Random number regeneration program. Random number generator online

Various lotteries, drawings, etc. are often held in many groups or publics in in social networks, Instagram, etc., and is used by account owners to attract new audiences to the community.

The result of such drawings often depends on the user's luck, since the recipient of the prize is determined randomly.

To make this determination, lottery organizers almost always use a generator random numbers online or pre-installed, distributed free of charge.

Choice

Quite often, choosing such a generator can be difficult, since their functionality is quite different - for some it is significantly limited, for others it is quite wide.

A fairly large number of such services are being implemented, but the difficulty is that they differ in scope.

Many, for example, are tied by their functionality to a specific social network (for example, many generator applications on VKontakte work only with links from this social network).

The simplest generators simply randomly determine a number within a given range.

This is convenient because it does not associate the result with a specific post, which means it can be used for sweepstakes outside the social network and in various other situations.

They essentially have no other use.

<Рис. 1 Генератор>

Advice! When choosing the most suitable generator, it is important to consider what it will be used for.

Specifications

For the fastest process of choosing the optimal online random number generation service, the table below shows the main specifications and functionality of such applications.

All applications discussed in the table are described in more detail below.

<Рис. 2 Случайные числа>

RandStuff

<Рис. 3 RandStuff>

You can use this application online by following the link to its official website http://randstuff.ru/number/.

This is a simple random number generator, characterized by fast and stable operation.

It is successfully implemented both in the format of a separate independent application on the official website, and as an application on the VKontakte social network.

The peculiarity of this service is that it can select a random number both from a specified range and from a specific list of numbers that can be specified on the site.

Pros:

• Stable and fast work;
• Lack of direct connection to a social network;
• You can select one or several numbers;
• You can only choose among the specified numbers.

Minuses:

• Inability to conduct a VKontakte drawing (this requires a separate application);
• Applications for VKontakte do not run in all browsers;
• The result sometimes seems predictable because only one calculation algorithm is used.

User reviews about this application are as follows: “We determine through this service the winners in VKontakte groups. Thank you,” “You are the best,” “I only use this service.”

Cast Lots

<Рис. 4 Cast Lots>

This application is a simple function generator, implemented on the official website in the form of a VKontakte application.

There is also a generator widget for inserting into your website.

The main difference from the previous described application is that this allows you to disable the repetition of the result.

That is, when carrying out several generations in a row in one session, the number will not be repeated.

• Availability of a widget for inserting into a website or blog;
• Possibility to disable result repetition;
• The presence of the “even more randomness” function, after activation of which the selection algorithm changes.

Negative:

• Inability to determine several results at once;
• Inability to select from a specific list of numbers;
• To select a winner in publics, you must use a separate VKontakte widget.

User reviews are as follows: “It works stably, it’s quite convenient to use”, “Convenient functionality”, “I only use this service”.

Random number

<Рис. 5 Случайное число>

This service is located at http://randomnumber.rf/.

Simple generator with minimum functions and additional features.

Can randomly generate numbers within a specified range (maximum from 1 to 99999).

The site does not have any graphic design, and therefore the page loads easily.

The result can be copied or downloaded with the click of a button.

Negative:

• Lack of a widget for VKontakte;
• There is no possibility of holding draws;
• There is no way to embed the result into a blog or website.

Here's what users say about this service: “A good generator, but not enough functions”, “Very few features”, “Suitable for quickly generating numbers without unnecessary settings.”

Randomus

<Рис. 6 Рандомус>

You can use this random number generator at http://randomus.ru/.

Another one, quite simple, but functional random number generator.

The service has sufficient functionality for determining random numbers, but it is not suitable for conducting draws and other more complex processes.

Negative:

• Impossibility of holding draws based on reposts of posts, etc.
• There is no application for VKontakte or a widget for the site;
• It is not possible to disable repeating results.

Note that ideally the random number distribution density curve would look as shown in Fig. 22.3. That is, ideally, each interval contains the same number of points: N i = N/k , Where N — total number points, k number of intervals, i= 1, , k .

It should be remembered that generating an arbitrary random number consists of two stages:

• generating a normalized random number (that is, uniformly distributed from 0 to 1);
• normalized random number conversion r i to random numbers x i, which are distributed according to the (arbitrary) distribution law required by the user or in the required interval.

Random number generators according to the method of obtaining numbers are divided into:

• physical;
• tabular;
• algorithmic.

