Analysis of lottery 4 out of 20 according to Lazarev. Analysis of lottery statistics based on frequency characteristics

So we continue to describe the main methods of analyzing lotteries. Today we’ll talk about frequency characteristics.

There are two main methods for such analysis

• Based on circulation
• Based on a continuous sequence of balls

In the first case, the basis for the analysis of each ball is the following characteristics:

• How long has it been since this ball was dropped? Or how many times has the ball not appeared in the draws?
• How often does this ball usually appear?
• To what extent do ball drops correspond to their drop frequency?

Well, everything is quite simple here, we take a certain ball and count how many days or circulations ago it came out. Let's say we took 3 balls number 1, 2 and 3 and determined that they had not been drawn 10, 20 and 30 draws ago, respectively.

Next, we count how many times the ball was dropped in total and how many runs there were in total and divide one by the other, we get the average frequency of balls being dropped. For example, for ball 1 we determined that its average drop frequency is 20, for the second 10 and for the third 35.

The simplest conclusion suggests itself, because ball 1 appears on average every 20th circulation, and now it has only the 10th circulation, so it is too early for it to appear. For the second ball, the situation is the opposite - on average, it appears every 10th draw, but now it has not appeared for 20 draws. There is only one conclusion - this ball should appear in the near future. For the third ball, the situation is similar to the second, but it has only 5 runs “overdue”, while the second one has 10, so it will be better to choose the second one than the third one.

In general, I think the idea is clear. Now let's complicate things a little! Let's see how often the balls stick to their average drop frequency. I think it’s clear how to do this. Let’s say it turns out that ball 1 on average deviates from the average value to a minus (i.e., it falls out earlier than it should) by 5 draws and to a plus by 3 draws. Thus, we can say that in most cases, ball 1 is drawn alone in the range of 15-23 draws. Those. those 10 runs that went through for him are not included in the range and it is clearly too early for the ball to fall out.

Let’s say for the second ball this range turned out to be very large: 5-20 runs! It turns out that the current delay of 20 circulations is not an anomaly and is quite normal. I think that there is no particular point in continuing further - everything is already clear.

Now let's look at the analysis of drops based on a continuous series of balls.

The point is that the lottery machine does not throw out balls in batches, but one at a time, so ideally consider the lottery machine as a kind of black box that gives out sequences of balls. Those. the balls must be analyzed as a continuous sequence. For example, we have 4 draws:

01 02 03 10 11 12

12 15 13 19 22 23

01 11 22 33 23 21

09 04 05 06 33 11

So they must be taken as one big sequence:

01 02 03 10 11 12 12 15 13 19 22 23 01 11 22 33 23 21 09 04 05 06 33 11

• How many balls ago did this ball come out?
• How often does this ball appear?
• Ball drop range

How effective is this technique? It’s hard to say... the main factors negatively affecting these statistics are the following factors:

• it takes quite a lot of plays to properly estimate the average frequency of a ball falling out
• It is necessary that the sequence was generated continuously by the same lottery machine, otherwise we do not know whether this lottery machine had any drops of balls in the intervals between draws. We also usually don’t know whether the organizers changed the lottery machine itself, which, of course, also negatively affects the reliability of the statistics

One of the most popular Gosloto lotteries - 4 out of 20, continues to occupy an honorable place in our ranking. And all thanks to its very attractive features: a multi-million dollar super prize, 20 other winning categories and an overall increased prize fund - 67% from the proceeds from each ticket sold.

The chances of winning a super prize in Gosloto are 4 out of 20 - 1 in 23,474,025. The overall probability of winning is estimated as 1 to 3.4.

Game Features

The lottery uses the so-called “double matrix”. That is, to place a bet, you must select numbers in two playing fields at once. Essentially it's (4 out of 20) x 2.

The minimum lottery combination is 4 numbers in the range from 1 to 20 in the first field and 4 numbers from 1 to 20 in the second field. Ticket price - from 200 rubles.

Super prize and 21 chances to win

The minimum guaranteed super prize of the lottery is 10,000,000 rubles. A multimillionaire will be the one who matches four numbers in the first playing field and four in the second.

In general, go for it! Personally, I like this lottery!

We welcome all players of the 647th draw of the Gosloto 4 out of 20 lottery to our portal of all-Russian lottery results. On our website at 10:00 Moscow time we will post the results of the 647th Gosloto draw 4 out of 20, by using them you will quickly check tickets dated November 18, 2018. Checking your ticket(s) by number will save you from having to study the rules of the game. All information will be provided by the organizer - the Stoloto lottery company.

You can use ticket number 647 of the draw or by watching the video or the numbers on the receipt (knowledge of the rules of the game is required). In the “Four”, 2 combinations are always formed using a lottery machine, which is located in the studio of the Stoloto company. If all the numbers drawn match the numbers on your ticket, then you receive the accumulated Jackpot, which is more 603,980,748 rubles .

Gosloto results 4 out of 20 draw 647 from November 18, 2018

Field 1: 20/05/04/01

Field 2: 10/04/18/19

Video of the Gosloto lottery 4 out of 20, draw 647 from 11/18/2018

Everything is correct. Fight, search, find and don’t give up

Grade: 5

Only constant play can give the opportunity
develop your own tactics. I've been playing for a long time and
almost always in plus or slight minus.
The overall balance is positive. This is thanks
my programs, which I give away for free, but with some conditions. I want to create a team of players. If you are interested, write to me and I will answer everyone. Vlad2018

Grade: 5

I've never been lucky, but I don't lose hope. Now I’ve started betting less often, the excitement has just gone away. But maybe before the new year. This year they promise a guaranteed prize for the new year of about a billion rubles. On the site you can look at the archives, you can select the numbers that appear most often. Lotteries are an excellent opportunity to improve your financial situation if you win, and the tickets themselves are inexpensive, so you can afford it, I think.

