balance of even and odd numbers. The ratio of small and large numbers must also be observed. Ideally, you need the same number of numbers ending in the same number. If 90 numbers are played, then the probability of getting numbers associated with 45 increases sharply. The probability of winning is very high. According to the results of each draw, 3-5 numbers out of 90 remain unused. That is, to receive a prize you need to buy at least 3 tickets and not use the same combinations in each of them.

Calculate winnings in SuperLoto, Stoloto or StateLoto

The chance of getting the jackpot in EuroMillions is 1:116 million, and in Gosloto “5 out of 36” - 1:376,992. Every ticket buyer can become lucky. You just need to know how to calculate winning combination numbers. Method 1 “Statistical” Usually state lotteries provide detailed statistics for each ticket circulation. Information on the organizers' website is updated daily:

statistics on frequent combinations - in the last 10 draws, throughout the history of the game; rare numbers; common pairs of numbers; common numbers in the first rounds of lotteries; archive of all lotteries.

You need to analyze 3-4 previous draws, find repeating combinations and use them in the current game. Method 2 “Emotional” Alex Bellos, author of the book “Beauty Squared,” argues that numbers serve not only as a tool for counting, but also evoke certain feelings. Based on the results of his research, he identified humanity’s favorite numbers: When filling out tickets, lottery winners repeatedly used numbers that were significant to them. For example, the winner of the 1054th edition of the game “6 out of 45” used the birth dates of seven sons, and the winner of the 200th edition of the same game bet on the page number from his favorite book. Any number can evoke emotions: the date of birth of a relative, wedding anniversary, day of promotion, etc. Method 3 “Random” The largest win in the Powerball lottery in 2015 was $188 million. The winner, Marie Holmes, did not develop a strategy, but used the option to automatically fill out the ticket on the computer. According to statistics, there are 70% of such winners, but with a smaller winning amount, all over the world. The option to autofill a ticket can be used by Sportloto players who purchase a coupon via the Internet. Method 4 “Observational” The day before purchasing a ticket, you should be very careful and record all unusual things that happen in everyday life. For example, the license plate number of the car that attracted attention, or the telephone number and advertisement.

What are the best lottery tickets to buy to win?

Professionals advise buying scratch lotteries. The chance of winning in them is 1:5. That is, by purchasing 5 tickets you will have a chance to receive a prize once. Or play in groups. Then expenses and prizes will have to be divided equally. Superstitious lottery winners claim that you need to buy the ticket that your hand reaches at the kiosk. It’s even better if, before buying a ticket, you have a dream foreshadowing an unexpected profit.

Is it possible to win the jackpot?

In the history of any major lottery there are lucky ones who managed to hit the jackpot at least once. The stories of these people confirm that you need to find the right game, study strategies for making money and learn how to choose the right combinations. Numerous research results have proven that:

There is always a chance of winning for any ticket purchased anywhere. There is no 100% winning strategy. The probability of any ball falling out of the lottery machine is uniform. There is no way to increase the probability of guessing the numbers.

From all that has been said above, it follows that it is impossible to win the lottery using the formula; you can only increase the chances of winning. It is not only the strategy that influences the amount of winnings. Suppose that hundreds of people chose the same combination of numbers, which, according to the results of the draw, became the winning one. In this case, the main prize is divided among all participants. From here it appears psychological feature lotteries. You need to choose those numbers on which the masses bet the least, that is, play not against the lottery machine, but against other players.

How to win a million in the lottery - the secret is revealed

A seven-time American lottery winner shares his secrets:

Find yours lucky numbers for each lottery. Take participation in the game seriously, that is, systematically buy a ticket. Make at least 10 bets in one draw, and even better, participate in joint games.

According to lottery winners, dark-colored clothing should be worn on the day of purchasing a ticket. Stripes, checks, lace, colored patterns and bright shades scare away luck. You should also not wear new wardrobe items or gold jewelry. For good luck, pin the pin head down to inside collar

The most winning lottery - reviews and statistics

In May 2017, a resident of Sochi won a super prize in the game “6 out of 49”, winning 365 million rubles. This is a new record not only in this game, but also in the industry as a whole. Until this moment, Gosloto “6 out of 45” was considered the most winning. In the 1138th draw, which took place on January 30, 2015, a super prize was drawn - 203.1 million rubles. The previous record was 202.4 million rubles. was delivered on 08/09/14 during the 915th edition. In total, in the history of the lottery, 67 Russians became millionaires. The secret of their success is in the large circulation rate. To increase your chances of winning a prize, you should bet several games in advance.