Physical RNG

An example of a physical RNG can be: a coin (“heads” 1, “tails” 0); dice; a drum with an arrow divided into sectors with numbers; hardware noise generator (HSG), which uses a noisy thermal device, for example, a transistor (Fig. 22.422.5).

Tabular RNG

Tabular RNGs use specially compiled tables containing verified uncorrelated, that is, in no way dependent on each other, numbers as a source of random numbers. In table Figure 22.1 shows a small fragment of such a table. By traversing the table from left to right from top to bottom, you can obtain random numbers evenly distributed from 0 to 1 with the required number of decimal places (in our example, we use three decimal places for each number). Since the numbers in the table do not depend on each other, the table can be traversed different ways, for example, from top to bottom, or from right to left, or, say, you can select numbers that are in even positions.

Dignity this method is that it produces truly random numbers since the table contains verified uncorrelated numbers. Disadvantages of the method: storing a large number of digits requires a lot of memory; There are great difficulties in generating and checking such tables; repetitions when using a table no longer guarantee randomness number sequence, and therefore the reliability of the result.

There is a table containing 500 absolutely random verified numbers (taken from the book by I. G. Venetsky, V. I. Venetskaya “Basic mathematical and statistical concepts and formulas in economic analysis”).

Algorithmic RNG

The numbers generated by these RNGs are always pseudo-random (or quasi-random), that is, each subsequent number generated depends on the previous one:

r i + 1 = f(r i) .

Sequences made up of such numbers form loops, that is, there is necessarily a cycle that repeats an infinite number of times. Repeating cycles are called periods.

The advantage of these RNGs is their speed; generators require virtually no memory resources and are compact. Disadvantages: the numbers cannot be fully called random, since there is a dependence between them, as well as the presence of periods in the sequence of quasi-random numbers.

Let's consider several algorithmic methods for obtaining RNG:

• method of median squares;
• method of middle products;
• stirring method;
• linear congruent method.

Midsquare method

There is some four-digit number R 0 . This number is squared and entered into R 1 . Next from R 1 takes the middle (four middle digits) new random number and writes it into R 0 . Then the procedure is repeated (see Fig. 22.6). Note that in fact, as a random number you need to take not ghij, A 0.ghij with a zero and a decimal point written on the left. This fact is reflected as in Fig. 22.6, and in subsequent similar figures.

Disadvantages of the method: 1) if at some iteration the number R 0 becomes equal to zero, then the generator degenerates, so the correct choice of the initial value is important R 0 ; 2) the generator will repeat the sequence through M n steps (at best), where n number digit R 0 , M base of the number system.

For example in Fig. 22.6: if the number R 0 will be represented in the binary number system, then the sequence of pseudo-random numbers will be repeated in 2 4 = 16 steps. Note that the repetition of the sequence can occur earlier if the starting number is chosen poorly.

The method described above was proposed by John von Neumann and dates back to 1946. Since this method turned out to be unreliable, it was quickly abandoned.

Midproduct method

Number R 0 multiplied by R 1, from the result obtained R 2 the middle is extracted R 2 * (this is another random number) and multiplied by R 1 . All subsequent random numbers are calculated using this scheme (see Fig. 22.7).

Stirring method

The shuffle method uses operations to cyclically shift the contents of a cell left and right. The idea of ​​the method is as follows. Let the cell store the initial number R 0 . Cyclically shifting the contents of the cell to the left by 1/4 of the cell length, we obtain a new number R 0 * . In the same way, cycling the contents of the cell R 0 to the right by 1/4 of the cell length, we get the second number R 0**. Sum of numbers R 0* and R 0** gives a new random number R 1 . Further R 1 is entered in R 0, and the entire sequence of operations is repeated (see Fig. 22.8).

Please note that the number resulting from the summation R 0* and R 0 ** , may not fit completely in the cell R 1 . In this case, the extra digits must be discarded from the resulting number. Let us explain this in Fig. 22.8, where all cells are represented by eight binary digits. Let R 0 * = 10010001 2 = 145 10 , R 0 ** = 10100001 2 = 161 10 , Then R 0 * + R 0 ** = 100110010 2 = 306 10 . As you can see, the number 306 occupies 9 digits (in the binary number system), and the cell R 1 (same as R 0) can contain a maximum of 8 bits. Therefore, before entering the value into R 1, it is necessary to remove one “extra”, leftmost bit from the number 306, resulting in R 1 will no longer go to 306, but to 00110010 2 = 50 10 . Also note that in languages ​​such as Pascal, “trimming” of extra bits when a cell overflows is performed automatically in accordance with the specified type of the variable.

