All possible combinations 5 out of 36 list. Secrets of luck or a step-by-step algorithm for winning the lottery

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.

Let's now try to evaluate what is best to play. Let’s say we take and buy back 1 percent of the 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 5 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.
• Time 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 methods described above play a cruel joke on the players. Everyone knows about such methods and, of course, uses them, so combinations built on similar principles are found 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 balls falling out are at least slightly aligned. Accordingly, we can say that the best combination will be the 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.

The lottery "GosLoto "5 out of 36" is one of the most popular in modern Russia. The rules of this lottery are simple. You need to buy a coupon, which contains 6 fields with numbers from 1 to 36. In one or more fields, cross out 5 numbers that, according to you think will come up in the next drawing. If you match all 5 numbers, you will win a large amount of money. How to win at "5 out of 36"?

Tips for playing the lottery successfully

There are some tricks you can use to help increase your chances of winning.

Same combination of numbers

Choose a combination of 5 numbers for yourself. And it doesn’t even matter which one, as long as you like it. Bet on it regularly. The "5 out of 36" draw is played twice a day. Sooner or later your combination will come up. There are already examples of the success of such a strategy.

Circulation statistics and probability theory

It only seems at first glance that the numbers appear randomly during the drawing. In fact, there are patterns here too, only very complex ones. Keep track of the statistics of the latest draws (which numbers appear frequently, which ones rarely, what is the sum of the drawn numbers), study the mathematical theory of probability, develop your own system, and your chances of success will increase.

Help magic

There are a great many magical ways to attract good luck and wealth. Find yourself a talisman, a spell, worship the gods of wealth, rearrange the furniture according to Feng Shui. Moreover, what is important is not so much what ritual you choose, but the sincerity and depth of your belief in the inevitability of a positive result. Constant concentration of consciousness on what you want and complete abstraction from outsiders lead to an effect inexplicable by logic: you get what you really want.

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

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

Odds of winning 5 out of 36

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

Odds of winning 6 out of 45

1 of 8 145 060

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

Odds of winning the lottery 7 out of 49

1 in 85 900 584

The odds of winning the 7/49 lottery are 1 in 85.9 million - winning the jackpot is usually low, but here they are completely prohibitive. Apart from luck, there is hardly anything that will help you achieve real success...

Probability of winning in KENO

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

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

Probability of winning in Russian Lotto, Golden Key, State Housing Lottery (GZHL)

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

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

Probability of winning in Gosloto TOP-3

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

Hello!

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

Sincerely,

Ivan Melnikov.

1. Mathematical odds of winning

   • Simple calculation with factorials

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

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

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

Therefore, here is the formula:

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

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

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

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

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

• A little about probability theory

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

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

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

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

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

1. Why doesn't probability theory work?

   • Less than ideal conditions

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

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

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

• Sum of winning numbers

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

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

• Even or odd?

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

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

• Popular groups of numbers

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

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

• Is it worth betting on numbers from past draws?

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

• Consecutive numbers. To choose or not to choose?

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

• Numbers with a single step: win or lose?

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

• More than one ticket: yes or no?

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

1. World lottery statistics

   • Mega millions

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

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

The remaining dependencies are shown in the table:

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

Statistics of golden balls drawn throughout the Mega Millions drawings.

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

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

1. Winners' stories

   • Lucky compatriots

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

• 390 million US dollars in one hand

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

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

1. conclusions

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

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

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

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

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

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

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

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

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

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

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.

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:

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

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:

Please note what a huge difference there is - two seemingly 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:

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:

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 occurrence of a lottery win, we 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.

Thus, we divide the total number of wins 376,992 by 155 and we get 1 win per 2,432 combinations.

For 3 guessed numbers:

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 draw 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 significantly greater than the number of combinations for classic lotteries such as 5 out of 36, 6 out of 45, as well as lotteries with additional 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 one should not assume that none of the tickets will hit the jackpot.