The paradox of the lottery and Bernoulli's law of large numbers. Research paper "probability of winning in numerical lotteries"

One of the most frequently asked questions is: “What is the probability of winning the lottery?” It’s easy to answer, because numerical lotteries are conducted according to certain formulas and each of them can be subjected to mathematical calculation. So, let's start calculating luck together with the most popular Russian state lotteries.

We win in Gosloto “4 out of 20”

The youngest of the Gosloto lotteries, “four,” has already managed to acquire fans. And all thanks to its remarkable features: a huge, multi-million dollar super prize, 20 other winning categories and an increased prize fund - 67% of the proceeds from each ticket sold go to it.
The chances of winning a super prize in Gosloto 4 out of 20 are 1 in 23,474,025. The overall probability of winning is estimated as 1 in 3.4.

Winning distribution table in Gosloto 4 out of 20:

Matched numbers in field 1 Matched numbers in field 2 Distribution prize fund
4 4 23.36% + accumulated Super Prize
4 3 2,56%
3 4 2,56%
4 2 0,58%
2 4 0,58%
4 1 0,89%
1 4 0,89%
4 0 1,02%
0 4 1,02%
3 3 0,98%
3 2 3,68%
2 3 3,68%
3 1 4,59%
1 3 4,59%
3 0 4,66%
0 3 4,66%
2 2 12,44%
2 0 13,63%
0 2 13,63%
2 1 100 rubles**
1 2 100 rubles**

To win a super prize, you need to match 4 numbers in the first field and 4 numbers in the second on your ticket. In the premiere edition of the “four”, which will take place on December 31 at 20:00 in live on the NTV channel, it will amount to 1 billion rubles!

To increase your chances of winning, take advantage of features such as expanded and multi-draw bets.

*Distribution of the prize fund, taken as 100% after accrual of fixed winnings.
**Fixed winnings per winning ticket.

We win in Gosloto “6 out of 45”

The queen of Gosloto lotteries, the “six,” regularly sets records for the amount of super prizes. Perhaps every lottery fan dreams of winning millions of rubles playing it. In this case, the chances of guessing two or more numbers are quite high. The main thing is to bet regularly and think like a winner!

How to increase your chances of winning the lottery? Firstly, the more bets you place, the higher the likelihood of winning a prize. Secondly, detailed and large-circulation bets have a significant impact on the balance of power. Using this method, some Gosloto 6 out of 45 fans have already become millionaires. Read more about the multi-circulation rate in our. Thirdly, it is important to believe in your luck! If you are confident in victory, it will not take long to arrive.

We win in Gosloto “5 out of 36”

As you know, most often million-dollar winnings go to Gosloto “5 out of 36” participants. The probability of winning a super prize in this lottery is indeed much higher than, for example, in Gosloto “6 out of 45”. That is why, on average, we honor new Russian millionaires every week. Now there are already 250 lucky people in this club!

Have you already noticed how tempting the Gosloto “5 out of 36” statistics look? It makes me want to place a bet as soon as possible! Regular participants know that they can participate in the “five” draws in any convenient way: by purchasing a ticket at one of the lottery kiosks or salons “Euroset” and “Svyaznoy”, a branch of the “Russian Post”, in a lottery online supermarket, using mobile application Stoloto or placing a bet via SMS. All means are good!

We win in Gosloto “7 out of 49”

Another remarkable lottery with many fans. First of all, Gosloto “7 out of 49” attracts the largest guaranteed super prize - 50,000,000 rubles for 7 guessed numbers. His win is real luck! The probability of triumph is, of course, less than in other lotteries, but the greater your joy from victory will be! Distribution circulations“Sevens” regularly increase the number of lottery millionaires in Russia.

We win in “Sportloto 6 out of 49”

The legendary lottery, which came to us from Soviet times and celebrates its 45th anniversary this year, still looks tempting. Not only because of the low cost minimum rate(only 20 rubles) and an impressive super prize, but also thanks to the introduction of a bonus ball into the game. This type of lottery is popular abroad and, as we see, lives successfully in Russia. Guessing the number on the bonus ball is the desired goal of many whose 5 numbers marked in the coupon have already matched the main combination. But the most persistent and lucky participants achieve it. And the more interesting it is to live, play and win!