Linear congruent method

The linear congruent method is one of the simplest and most commonly used procedures currently simulating random numbers. This method uses the mod( x, y) , which returns the remainder when the first argument is divided by the second. Each subsequent random number is calculated based on the previous random number using the following formula:

r i+ 1 = mod( k · r i + b, M) .

The sequence of random numbers obtained using this formula is called linear congruent sequence. Many authors call a linear congruent sequence when b = 0 multiplicative congruent method, and when b ≠ 0 — mixed congruent method.

For a high-quality generator, it is necessary to select suitable coefficients. It is necessary that the number M was quite large, since the period cannot have more M elements. On the other hand, the division used in this method is a rather slow operation, so for a binary computer the logical choice would be M = 2 N, since in this case finding the remainder of division is reduced inside the computer to binary logical operation"AND". Choosing the largest prime number is also common M, less than 2 N: in the specialized literature it is proven that in this case the low-order digits of the resulting random number r i+ 1 behave just as randomly as the older ones, which has a positive effect on the entire sequence of random numbers as a whole. As an example, one of the Mersenne numbers, equal to 2 31 1, and thus, M= 2 31 1 .

One of the requirements for linear congruent sequences is that the period length be as long as possible. The length of the period depends on the values M , k And b. The theorem we present below allows us to determine whether it is possible to achieve a period of maximum length for specific values M , k And b .

Theorem. Linear congruent sequence defined by numbers M , k , b And r 0, has a period of length M if and only if:

• numbers b And M relatively simple;
• k 1 times p for every prime p, which is a divisor M ;
• k 1 is a multiple of 4, if M multiple of 4.

Finally, let's conclude with a couple of examples of using the linear congruent method to generate random numbers.

It was determined that a series of pseudo-random numbers generated based on the data from example 1 would be repeated every M/4 numbers. Number q is set arbitrarily before the start of calculations, however, it should be borne in mind that the series gives the impression of being random at large k(and therefore q). The result can be improved somewhat if b odd and k= 1 + 4 · q in this case the row will be repeated every M numbers. After a long search k the researchers settled on values ​​of 69069 and 71365.

A random number generator using the data from Example 2 will produce random, non-repeating numbers with a period of 7 million.

The multiplicative method for generating pseudorandom numbers was proposed by D. H. Lehmer in 1949.

Checking the quality of the generator

The quality of the entire system and the accuracy of the results depend on the quality of the RNG. Therefore, the random sequence generated by the RNG must satisfy a number of criteria.

The checks carried out are of two types:

• checks for uniformity of distribution;
• tests for statistical independence.

Checks for uniformity of distribution

1) The RNG should produce close to the following values ​​of statistical parameters characteristic of a uniform random law:

2) Frequency test

A frequency test allows you to find out how many numbers fall within an interval (m r – σ r ; m r + σ r) , that is (0.5 0.2887; 0.5 + 0.2887) or, ultimately, (0.2113; 0.7887). Since 0.7887 0.2113 = 0.5774, we conclude that in a good RNG, about 57.7% of all random numbers drawn should fall into this interval (see Fig. 22.9).

It is also necessary to take into account that the number of numbers falling into the interval (0; 0.5) should be approximately equal to the number of numbers falling into the interval (0.5; 1).

3) Chi-square test

The chi-square test (χ 2 test) is one of the most well-known statistical tests; it is the main method used in combination with other criteria. The chi-square test was proposed in 1900 by Karl Pearson. His remarkable work is considered as the foundation of modern mathematical statistics.

For our case, testing using the chi-square criterion will allow us to find out how much the real The RNG is close to the RNG benchmark, that is, whether it satisfies the uniform distribution requirement or not.

Frequency diagram reference The RNG is shown in Fig. 22.10. Since the distribution law of the reference RNG is uniform, then the (theoretical) probability p i getting numbers into i th interval (all these intervals k) is equal to p i = 1/k . And thus, in each of k intervals will hit smooth By p i · N numbers ( N total number of numbers generated).