Where and how to get your lottery winnings

The lottery usually involves winning money, a car, an apartment or Appliances. It is not at all necessary to pick up the “goods”. You can request the monetary equivalent of its price. In addition, during the circulation period, the studio usually holds competitions with special prizes. To receive a prize you must:

Check the lottery website for your ticket number. All paid coupons are registered in the system. The ticket must contain the following details: name of the lottery; number, date and time of circulation; game combination; price; date and time of purchase; ticket barcode. If any of these details are missing, the ticket is considered invalid. Visit the organizers’ office within 180 days from the date of the draw. Provide the ticket, payment receipt and secret code. Pay 13% tax to the Federal Tax Service.

If the winning amount is not large, then it can be received at a retail point of sale, by postal order or through a quick payment terminal. If a telephone number was specified when purchasing a ticket, then based on the results of the draw, the winner will receive an SMS with a secret code. If the message was not delivered, then either the operator has problems technical problems, or the telephone number was entered incorrectly. In the second case, you will have to contact the organizer’s office to change the phone number in the database. Only using a secret code can you log in personal account on the exchange website and choose the method of receiving the prize.

People who won a lot of money in the lottery

Russian players will probably remember the story of Albert Begryanka. He bought lottery tickets for several years, until in 2009 he hit the jackpot worth 100 million rubles in Gosloto. Most big win Kristen and Colin received €185 million in EuroMillions in 2011. A young couple bought a lottery ticket for the first time to try their luck. Both victories are recognized as records in the history of domestic and world games. Even earlier, Ed Nabors, a driver from Georgia, and the Messners from New Jersey guessed the combination of the MegaMillions draw, which brought them $390 million. Of course, the prize had to be divided among all the winners .In the crisis year of 2009, Russian Evgeny Sidorov won 35 million rubles. Given the unstable exchange rate of the national currency, this amount was more attractive than it is now. Evgeniy, as an avid gambler, hoped for success every time he bought a ticket. He profitably invested the money he earned in his own business.

Frequency analysis. The essence of the strategy comes down to tracking winning combinations for one month. The numbers that come up more often than others are called “hot”. If the same number appears at least 2 times out of 4 games, then most likely it will appear in next editions. This strategy helped American Jeni Callus hit the $21 million jackpot in Texas Lotto. Moreover, she did not have enough information to analyze a specific game. She used data from other games. Multi-draw bets are the choice of the same combination in each game. This strategy helped the winner of the 1157th tirade of the “5 out of 36” lotto receive a prize of 1.8 million rubles. As Vitaly Dmitrievich admits, he simply went ahead, because he was sure that his strategy would work sooner or later. It took six months to turn the dream into reality. The same strategy brought 185 million rubles to the winner Valeria T. from Omsk in the 735th draw. - the largest win in the history of the domestic lottery.

Lucky numbers and lucky numbers for lottery

If you have to cross out numbers in the lottery, then let at least one of them be significant to you. For example, if your date of birth is 05/20/1966, then you need to select 20 or 5 or 22 on the ticket (the four digits of the year should be summed up). Some players believe that the date the ticket was purchased is also important. To increase your chances of winning, it is better to purchase a coupon on your birthday. If you were born on October 11, then you should purchase a lottery ticket on the 11th of each month. As for the days of the week, Monday and Tuesday (first half of the day) and Saturday and Sunday (afternoon) are considered the most favorable for purchasing.

How did life turn out after winning, where was the money spent?

As sociological research shows, lottery winners behave cautiously, strive to preserve their wealth and try their luck again. The lucky ones are very afraid of the money that has fallen on them, and therefore they minimize its volume, spend it on paying off debts, and hide the rest in a piggy bank. At the same time, random money is practically not spent on entertainment and tourist trips. These statistics were shown by 11 millionaires of the Swedish national lotto, who in different time won 100-600 million euros. Victor Ballon, winner of the 1082nd draw of the Russian Lotto, received 1 million rubles on the eve of his 47th birthday. invested in the purchase of real estate. Also entered was entrepreneur Albert Begryan from St. Petersburg, who received 110.1 million rubles in the 36th edition of the game “6 out of 45”. He purchased one apartment for his family. He bought two more apartments, as well as a plot of land, as an investment. The remaining 2 million rubles. were sent to charity. Winners of lotteries abroad have many more questions. In 2016, an Australian resident became the proud owner of a tropical island, which can be reached by plane or ship. The former owners decided to sell the “real estate” very in an original way. They organized a lottery, releasing 55 thousand tickets, costing 49 aust. dollars. They received 2.6 million aust for the island. Dollars. Stuart Grand from the UK planned all expense items in advance. Being disabled since childhood, he was forced to lead a reclusive life. But the jackpot National Lottery worth £3.5 million Strelings changed his life. He paid off all his debts, built a house, started a family and became a VIP client of the country's leading bank.