The principle of numbers falling out

A generator is used to determine winning combinations random numbers. This is the most modern technology, which is responsible for drawing numbers in the world's leading lotteries. In this case it is absolutely excluded human factor, which means that the entire drawing process can be trusted unconditionally.
How do you choose numbers when placing bets? Do you mark your favorite numbers that you consider to bring good luck, or use the Automatic Bet feature? Are you keeping track of the combinations that come up? For those who make strict strategic calculations or simply want to know which numbers win more often and which ones win less often, statistics for each lottery are regularly updated on the Stoloto website.

The most unusual combination of numbers

The imagination of seasoned lottery strategists was amazed on April 5, 2015, when in the 17,053rd draw quick game“Rapido” brought a super prize of 4,269,583 rubles with a beautiful combination: 1, 2, 3, 4, 5, 6, 7, 8 in the first part of the field, 4 in the second part. Indicate the first eight numbers on the ticket, pay 30 rubles (that’s how much the lucky bet cost) and thus become a millionaire - great luck! This victory has already gone down in lottery history. And not only because of such a rare combination of numbers, but also because the win was a record for Rapido.

Winning bingo lotteries

The most popular state bingo lotteries in Russia - Russian lotto and Housing Lottery. Apartments are played in them, country houses, cars and large cash prizes.

The chances of winning the bingo lottery increase significantly when the game is played until the 87th move. This means that Mikhail Borisov, the host of the Russian Lotto, has three barrels left in his bag (instead of the usual four), and three balls in the Housing Lottery machine. And if you don't find these numbers on your ticket, you've won!
Winning in Russian Lotto and Housing lottery depends entirely on your luck, because here you won’t be able to make a spread bet or use a multiplier. These are lotteries for those who prefer to surrender to fate and give fortune the opportunity to choose their favorite on Sunday morning during the drawing (broadcast on Sundays at 8:15 on the NTV channel, in the program “Russian Lotto Plus”). There are several ways to influence the balance of power. Choose a ticket with your favorite numbers printed on the playing field. Buy multiple tickets to increase your chances of winning. Or become the owner of block tickets in which all 90 numbers are marked. Such tickets are issued for the country's main holidays and other important dates.
If you can’t wait to test the theory of probability of winnings in practice, hurry up to purchase lottery tickets or place a bet at your nearest lottery kiosk, Euroset communication store, Svyaznoy store, Russian Post office or on the website of the Russian online lottery supermarket Stoloto. in the Stoloto mobile application or via SMS.
May luck smile on you!

The most convenient way to buy lottery tickets

Your whole life is on the run and you don’t have time to go to a lottery kiosk? With our Stoloto mobile application, all problems will disappear overnight. After downloading it, you can purchase a ticket at any time, find out the results of previous draws, top up your Stoloto wallet and read about latest news world of lotteries. The Stoloto application is available in two versions: for Android and iOS. Choose the version that suits your smartphone and use the most convenient and fastest way to purchase lottery tickets.

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 drawing, the easier it is to win. Participate in Russian lotteries possible without intermediaries.
Result instant lotteries the player will know 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:
    choose certain numbers and write them down on the ticket or cross them off the list; receive a company 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 lottery numbers. Professionals advise indicating on the new ticket at least one of winning numbers in the previous game. 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

Beginners should 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.
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 is loved by millions of Russians. 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. 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” it is 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 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 history 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 Grand Prize 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”. Can be requested monetary equivalent its prices. 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 you can get it in retail point sales, postal order or through a quick payment terminal. If a phone 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 encountered 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 with the help secret code you can 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 Begryank. 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 in 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. – biggest win in the history of the domestic lottery.

Lucky numbers and lucky numbers for the 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 downplay 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” in a very original way. They organized a lottery, issuing 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 a £3.5 million National Lottery jackpot 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 online 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 completely - 4 chances. By linking accounts social networks– 4 chances. Daily publishing the results of your drawings on social networks – 1 chance. Daily visiting the lottery website – 5 chances. Participating in the affiliate program – 1 chance for each person attracted.
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.

It's not a problem to calculate the probability. For example, for 5 out of 36, the probability that one number from our 5 will fall out will be 5/36. The probability that the second digit from the remaining four will fall out of the remaining 35 is 4/35, etc. By multiplying all the numbers, we get the total probability.