A real RNG will produce numbers distributed (and not necessarily evenly!) across k intervals and each interval will contain n i numbers (in total n 1 + n 2 + + n k = N ). How can we determine how good the RNG being tested is and how close it is to the reference one? It is quite logical to consider the squared differences between the resulting number of numbers n i and "reference" p i · N . Let's add them up and the result is:

χ 2 exp. = ( n 1 p 1 · N) 2 + (n 2 p 2 · N) 2 + + ( n k – p k · N) 2 .

From this formula it follows that the smaller the difference in each of the terms (and therefore the less valueχ 2 exp. ), the stronger the law of distribution of random numbers generated by a real RNG tends to be uniform.

In the previous expression, each of the terms is assigned the same weight (equal to 1), which in fact may not be true; therefore, for chi-square statistics, it is necessary to normalize each i th term, dividing it by p i · N :

Finally, let’s write the resulting expression more compactly and simplify it:

We obtained the chi-square test value for experimental data.

In table 22.2 are given theoretical chi-square values ​​(χ 2 theoretical), where ν = N 1 is the number of degrees of freedom, p this is a user-specified confidence level that indicates how much the RNG should satisfy the requirements of a uniform distribution, or p — is the probability that the experimental value of χ 2 exp..

1.64 p 0.674.

Considered acceptable p from 10% to 90% If χ 2 exp. much more than χ 2 theory. n i(that is p i · N is large), then the generator

does not satisfy

the requirement of uniform distribution, since the observed values p go too far from theoretical If χ 2 exp. and cannot be considered random. In other words, such a large confidence interval is established that the restrictions on the numbers become very loose, the requirements on the numbers become weak. In this case, a very large absolute error will be observed. n i Even D. Knuth in his book “The Art of Programming” noted that having χ 2 exp. p i · N In general, it’s not good for small children either, although at first glance this seems wonderful from the point of view of uniformity. Indeed, take a series of numbers 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, they are ideal from the point of view of uniformity, and χ 2 exp.

But if χ 2 exp. p lies in a certain range between two values ​​of χ 2 theor. , which correspond, for example, p= 25% and

= 50%, then we can assume that the values ​​of random numbers generated by the sensor are completely random. p i · N In addition, it should be borne in mind that all values

must be large enough, for example more than 5 (found empirically). Only then (with a sufficiently large statistical sample) can the experimental conditions be considered satisfactory.

So, the verification procedure is as follows.

Tests for statistical independence

1) Checking for the frequency of occurrence of numbers in the sequence

Let's look at an example. The random number 0.2463389991 consists of the digits 2463389991, and the number 0.5467766618 consists of the digits 5467766618. Connecting the sequences of digits, we have: 24633899915467766618. p i It is clear that the theoretical probability i loss

The th digit (from 0 to 9) is equal to 0.1.

2) Checking the appearance of series of identical numbers n Let us denote by L Let us denote by number of series of identical digits in a row of length Let us denote by. Everything needs to be checked m from 1 to m, Where

this is a user-specified number: the maximum occurring number of identical digits in a series. n In the example “24633899915467766618” 2 series of length 2 (33 and 77) were found, that is n 3 = 2 .

2 = 2 and 2 series of length 3 (999 and 666), that is Let us denote by The probability of occurrence of a series of length p Let us denote by is equal to: Let us denote by = 9 10 p(theoretical). That is, the probability of occurrence of a series one character long is equal to: p 1 = 0.9 (theoretical). The probability of a series of two characters appearing is: p 2 = 0.09 (theoretical). The probability of a series of three characters appearing is:

3 = 0.009 (theoretical). p Let us denote by For example, the probability of occurrence of a series one character long is

= 0.9, since there can be only one symbol out of 10, and there are 9 symbols in total (zero does not count). And the probability that two identical symbols “XX” will appear in a row is 0.1 · 0.1 · 9, that is, the probability of 0.1 that the symbol “X” will appear in the first position is multiplied by the probability of 0.1 that the same symbol will appear in the second position “X” and multiplied by the number of such combinations 9. p Let us denote by .

The frequency of occurrence of series is calculated using the chi-square formula we previously discussed using the values

In conclusion, we note that the third chapter of Donald E. Knuth's book The Art of Programming (Volume 2) is entirely devoted to the study of random numbers. It studies various methods generating random numbers, statistical tests of randomness, and converting uniformly distributed random numbers to other types random variables. More than two hundred pages are devoted to the presentation of this material.