Grade: 5

Its main difference is that there are 2 lottery machines, whereas usually 1 is involved in the lottery. The balls fall out in a random order under the action of a pneumatic installation. Participants mark the numbers on their tickets. The fewer uncrossed numbers remain, the greater the winnings.
Having spent about 2 thousand rubles on my tickets to this lottery, I have already won 2.5. The risk of losing the lottery is also high. One thing I can say for sure is that winning money is given out quite quickly, small amounts almost immediately. I usually spend it on buying new tickets. You can also check tickets on the website. The lottery is reliable and it all depends on luck.

Grade: 4

You should not expect to win a big jackpot in the lottery right away. 4 out of 20 is a state lottery with a combination that actually brings profit to participants more often. This was noticed not only by me, but also by experienced gamers. Playing the lottery is exciting and does not allow you to relax, you can feel the excitement and tickle your nerves.

Grade: 4

The lottery is interesting, but has its own specific differences. The downside for me is that draws are held only 3 times a week, which means waiting and delaying time. I prefer those lotteries that have draws 3 times a day. Live broadcast is carried out, as in others.
But the big plus is that 1 ticket can take part in several drawings simultaneously, but no more than 10. You can subscribe to the lottery and the selected numbers will participate in all Gosloto “4 out of 20” draws. The ticket has 2 fields, in each you need to mark 4 digits, but no less - this is called a bet, but if you select more than 4 digits in any field, then the bet turns out to be expanded, with at least 5 combinations appearing in it. But you need to understand that the detailed rate for the price is very different from the simple one.
Another plus is that the prize is cumulative; if no one wins in the draw, the prize amount is automatically transferred and added to the next draw.

Grade: 4

The 4 out of 20 lottery involves 2 playing fields at once, which distinguishes it from other lotteries, where there is usually only 1 playing field for selecting numbers. The prize fund is more than 60% of the proceeds, which is much higher than in other similar lotteries.
This is a relatively new state lottery. There are already statistics on winnings in such lotteries: 6 out of 36, 4 out of 20, 7 out of 49, etc. I don’t really trust these statistics; I still have faith in a miracle. In addition, I personally know people who actually won, albeit small, but still money. Actually, that’s the only reason I continue to play sometimes. I receive winnings immediately after the drawings, they are paid out quickly.

Grade: 4

The bet is very small - 100 rubles. The probability of winning a super prize is very low - there can be 23.5 million combinations. Tickets can be purchased both paper and electronic. Draws take place on Monday, Wednesday and Saturday. The results are published on several websites at once, including the official Stoloto website. I have never won large sums. Small ones almost always come across - 120, 300 rubles. I consider this kind of lottery just fun and I don’t recommend getting too carried away - the likelihood of losing is much higher, and with it comes disappointment and depression.

Grade: 3

There are only 2 fields in the game, you need to mark the numbers in both. By marking the balls drawn in the lottery machine, you get closer to the main prize. The problem is that there seems to be no way to close both fields. In my opinion, the probability of winning the lottery with such a combination is very low, which is why there are so few winners of big prizes.

Grade: 4

I understand that the chances are slim, but the main thing in the game is passion, emotions and experiences. If it were easy to win, mathematicians would have calculated the formula long ago. But that’s what the game is all about: it’s impossible to calculate anything in it! The rule here is simple, but interesting: you fill in 2 fields, if at least 2 numbers match, then you win. It is curious that they even calculated the number of frequently appearing numbers: 11, 13, 19, 15. But still, the winning was 10 million only once, in November 2017.

Grade: 4

I like that this lottery offers simple, understandable conditions. The minimum ticket price is 100 rubles. To win, you need to guess 4 numbers in the 1st field and 4 numbers in the 2nd playing field. The point is that 1 ticket has 5 parts, which are marked with the letters A, B, C, etc., you need to fill out each field. If you wish, you can not choose the numbers yourself, but rely on chance and mark the “Automatic” option on the ticket. This option implies that the numbers will be selected randomly by a computer.
For 1 ticket you can select the maximum number of circulations - 10 pieces. This means that he will participate in the next 10 draws. You can check your ticket by watching the episode on Mondays, Wednesdays and Saturdays. You can also find out the results at lottery distribution points, install a mobile application, go to the website or by phone.
The advantage of the lottery is that it operates on the basis of government support, which indicates an honest approach.

Grade: 5

The fastest draw takes place in the StateLoto 4 out of 20 lottery. It does not take much time. Here is the highest percentage of winning probability of all known combinations in lotteries, I have calculated. The GosLoto 4 out of 20 lottery is a state lottery, that is, it is controlled by the state, so I trust it more than other similar lotteries.
The principle of the drawing is similar to other lotteries - there are lottery machines in the studio, the balls are mixed with the help of air without human intervention, so the human factor is excluded during the drawing process. Winning depends only on the automatic actions of the machine. For me, this is the only lottery that I trust.

Grade: 5

You can fill out from 1 to 5 parts, selecting numbers in each field. The more parts you fill out, the higher the cost of the ticket and the higher the chance of getting the maximum win. The numbers must be guessed in each of the 2 fields. When filling out the 1st part, the ticket price is 100 rubles.
As with many lotteries, it is possible to rely on chance and select "automatic choice". There are times when people win this way. By the way, the lottery rules make it possible to cross out more than 4 numbers in the field and make a detailed bet. You can also select the number of draws in which the ticket will participate. The lottery is held 3 times a week. Tickets can be purchased at any time, taking into account that sales end 20 minutes before the start of the drawing.

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!