5 out of 36 1/376992
6 out of 45 1/8145060
7 of 49 1/85900584

Let's now try to evaluate what is best to play. Let's say we take and buy back 1 percent of total circulation, what will happen?

As we see, in 6 out of 36 we are allowed to multiply our costs by 31 times (with the same probability of winning). At the same time, we need to spend almost 15 times more money than in 5 out of 36. So it turns out that the five will be better than all the others.


How to increase your probability of winning?

There are a huge number of game tactics. The most popular of them are the following:

  • Frequency principle. The idea is that you need to bet on those balls that fall out the least. A simple analysis shows that such balls will have a better chance of being drawn than others.
  • Temporal principle. The idea is that you need to bet on those balls that have not dropped out for a long time.
  • Mixed - part of the balls is taken according to the frequency principle and part according to the time principle.

You can see ball drop statistics here:

Now let's talk about those who actually conduct such lotteries. The trick is that the founders know who bet on what. Therefore, when conducting, they “try” so that those balls on which people place do not fall out. This means that all the above methods play with players cruel joke. Everyone knows about similar methods and of course they are used, so combinations built on similar principles occur quite often.

Therefore, some especially gifted people use the opposite principles. Those. on the contrary, they avoid using these methods or use them altogether, on the contrary, the most frequency balls. All this plays exactly the same role! Those. people bet a lot on such balls and therefore such balls become “forbidden” again among the organizers.

The situation is complicated by the fact that many people keep track of the frequency and time of balls falling out, and if such balls do not fall out at all, a conversation will arise about the unevenness of the balls falling out.

I think that the organizers do not really worry about the loss of this or that combination (since it is technically quite difficult to organize). Most likely, they have 2-3 rigged balls in the lottery machine (and these are the balls on which people bet the least in this drawing) and the rest are chosen completely randomly. This needs to be done so that the frequency graphs of ball drops are at least slightly leveled. Accordingly, we can say that the best combination will be one in which there will be 2-3 balls from high-frequency and most probable balls and 2-3 from the middle ones, but which no one will bet.

What is the probability of winning the lottery? This article is all about the chances of winning in various lotteries around the world with the calculation of the number of combinations.

It is logical to assume that anyone who buys a lottery ticket wants to win the main prize. In the vast majority of lotteries there is only one jackpot. If there are several winners, the amount is simply divided by their number. Of the well-known world lotteries, the only exception is the Spanish national lottery and its variations - Christmas El Gordo and New Year's El Niño, where there are several main prizes.

Based on this, to calculate the probability of winning the lottery you just need to count the number of combinations. This will be the mathematical basis for the lottery.

Below we have compiled a table for you that shows the probability of winning for the most famous Russian, European and American lotteries.

Number

Lottery

Probability of winning the main prize

Megamillions-Megamillions

1 in 175 711 536

Powerball -PowerBall

1 to 175 223 510

Euromillions -EuroMillions

1 to 116,531,800

Eurojackpot -Eurojackpot

1 to 59 325 280

La primitive -La Primitiva

1 to 139 838 160

Gosloto 6 out of 45

1 to 8 145 060

Gosloto 5 of 36

1 in 376,992

Below are formulas and examples for calculating the number of combinations and the probability of winning some Russian lotteries and European lotteries. You must also remember that in all modern lotteries, in addition to the jackpot, there are other categories of winnings, when, for example, 6.5 is guessed from the 7th number, and so on.

To calculate the probability of winning, we do not need probability theory, but rather combinatorics.

So, a little math. A combination is the selection of k elements from n data without regard to order (for example, by selecting all at the same time or even sequentially if, as a result of the selection, this order is considered unimportant).

The number of combinations is calculated by the formula:

The number n!, which is equal to n*(n-1)*(n-2)*(n-3)..*1 is called n-factorial or simply factorial. For example, 5!=5*4*3*2*1=120. That is, we present the above formula as follows:

xnumbers from n =

(n)
( x)

=

n * ( n - 1) * ( n - 2) * ( n - 3) … * [ n - ( x -1)]
1 * 2 * 3 * 4* .. x

For example, for a lottery gosloto 5 out of 36 total number of combinationscalculated like this:

5 out of 36=

(36)
(5)

36 * 35 * 34 * 33 * 32
1 * 2 * 3 * 4 * 5

376 992.