It is an obvious fact that luck plays an important role in any undertaking. But when playing the lottery, you need to understand that fortune is the only factor on which the fulfillment of your dreams depends. In most lotteries, to get the jackpot you just need to guess certain numbers in a certain range. In this case, the one presented on our website can help.

We offer a free trial of a simple generator that can completely eliminate the influence human factor And increase your chance of winning. We also present the best and most functional, but simple generators, as well as services that can predict winning combinations of numbers based on special analysis algorithms.

If you want to try your luck in one of the popular lotteries (4 out of 20, 5 out of 36, 6 out of 45), but don’t know what numbers can increase your probability of winning, then we can help. Next we present to your attention review of the TOP 5 most functional, but at the same time easy-to-use lottery number generators with many additional functions and capabilities.

First, let's look at the main criteria of the list.:

TOP 1 - Number generator GSgen.RU

Description: Built-in software implemented in the Javascript programming language and is a pseudo-random number generator. Distributes evenly random numbers, thereby eliminating the subjective perception of players, which influences manual selection.

Advantages: The RNG script allows you to select lucky numbers for Gosloto (and not only) various variations from preset modes. There is the possibility of individual settings for other types of lotteries. Available for free use.

Flaws: There is no way to enter exclusion numbers that you don’t want to see, you can’t get several combinations at once and get a link to the finished result.

TOP 2 – Soft-Arhiv Generator

Description: Another service for generating midrange frequencies for Russian lotteries. Just select the required combination and get the finished result. You don't need any additional software to use it, as it works great online.

Advantages: Has a simple, clear form to fill out and get results. The ability to select a ready-made lottery type, generation settings allows you to include exceptions and the number of required combinations make the service very convenient to use. Also completely free functionality.

TOP 3 - RNG: Calculator888

Description: Calculator888 is in honorable third place among the services under consideration. Like the previous options, it allows you to get the required number of numbers without much effort. Even a novice network user can use the random number generator, as everything is intuitive.

Advantages: Extensive settings will allow you to generate the required number of numbers, set their range, and also determine input options. In addition, unlike previous services, it allows you to get a link to the result. Completely free.

Flaws: The disadvantages include the lack of a choice of ready-made lottery types, which forces you to create the task yourself. You cannot introduce exceptions and get several combinations at once. Accounting of past circulations is also not carried out.

Number generators based on past draws

It is worth drawing your attention to the fact that there are special services that can predict lucky numbers on which you need to bet. Their creators assure users that the analysis and presentation of results is carried out on the basis of the results of the draws, the use probability theory and other mathematical calculations.

However, you should not believe in this unconditionally. We definitely don’t believe in this and believe that any of these services are ones that randomly produce results similar to any other RNG.

However, you can check this yourself. Below we present two more services that provide the ability to select results for state lotto, Viking lotto, keno, sports lotto, etc. taking into account their past circulations. The functionality of some of them is paid.

Let us draw your attention to the fact that you should not pay money for a paid forecast, since this is just money down the drain for combinations that anyone else can give free service. So, continuation best services for generation taking into account the analysis of past circulations:

TOP 4 - RNG taking into account circulations: Fortunablog

Description: According to the developer, the script is capable of not only issuing digital combinations at random, but also analyzes previously dropped balls based on a number of algorithms and probability theory. It is also stated that the purpose of the generator is to select a combination for the jackpot.

Advantages: There are two preset lottery types from which you can try your luck in selecting. However, the main advantage is positioned as taking into account the results of past circulations and, importantly, free use.

TOP 5 - Generator for lottery taking into account draws: Igraivloto

Description: The presented service allows you to get combinations of the most probable winning combinations. The principle of operation is similar to the previous options under consideration, with the exception of certain functionality items.

Advantages: This is a ready-made script for issuing a forecast for the Gosloto 6 out of 45 lottery, which eliminates the need to select the required draw. Positions itself as a site that operates on special algorithms and filters that create the most likely forecasts based on the draws carried out. Allows you to get multiple results at once and share a link to the result.

Flaws: There is no possibility to enter a range of numbers and necessary exceptions. However biggest disadvantage is the provision of paid forecasts, which clearly distinguishes it from its free previous analogues.

Conclusion

Whether you use the services discussed or not, of course, is up to you. On the one hand, the use of such sites can help you select certain combinations, freeing you from difficult choice, since, for example, for a 5 out of 36 draw, absolutely any combination generated or manually selected by the player himself has a probability of winning of 1 in 376,992.