Is it possible to make a permanent income from lotteries?

You can constantly make money from lotteries. Another question is that the income will be small and unpredictable. You can, for example, play the online lottery “Social Chance” for free. To participate in the draw, just register on the website by entering your email address. Immediately after this, the chance to play the lottery once will be available. After filling out your profile, the number of chances will increase to 5, and then will be updated daily. The essence of the game comes down to guessing 6 numbers that will appear on the scoreboard after pressing the lever. If a person used the services of a computer instead of plugging in the numbers himself, then the amount of his winnings will be less. Numbers are viewed from left to right. The table below shows a list of prizes if the numbers match: No clever schemes, tricks or tips. You can make money just by having fun. Withdrawal of funds (minimum 50 rubles) is carried out to an electronic wallet within 2-4 weeks. To get an additional chance and increase the likelihood of winning, you can:

By joining a group on social networks - 4 chances. By filling out your profile in full - 4 chances. By linking social network accounts - 4 chances. By publishing the results of your draws on social networks daily - 1 chance. By visiting the lottery website daily - 5 chances. By participating in the affiliate program - for Each person you refer gets 1 chance.

Similar online lotteries There are many on the Internet. They all work pretty much the same way. They allow participants to play for free and pay money for promoting the lottery website on social networks.

Kokorin Artem, student of MAOU Secondary School No. 11

The work examines winning lottery situations:

· Lottery "5 out of 36".

· Lottery “5 out of 40”.

· Lottery “6 out of 49”».

The work received a diploma at the regional research conference.

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Municipal educational institution

"Average comprehensive school No. 11"

Probability of winning in number lotteries

Kokorin Artem,

10th grade student
Municipal educational institution secondary school No. 11, Tchaikovsky

Batueva Lyubov Nikolaevna,

higher category mathematics teacher

Municipal educational institution secondary school No. 11, Tchaikovsky

Tchaikovsky

1. Introduction.
2. Goals and objectives.
3. The 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 application of the results obtained.
10. Conclusion and recommendations.

Introduction.

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

Relevance of the problem.

My topic is relevant because mathematics comes into contact with everyday life much closer than is traditionally taught in school. W. Weaver writes: “Probability theory and statistics are two important areas that are inextricably linked with our daily activities. World of Industry, Insurance companies to a greater extent are debtors to the laws of probability. Physics itself is essentially probabilistic in nature; So is biology at its core. Meanwhile, despite this importance, the universal nature of probability theory and statistics has not yet become generally accepted. Lotteries, gambling, election companies, insurance companies, etc. How to predict the result?.. Which position to choose?.. To answer these questions, I decided to do this research.

Hypothesis : Most people believe that it is impossible to predict the outcome of a chile lottery, in which chance reigns. This is wrong. Expected value winnings - a value that will help us determine whether a particular 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 research: numerical lotteries

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

When starting the research, I set myself the main target – conduct probabilistic analysis numerical lotteries, that using the formulas of probability theory, which will help us determine whether this or that lottery is fair, and whether it is profitable for us to play it. This goal leads to 4 main tasks, which I strived to achieve during the research:

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

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

To accomplish the tasks I used, I used the following: methods studies such as comparison, induction, deduction, analogy, experiment and questioning.

History of origin.

Many fans of sports-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 Italian city Genoa. The fact is that in the Genoese Republic, 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 final round of voting, from which only five people had to be selected. The elections took place like this: each candidate member of 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 drawn balls named the members of the Great Council of Genoa!
This lottery principle of choice received universal recognition in Italy and, having crossed state borders, began to spread throughout other European countries.
Currently in different countries There are several types of numerical lotteries. It was not my goal to talk about each of them here..