Thus, the chance of winning for state lotto, or any other lottery in which you need to guess 5 numbers out of 36, is 1 in 376 thousand 992.

For lotteries using the 6 out of 45 formula, the specified formula will look like this:

6 out of 45 =

(45)
(6)

45 * 44 * 43 * 42 * 41 * 40
1 * 2 * 3 * 4 * 5 * 6

8 145 060.

Please note what a huge difference there is - it would seem that two similar lotteries, but the probability of winning in the first case is 21 times greater than in the second.

In lotteries7 out of 49 total number of combinationswill be:

7 out of 49 =

(49)
(7)

49 * 48 * 47 * 46 * 45 * 44 * 43
1 * 2 * 3 * 4 * 5 * 6 * 7

85 900 584

As you can see, the calculation formula is suitable for any lotteries according to the formula XfromY.

For the popular 6 out of 49 scheme in Europe, the probability of hitting the jackpot according to this formula is 1 in 13,983,816.

If we are talking about lotteries like EuroMillions , where there are additional balls, then the number of combinations is simply multiplied

So, for the mentioned EuroMillionsthe formula looks like this:

“5 out of 50” =

(50)
(5)

50 x 49 x 48 x 47 x 46
1 x 2 x 3 x 4 x 5

2,118,760 combinations.

“2 out of 11” =

(11)
(2)

11 x 10
1 x 2

55 combinations.

Total - 2,118,760 x 55 = 116,531,800 combinations Euro Millions.

For Euro Jackpot number of combinations equals respectively - 2,118,760 x28 = 59,325,280 combinations.

To calculate the dropout lottery winnings Let's introduce the concept of probability:

Consider the case of lottery 5 out of 36:

As we already know, the total number of combinations is 376,992.

Probable number of wins = C(4.5)*C(1.31).

Those.

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

31
1

Thus, we divide total number winnings are 376,992 per 155 and we get 1 win per 2,432 combinations.

For 3 guessed numbers:

5 x 4 x 3
1 x 2 x 3

x
1 x 2 x 3

44 950

Those. 1 win per 8 combinations.

Using this data we can calculate the lottery return percentage. Let's say we play state lotto using the formula 5 out of 36 and marked 2432. With the current ticket price of 40 rubles, we will spend 97,280 rubles. On average, according to the above calculations, we will get one four, 30 threes and 300 twos. Multiplying by the winning rates (4000, 400 and 40 rubles, respectively) we get 28,000 rubles. Divide 97280 by 28,000 and we get that the return is about 34.7%.

According to data from the official Gosloto website, the results of draw No. 1336 dated July 30 look like this (up-to-date information on the results of the draws of all the most popular Russian and world lotteries can be found in the lottery draws section):

180,777 bets in the amount of 7,231,080 rubles. According to the results of the draw, the winnings amounted to 2,110,040 rubles. Those. still the same 34%. About 2.3 million rubles went into the jackpot. Gosloto's profit for the circulation from game 5 out of 36 alone amounted to approximately 2.8 million rubles. Those. Gosloto, or rather a commercial company (more about the legal structure gosloto), the company behind this brand, keeps 30% of the proceeds for itself.

Now let's look at probability of winning the lottery like Russian lotto, i.e. those in which there are 90 barrels, and 30 numbers are crossed out on the ticket.

According to the lottery rules, a ticket wins the jackpot if all 15 numbers are on the ticket on the 15th move. The result is lottery 15 out of 90. According to the above formula, the number of such combinations without taking into account the order is 45795673964460800.

As you can see, this number is significant more quantity combinations for classic lotteries such as 5 out of 36, 6 out of 45, as well as lotteries with extra balls– such as Euromillions and American lotteries – Megamillions and Powerball.

Spanish lotteries such as ElGordo and LotereaNacional stand apart, in which a number from 00000 to 99999 is written on each ticket. That is, for these lotteries the probability of winning is 1 in 100,000.

Based on the above information, using the above formulas, you can easily answer the question of what is the chance of winning the lottery.