Table showing the probability of winning the lottery:

Compared to other lottery strategies, this option has good chances of winning. However, you should understand that using paid forecasts in this case is not advisable and does not correspond to the probability of winning.

Submitted by online generator random numbers works based on a pseudo-random number generator with a uniform distribution built into JavaScript. Integers are generated. By default, 10 random numbers are output in the range 100...999, the numbers separated by spaces.

Basic settings of the random number generator:

• Amount of numbers
• Number range
• Separator type
• Turn on/off the function of removing repetitions (duplicates of numbers)

The total number is formally limited to 1000, with a maximum of 1 billion. Separator options: space, comma, semicolon.

Now you know exactly where and how to get a free sequence of random numbers in a given range on the Internet.

Application options for a random number generator

A random number generator (RNG in JS with uniform distribution) will be useful for SMM specialists and owners of groups and communities on the social networks Instagram, Facebook, VKontakte, Odnoklassniki to determine the winners of lotteries, competitions and prize draws.

A random number generator allows you to draw prizes among an arbitrary number of participants with a specified number of winners. Contests can be held without reposts and comments - you yourself set the number of participants and the interval for generating random numbers. You can get a set of random numbers online and for free on this site, and you do not need to install any application on your smartphone or program on your computer.

Also, an online random number generator can be used to simulate tossing a coin or dice. However, we have separate specialized services for these cases.

Numbers accompany us everywhere - house and apartment numbers, telephone numbers, car numbers, passport numbers, plastic cards, dates, passwords. Email. We choose some combinations of numbers ourselves, but most we get by chance. Without realizing it, we use randomly generated numbers every day. If we come up with PIN codes, then unique credit or salary card codes are generated by reliable systems that exclude access to passwords. Random number generators provide security in areas that require processing speed, security, and data independence.

The process of generating pseudorandom numbers is subject to certain laws and has been used for a long time, for example, in lotteries. In the recent past, drawings were carried out using lottery machines or lots. Now in many countries winning numbers state lotteries are determined precisely by the set of generated random numbers.

Advantages of the method

So, a random number generator is an independent modern mechanism for random determination combinations of numbers. The uniqueness and perfection of this method lies in the impossibility of external intervention in the process. The generator is a set of programs built, for example, on noise diodes. The device generates a stream of random noise, the current values ​​of which are converted into numbers and form combinations.

Generating numbers provides instant results - it takes a few seconds to create a combination. If we talk about lotteries, participants can immediately find out whether the ticket number matches the winning one. This allows drawings to be held as often as participants want. But the main advantage of the method is its unpredictability and the impossibility of calculating the algorithm for selecting numbers.

How pseudorandom numbers are generated

In fact, random numbers are not random - the series starts from a given number and is generated by an algorithm. A pseudorandom number generator (PRNG or PRNG - pseudorandom number generator) is an algorithm that generates a sequence of seemingly unrelated numbers, usually subject to a uniform distribution. In computer science, pseudorandom numbers are used in many applications: cryptography, simulation modeling, Monte Carlo method, etc. The quality of the result depends on the properties of the PRNG.

The source of generation can be physical noise from cosmic radiation to noise in a resistor, but such devices are almost never used in network security applications. Cryptographic applications use special algorithms that generate sequences that cannot be statistically random. However, a properly chosen algorithm can produce series of numbers that pass most randomness tests. The repetition period in such sequences is greater than the working interval from which the numbers are taken.

Many modern processors contain a PRNG, such as RdRand. As an alternative, sets of random numbers are created and published in a one-time pad (dictionary). The source of numbers in this case is limited and does not provide complete network security.

History of PRNG

A prototype of a random number generator can be considered board game Senet, common in Ancient Egypt in 3500 BC. According to the conditions, two players participated, the moves were determined by throwing four flat black and white sticks - they were a kind of PRNG of that time. The sticks were thrown at the same time, and points were counted: if one fell up with the white side, 1 point and an additional move, two white ones - two points, and so on. The maximum result of five points was received by the player who threw four sticks with the black side.

Nowadays, the ERNIE generator has been used for many years in the UK for lottery draws. There are two main generation methods winning numbers: linear congruent and additive congruent. These and other methods are based on the principle of random selection and are provided by software that endlessly produces numbers, the sequence of which is impossible to guess.

The PRNG operates continuously, for example, in slot machines. According to US law, this required condition, which all software providers must comply with.