Mathematical basis for numerical lotteries

Each numerical lottery with any numerical formula has its own mathematical basis. It is necessary in order to know how many classes of winnings there should be in the lottery, and what is the probability of winning each class.
The mathematical basis for the number lottery is calculated using probability theory 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 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 winnings of each class and what the amount of each win should be.
The total number of combinations in a 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 with 5 or even 4 numbers matching were also won. How many cards would you need to buy and fill out so that they have all the combinations of 6 numbers out of 49 possible, that is, to win for sure? The number of cards is equal to the number of combinations of 49 elements of 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 have been difficult to get rich in this case, since the winnings were not fixed, and in each drawing only a portion of the amount collected from ticket sales was allocated to the prize fund. But someone 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 a given event was observed in a series of experiments.Relative frequency(sometimes simply called 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 for winning if 3 numbers are guessed.

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

Designated by R 6, P 5, P 4, P 3, P 2, P 1, P 0 the probability that 6, 5, 4, 3, 2, 1 or 0 numbers marked by the player turned out to be winning. The number of all outcomes of the experiment is equal to = 13,983,816, - the number of choices of 6 numbers that do not match the given 6 numbers.According to the theory of probability, the probability of guessing n (from 0 to 5) numbers out of 36 can be expressed by the formula: According to the theory of probability, 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

P 0 ≈ 0.435965

· - number of choices of 1 number from 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 from 6 given numbers and 4 numbers that do not match the given 6 numbers

· =

P 2 ≈ 0.132378

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

· =

P 3 ≈ 0.0176504

· - the number of choices of 4 numbers from 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

4! · 2! · 2! · 41! 2 2

P 4 ≈ 0.000969

· - the number of choices of 5 numbers from 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!

P 5 ≈ 0.000184

It follows that the probability of losing is equal to

P 3 + P 2 + P 1 + P 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 a player will not guess a single number is 0.514757143

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

The difference is not very large, 0.101738, and may 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 relative frequency of a player guessing 1 number is 0,366342857 .And according to calculations, the probability that the player will guess 1 number is 0.413019. The difference between the calculations and the data obtained using the experiment is equal 0,0466761 .

Experiment number
	0,13
	0,045
	0,045

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

Experiment number
	0,045
	0,045

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

In total, the “6 out of 49” lottery contains 13,804 winnings, i.e. 1 winning per 1,013 combinations.

13.983.816 13.545

1 to 1,032 combinations

Lottery 5 out of 36

To win you need to match 5 numbers out of 35. I conducted experiments with this lottery as well. Each student who took part in the experiment received a card.

5 out of 35

Let's calculate the probability that the player will not guess a single number.

5!∙30! 1∙2∙3∙4∙5

5!∙25! 2∙3∙4∙5

P 0 ≈ 0.438977.

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

4! · 4! · 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

P 2 ≈ 0.284900

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

3! · 2! · 2! · 28! 2 2

P 3 ≈ 0.030525

P 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 largest win in the same lottery. But there was not a single win in the experiments.

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 winnings

In total, the “5 out of 36” lottery thus contains 4,806 winnings, i.e. 1 winning per 78 combinations.
The probability of each class of winnings is determined by the ratio of the probable number of winnings to the total number of winning cases, 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 that a player will not guess a single number is 0.4865875.

From 35 = 35! = 31∙32∙33∙34∙35 = 324,632

5!∙30! 1∙2∙3∙4∙5

From 30 = 30! = 26∙27∙28∙29∙30 = 142,506

5!∙25! 2∙3∙4∙5

P 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 will guess 1 number is 0.3865875. Let's calculate the probability that the player will guess 1 number.

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

4! · 4! · 26! 2 3 4

Р 1 ≈ 0.422093

The difference in 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 relative frequency of a player guessing 2 numbers is 0.151475.

Let's calculate the probability that the player will guess 2 numbers. 2 3

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

2! · 3! · 3! · 27! 2 2 3

P 2 ≈ 0.284900

The difference in values ​​obtained through experiments and calculations was equal to 0.133425.

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

The average relative frequency of a player matching 3 numbers is 0.0225.

Let's calculate the probability that a player will guess 3 of the same number.