And if we take into account that in such lotteries the winning rules for other classes of winnings sometimes also depend on the line numbers, the order of the barrels, etc., then it is obvious that in terms of the probability of winning, such lotteries are noticeably inferior to classical schemes.


In conclusion, we would like to cite an interesting paradox of the lottery:

It is quite expected that this particular ticket will not hit the jackpot, but you should not think that it will not hit any of the tickets.

There is no doubt that at least once in life everyone has asked themselves the question: how to win the 6 out of 45 lottery? Indeed, the winning ticket is real chance improve your financial situation and fulfill your cherished desires, and at the same time invest as little as possible in it. But practice shows: the lucky ones who won large sums very little money. I wonder what it depends on? Is there some kind of pattern or is this a matter of luck?

What are the chances of winning?

Surely each of us, when buying another lottery ticket, hopes that it will certainly be a winner. One only has to think about the fact that there are a huge number of combinations in the 6 out of 45 lottery and only one of them can instantly turn ordinary person into a multimillionaire.

So, using a mathematical formula, it was established that the number of possible combinations in the 6 out of 45 lottery is 8,145,060. Just think about it: the chance of winning is negligible. But despite this, in history there are many cases of winning large cash prizes. Based on them, we can come to the conclusion, 6 out of 45.

How to guess the numbers?

The principle of the lottery is that the player must choose 6 numbers out of 45 on the playing field. The one who correctly guesses the combination completely will receive a super prize. As a rule, it amounts to more than one million rubles in Russia. Some people bet numbers “at random”, others use some strategy, others use the same combination over and over again, in the hope that sooner or later it will turn out to be winning. In general, everyone has their own way to win the 6 out of 45 lottery.

There are also methods for determining winning numbers using magical attributes. One of these methods is called dowsing. So, how to win the 6 out of 45 lottery using a pendulum? In fact, the method is quite simple and accessible, not requiring special knowledge and skills. For the ritual you will need a sheet of paper on which you need to write all 45 numbers. Next, you need to take some kind of pendant and hold it over each number in turn; if it starts to swing over one or several of them, then perhaps it’s worth noting this particular number. The method, of course, at first glance does not inspire confidence, but clairvoyants often use pendulums, which means it can also be considered for this purpose.

Statistics

In each game, the organizers keep statistics, in this case we're talking about about the frequency of occurrence of certain numbers. This information is widely available to players, and you can view it on the official lottery website, if there is one, of course. Regular buyers of lottery tickets use this method to play, while others, by the way, on the contrary, bet on numbers that appear less frequently according to statistics.

Also, many players believe that lottery organizers calculate combinations in advance so that there are as few winning tickets. In fact, this is extremely difficult to do, unless, of course, we are talking about playing online, and winning numbers automatically selected by the computer program.

So, one of the methods for determining a “lucky” combination is to determine the system for the occurrence of certain numbers, that is, to keep statistics. But this, of course, does not provide any guarantees, as do other methods. And it is also not possible to definitively answer how to win the 6 out of 45 lottery using statistics.

What do players who managed to get cash prizes in the 6 out of 45 lottery say:

  1. There is no need to bet on numbers that are associated with any events; it is better to bet at random.
  2. In one game, either even numbers do not appear, or therefore it is worth combining the choice of both in one ticket.
  3. Numbers need to be distributed evenly throughout playing field, because it is rare that all zithers are located in one part.
  4. Need to count total amount selected numbers, it should not be less than 106 and more than 179.
  5. Experienced players testify that you should not play on one bet, it is better to spend money and buy several tickets and increase your chance of winning.

This is a few simple tips how to win lottery 6 out of 45. Reviews experienced players indicate that in order to win, you must first play. Because many of those who received good cash prizes said that they played for years and regularly, and in the end luck smiled on them.

How to win the lottery?

Apparently, there are quite a lot of gamblers in our country. And even though there are many tips, recommendations, and secrets on how to win the 6 out of 45 super prize in the lottery, not everyone is lucky. From this we can conclude that you shouldn’t rely too much on them; most likely, victory really depends largely on luck.

Some people participate in the drawing only because they enjoy the process itself. Others constantly entertain the hope of a big cash winnings. And someone completely unexpectedly becomes a millionaire. In general, the conclusion is clear - you need to listen to your intuition and believe in luck.

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