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

3! · 2! · 2! · 28! 2 2

P 3 ≈ 0.030525

The difference in the value obtained through experiments and calculations was equal to 0.008025. The probability of winning in this lottery is

P 5 ≈ 0.00000308041

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

Class 2 winnings (for 4 correctly guessed numbers):

(5) (4)

(35) (1)

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

35 1

175 wins

3rd class winnings (for 3 correctly guessed numbers):

(5) (3)

(35) (2)

5 x 4 x 3 1 x 2 x 3

35 x 34 1 x 2

5,950 winnings

In total, the “5 out of 40” lottery contains 6,126 winnings, i.e. There is 1 win per 107 combinations.
The probability of each class of winnings is determined by the ratio of the probable number of winnings to the total number of winning cases, equal to the total number of combinations in the lottery:
Winning 1st class (for 5 guessed numbers):

Winning 3rd class (for 3 correctly 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 conducted experiments with this lottery. Each student who took part 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 that a player will not guess a single number is 0.4865875.

Let's calculate the probability that the player will not guess a single number. 5

WITH35 = 35! = 31∙32∙33∙34∙35 = 324 632

5!∙30! 1∙2∙3∙4∙5

5

WITH30 = 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 will guess 1 number is 0.3865875. Let's calculate the probability that the player will guess 1 number.

1 4

WITH5 · WITH30 = 5! · thirty!= 5 27 28 29 30= 137025

4! · 4! · 26! 2 3 4

R1 ≈ 0,422093

The difference in 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 relative frequency of a player guessing 2 numbers is 0.151475.

Let's calculate the probability that the player will guess 2 numbers. 2 3

WITH5 · WITH30 = 5! · thirty!= 4 5 28 29 30= 40600

2! · 3! · 3! · 27! 2 2 3

R2 ≈ 0,284900

The difference in values ​​obtained through experiments and calculations was equal to 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 relative frequency of a player matching 3 numbers is 0.0225.

Let's calculate the probability that a player will guess 3 of the same number.

3 2

WITH5 · WITH30 = 5! · thirty!= 4 5 29 30= 4350

3! · 2! · 2! · 28! 2 2

R3 ≈ 0,030525

The difference in the value obtained through experiments and calculations was equal to 0.008025. The probability of winning in this lottery is

R5 ≈ 0,00000308041

. There was not a single win in the experiments.

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:
1st class winnings (for 6 matched 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

Class 2 winnings (for 5 correct 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

3rd class winnings (for 4 correctly 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 winnings, i.e. 1 winning per 718 combinations.
The probability of each class of winnings is determined by the ratio of the probable number of winnings to the total number of winning cases, equal to the total number of combinations in the lottery:
Winning 1st class (for 6 correctly guessed numbers):

Winning 3rd class (for 4 correctly guessed numbers):

8.145.060 11.115

1 in 733 combinations

Conclusion:

All assigned tasks were completed, the hypothesis that with the help of the probability of winning in numerical lotteries was proven. I would like my work to help people avoid making 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 people believe that it is impossible to predict the results of lotteries in which chance reigns, I present the results of my survey among ninth-graders on the topic “Is it possible to predict the result of a game in which chance reigns?”

Here are his results, presented in chart form:

As you can see, this confirms my hypothesis that students have a misconception about the possibilities of probability theory.

Literature.

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

Examples of lottery tickets.

Slide captions:

Probability of winning in numerical lotteries Work completed by: student 10 “A” of class MOU Secondary School No. 11 Kokorin Artyom

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

Relevance of the problem. Hypothesis. My topic is relevant because mathematics comes into contact with everyday life much more closely than 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 wrong. The probability of winning is a value that will help us determine whether a particular game is fair and whether it is profitable for us to play it

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

History of the creation of lotteries. Many fans of sports-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 Genoese Republic, 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 final round of voting, from which only five people had to be selected. The elections took place like this: each candidate member of 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 drawn balls named the members of the Great Council of Genoa! This lottery principle of choice received universal recognition in Italy and, having crossed state borders, began to spread throughout other European countries. Currently, there are several types of numerical lotteries in different countries.

Subject of study. Number lotteries: “6 out of 49” “5 out of 36” “5 out of 40”

Number lottery “6 out of 49” Rules: To get a big win, you had to guess 6 numbers out of 49. Cards were also won if 5 or even 4 numbers matched

References: Encyclopedia for children. Mathematics. Volume 11. Moscow, Akvanta +, 2001 I explore the world. Mathematics. Moscow, Ast, 1998 M.F. Rushailo Elements of probability theory and mathematical statistics. Moscow, 2004 E.A. Bunimovich, V.A. Bulychev Probability and statistics grades 5 – 9. Bustard, Moscow, 2002

Many lottery fans are asking a very fair question, how to win the 5 out of 36 lottery. Before we try to answer these questions, you need to familiarize yourself with the rules and calculate the probability of winning the 5 out of 36 lottery.

Gosloto lottery 5 out of 36 can be called the smartest choice of all existing lotteries V this moment, since this lottery has the maximum chances of winning the main prize.

Of course, when talking about maximum odds, we must understand that this is a lottery and the chances of winning the main jackpot are not great.

Number of combinations in lottery 5 out of 36

It would be logical to move on to the facts and voice exact numbers. Number of lottery combinations 5 out of 36:

376992
three hundred seventy six nine hundred ninety two

and only one of them becomes winning.

Why did we write above that players in 5 out of 36 act wisely - because compared to the Gosloto lottery 6 out of 45, here the chances of winning a super prize are almost 22 times greater!

Are you thinking about how to win at Gosloto? big prize– play 5 out of 36! Yes, this lottery does not accumulate big jackpot, however, the chances of winning are much greater.

How to calculate a winning combination 5 out of 36

Deployed system - in pursuit of 100% jackpot winnings

A 100% chance of winning the lottery will only be given by a comprehensive system, which will include all 36 numbers, that is, a bet on all possible combinations. However, it will not be possible or reasonable to make such a bet for several reasons:

1. Restrictions by rules. The number of selected numbers in an expanded bet, according to the lottery rules, does not exceed 11; it is impossible to place a bet in which all the numbers will be crossed out on one ticket.

2. Let’s assume that someone manually or automatically decides to buy all possible combinations for the upcoming circulation.

With a ticket price of 80 rubles, this will require a very significant amount of 30,159,360 rubles.

Such a bet would be quite feasible if its economic component were logical. The Gosloto jackpot 5 out of 36 has never even come close to this amount, and will never come even close to this amount. Winning the jackpot with such a bet will, of course, have a 100% probability, but the winning amount will not cover the amount needed to spend on purchasing such a number of tickets.

Four deployed systems - in pursuit of winning.

All 36 lottery numbers can be divided equally into four bags.

Each bag will contain 9 numbers. In total, five numbers appear during the drawing.

Accordingly, if the first four numbers drawn end up in different bags, then the fifth number will end up in one of the bags that already contains the number drawn. That is, whatever one may say, in the worst case scenario, one of the bags will contain 2 winning numbers, that is, it will be winning.

Thus, in order to be guaranteed to win the lottery, you need to make 4 detailed systems in which all the numbers will be involved.

The cost of four such bets with a ticket amount of 80 rubles will be equal to 40,320 rubles with a guaranteed win of 80 rubles.

It would seem that the economic feasibility of such a bet is also questionable, but we must not forget that such a bet can rob the prize of more than large category, but here without any 100% guarantees.

Thus, the probability of matching three numbers in such a bet will be less than 30%, and the probability of winning the jackpot will be equal to the standard probability, as when buying 504 tickets with random combinations.

A few more game systems in Gosloto 5 of 36

Our program, called Nostradamus, tries to guess the winning combination of the nearest draw based on statistical analysis and other factors, forming only one combination.

Incomplete systems 5 out of 36 are a more cost-effective analogue of deployed systems. Many players find this system central to their gameplay.

A balanced strategy subjects the winning combinations to elementary mathematical analysis.

Conclusion

The lottery remains a lottery - a gambling hobby that brings millions of winnings to a few winners. The article discusses some possible methods of winning and the theory of probability in the Gosloto 5 out of 36 lottery.

Read also other blog posts:

How to win the 6 out of 45 lottery? Let's make a lucky combination. How to win the right to obtain US citizenship in the lottery?

How to win the lottery? Every year thousands of people go broke trying in vain to realize the dream of becoming a millionaire without special effort, and only a few become happy winners. From the article you will learn whether it is possible to win the lottery, what chances there are in different types of these competitions and how to increase the likelihood of winning, as well as several stories about how some managed to become owners of large monetary rewards for a small amount of effort.

What are the types of lotteries?

The lottery has gained immense popularity among the people as the cash rewards offered attract a large number of people. Of course, under such circumstances, the development of pranks did not stop at the initial level; they acquired many different types, which are fundamentally different from each other. But what exactly is the difference between them and which lotteries do people win? Let's look at everything in detail existing species lotteries to understand this issue.

Instant

The instant lottery lives up to its name. Typically, a drawing involves purchasing a ticket, and whether you win or not depends on what is hidden in it. Typically, a ticket has one or more fields that must be erased to read the winning information. Sometimes the ticket is something like a sealed envelope that you need to open and read the information inside.

Small rewards are usually paid out directly at the same location where you purchased your ticket. To receive major awards, you must contact the competition organizer. But in instant lotteries, large draws are extremely rare.

You can also buy a ticket online, but in electronic format it doesn't instill as much confidence as a paper ticket does. After all, the organizer can easily generate results after a purchase, which cannot be verified in any way, unlike the paper method.

The advantage is that you can find out the result immediately after purchase, without waiting for a circulation. It makes me happy pleasant wait, which comes at the moment the protective layer is erased.

However, the instant lottery has many disadvantages. Firstly, the winnings are usually small. Secondly, you cannot choose the number yourself. Thirdly, there is no guarantee that the ticket seller is not a scammer. The latter can be avoided if you buy tickets only from well-advertised organizers. They usually have a special security code.

circulation

They are divided into two types. The only difference is that in one case you are given a choice of numbers, and in the other the numbers are pre-printed on the ticket.

In the first case, you can rely on your forecasts and calculations, reinforcing your confidence in winning with your knowledge. The chance of winning the second type of lottery seems more realistic. In such lotteries, winnings reach the largest sizes, and the drawing takes place in full view of all participants using a lottery machine, which consists of a drum and randomly rolling out balls or a random number generator.

We will look at how to win a draw-type lottery and what organizers exist below.

The main advantage is that a huge number of participants generates a large amount at stake. You can choose the numbers yourself, which also significantly increases the chance of winning. And you can play with a united group of people so that the probability is greater.

There are also some serious downsides. The numbers are completely random, and their large number reduces the probability to a minimum, and some lotteries draw once a week, or even less often.

Promotions, competitions, quizzes

This is not exactly a lottery, but the similarities are very great. It all usually starts with an advertising campaign large company, which gives away a cash or other prize to attract customers. Such draws are not complete without avid lottery players who will not miss the chance to grab their piece. Even if you receive some unnecessary product as a prize, do not forget that it can be exchanged for sum of money.

You can always stay up to date by following promotions on lottery websites. There is always information about where and what draws are being held.

The prize fund is formed in advance, and you can be sure that you will not have to pay any commission on your winnings. Promotions are held frequently; as a rule, purchased goods are used instead of tickets. The product can also be purchased from large quantities, which increases the chance of winning the lottery, and these purchases, unlike a ticket, can be beneficial.

Most often the winner is the one who bought more products and, accordingly, invested more money. You need to find out about the reward in advance; there is a chance that you will receive some kind of T-shirt or mug with the organizer’s logo. It's hardly worth the effort. Even large brands may neglect to send the goods to the winner, citing the fact that all the prizes have already ended.

Probability of winning the lottery

Before you talk about which lottery you can actually win, you need to figure out what the probability of winning is. It is calculated using a certain combinatorics formula, so before buying a ticket, carefully consider all possible options.

Here is an example of the most famous lotteries and the probability of winning them.

Number	Lottery	Probability of winning the main prize
		1 in 175 712 536
		1 to 176 213 110
		1 to 120 331 800
	Gosloto 6 out of 45
	Gosloto 5 of 36

Probability formula

The formula is quite simple if you know math. For those who don't know what factorial is:

n!=(n-1)*(n-2)*(n-3)*…*(n-n+1)

That is, the factorial n is the product of all numbers in order up to the number n.

The formula is the division of the factorial of the number of selected numbers by the factorial of the number of selected ones, that is: probability of winning = (number of all numbers)!/(number of selected numbers on the ticket)!

For “Gosloto 5 out of 36” the formula is as follows: probability of winning = 36!/5! = 376,992.

Based on this formula, it is obvious that to win the lottery you need to choose the one in which the probability is greater, that is, with the smallest number of calculation results.

How to win the Russian Lotto lottery

« Russian Lotto"is one of the most popular lotteries in Russia. Of course, this is also the most lucrative competition in which you can win a huge amount.

First of all, decide what you want - to win a small amount or hit the jackpot? The more often you participate, the greater your chance of winning. Therefore, you must firmly decide that you will not stop. So, if you are sure that victory is necessary at any cost, then the following information is for you.

You've probably already tried to play something many times, but you haven't yet dared to seriously win the lottery. Since now you intend to take a firm step towards victory, you should learn some information.

Five rules on the path to victory

1. The organizers win anyway. And definitely their winnings will be greater than yours, it’s not for nothing that they are involved in the lottery. As for the players, the situation is completely opposite. Therefore, you should not send all your money to buy tickets; distribute your efforts evenly.
2. Remember: winning the lottery is real. Don’t forget, judging by its popularity, the safest and most honest lottery is still the Russian Lotto. How to win with this large quantities participants, another question. A lot always depends on you, even in the lottery.
3. Regular participation in lotteries increases your chances of winning. Don't despair, even if you have lost many times.
4. You shouldn’t rush into all the pranks when they appear. After all, there are many different promotions and holiday increases in winnings.

This is the answer to the question of how to win the lottery. If you follow these rules, prepare mentally in advance and determine the amount of money you are going to spend, then sooner or later victory will definitely be on your side.

You can, of course, like most people, just buy a bunch of tickets and wait for one of them to be lucky, but experience shows that this is the tactic of losers. Even the lottery must be approached wisely.

And what is important is that you must participate for the sake of victory, and not for the sake of winning. You must desire the result of your actions, only then it will be positive.

Alternative ways to win

There are many alternative systems to increase your chances of winning. Some people believe that you can win with the help of mathematical calculations, while others, on the contrary, turn to the old school - magic.

It is difficult to say whether it is possible to win the lottery using such manipulations. But the fact that the Internet is full of such advice is quite obvious. There are many conspiracies and rituals to attract money. If you are a supporter of the idea that magic can help you, then you have the right to use this method.

As for mathematical calculations, the chances are much less, since the winner is determined randomly, and all you can do is show persistence and endurance. There can be no pattern between winnings, so either hope for luck or play calmly and wait for victory. In any case, you need to remain extremely careful and not get carried away too much.

Game addiction

When wondering how to win the lottery, first make sure that you do not have a gambling addiction. This disease is sometimes more dangerous than any drugs or alcohol.

Gambling addiction is a morbid attraction to gambling. Can start with the usual computer games and gradually develop into a terrible addiction that destroys everything in its path. It is more of a mental illness, as opposed to drug addiction and alcoholism, and should not be underestimated. Therefore, make sure that it is missing before you start participating in the lottery.

Winners

No one in our country would be confident in the possibility of winning if there were no people who won the lottery in Russia. The United States is known for its huge prizes and many winners. Sometimes even news channels often show lucky people who have made millions from nothing in a few hours. It was from the West that this popular game, and our television also does not treat such competitions indifferently. There are many TV versions of the lottery. Tickets for participation can be bought at kiosks or bookmakers, and the drawing process can be watched on TV. By winning such a lottery, you can not only receive a substantial amount, but also be seen throughout the country. This is one way to attract people, but there are lucky ones who still grab their piece.

Winner 2014

Let's immediately move on to the “freshest” millionaire, who is the Siberian Valery, whose last name is still unknown. The winner of the 735th Gosloto 6 out of 45 draw won 184,513,512 rubles. According to him, he did not immediately come for his winnings, since the amount of almost two hundred million rubles plunged him into a state of shock.

Valery walked towards success for a very long time. Every month, for many years in a row, he spent 800 rubles on lottery tickets. The amount is small, especially considering his winnings, but it played a role in his life.

By the way, “Gosloto 6 out of 45” is least famous for winners with such a large winnings, in contrast to “Gosloto 5 out of 35”. However, the maximum gain in the second case is much smaller.

The state lotto attracts people most of all because you will never be deceived here, since it is for everyone famous game, which is broadcast on television, where millions of people continuously watch its progress, and tickets cannot be faked, since each of them has its own code.

So, when asked which lottery you can actually win, any avid player will most likely say that it is “Gosloto 5 out of 35”.

Conclusion

The lottery is not the best The best way become rich, but the easiest and fastest. Winning can happen as soon as you buy your first ticket, or maybe after a few years, or even bypass you altogether. Before you run to the kiosk to buy hundreds of tickets and dream of winning a million in the lottery, you need to think carefully about whether your time and effort is worth it, and how much you are willing to give for just the chance of winning. But the conclusion from all that has been said is quite concrete: it is possible to win the lottery, and people become winners. Although the chances of winning are not very high, a competent approach and patience will always help much better than a one-time decision. Who knows, maybe the next win will go to you?