The best random number generator. Random number generator online
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Online number generator in 1 click
The random number generator, which is presented on our website, is very convenient. For example, it can be used in sweepstakes and lotteries to determine the winner. The winners are determined in this way: the program produces one or more numbers in any range specified by you. Fraudulent results can be immediately ruled out. And thanks to this, the winner is determined by an honest choice.
Sometimes it is necessary to obtain a certain number of random numbers at once. For example, you want to fill out a “4 out of 35” lottery ticket, trusting to chance. You can check: if you toss a coin 32 times, what is the probability that 10 reverses will appear in a row (heads/tails may well be assigned the numbers 0 and 1)?
Random number online video instruction - randomizer
Our number generator is very easy to use. It does not require downloading a program to your computer - it can be used online. To get the number you need, you need to set the range of random numbers, the quantity and, if desired, the number separator and eliminate repetitions.
To generate random numbers in a specific frequency range:
- Select a range;
- Specify the number of random numbers;
- The “Number separator” function serves for the beauty and convenience of their display;
- If necessary, enable/disable repetitions using the checkbox;
- Click the "Generate" button.
As a result, you will receive random numbers in a given range. The result of the number generator can be copied or sent by e-mail. It would be best to take a screenshot or video of this generation process. Our randomizer will solve any of your problems!
Random number generator for lottery tickets is provided free of charge in an “as is” format. The developer does not bear any responsibility for material and non-material losses of script users. You may use this service at your own risk. However, no matter what, you definitely don’t want to take risks :-).
Random numbers for online lottery tickets
This software (RNG in JS) is a pseudo-random number generator implemented using the Javascript programming language. The generator produces a uniform distribution of random numbers.
This allows you to knock out a “wedge with a wedge” on the RNG with a uniform distribution from the lottery company to respond with random numbers with a uniform distribution. This approach eliminates the subjectivity of the player, since people have certain preferences in choosing numbers and numbers (Birthdays of relatives, memorable dates, year, etc.), which affect the selection of numbers manually.
The free tool helps players select random numbers for lotteries. The random number generator script has a set of pre-configured modes for Gosloto 5 out of 36, 6 out of 45, 7 out of 49, 4 out of 20, Sportloto 6 out of 49. You can select a random number generation mode with free settings for other lottery options.
Lottery winning predictions
A random number generator with uniform distribution can serve as a horoscope for a lottery draw, although the probability that the forecast will come true is low. But still, using a random number generator has good probability winnings compared to many other lottery strategies and additionally frees you from the agony of complex selection of lucky numbers and combinations. For my part, I do not advise you to give in to the temptation and buy paid forecasts; it is better to spend this money on a textbook on combinatorics. You can learn a lot of interesting things from it, for example, the probability of winning the jackpot in Gosloto is 5 out of 36 1 To 376 992 . And the probability of getting the minimum prize by guessing 2 numbers is 1 To 8 . The forecast based on our RNG has the same probabilities of winning.
There are requests on the Internet for random numbers for the lottery, taking into account past draws. But provided that the lottery uses RNG with a uniform distribution and the probability of getting one or another combination does not depend on each draw, then it is pointless to try to take into account the results of past draws. And this is quite logical, since it is not profitable for lottery companies to allow participants to simple methods increase your likelihood of winning.
There is often talk that lottery organizers are rigging the results. But in fact, this makes no sense, even, on the contrary, if lottery companies influenced the results of the lottery, then one could find winning strategy, but so far no one has succeeded. Therefore, it is very profitable for lottery organizers that the balls fall out with uniform probability. By the way, the estimated return on lottery 5 out of 36 is 34.7%. Thus, the lottery company retains 65.3% of the proceeds from the sale of tickets, part of the funds (usually half) is allocated to the formation of the jackpot, the rest of the money goes to organizational expenses, advertising and net profit companies. Circulation statistics perfectly confirm these figures.
Hence the conclusion - do not buy meaningless forecasts, use a free random number generator, take care of your nerves. Let our random numbers be for you lucky numbers. Have a good mood and have a nice day!
Etc., and is used by account owners to attract new audience 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 an online or pre-installed random number generator that is 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 only work with links from this one).
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.
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.
| Name | Social network | Multiple results | Select from a list of numbers | Online widget for the site | Select from a range | Disabling repetitions |
|---|---|---|---|---|---|---|
| RandStuff | Yes | Yes | No | Yes | No | |
| Cast Lots | Official website or VKontakte | No | No | Yes | Yes | Yes |
| Random number | Official site | No | No | No | Yes | Yes |
| Randomus | Official site | Yes | No | No | Yes | No |
| Random numbers | Official site | Yes | No | No | No | No |
All applications discussed in the table are described in more detail below.
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 stand-alone application on the official website, and as an application in .
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.
- 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.
User reviews about this application are as follows: “We determine winners in VKontakte groups through this service. Thank you,” “You are the best,” “I only use this service.”
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.
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 .
generated theoretically by an ideal generator
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 (HS), which uses a noisy thermal device, for example, a transistor (Fig. 22.422.5).
| Task “Generating random numbers using a coin” | |
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Generate a random three-digit number, uniformly distributed in the range from 0 to 1, using a coin. Accuracy three decimal places. |
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The first way to solve the problem
Draw an interval from 0 to 1. Reading the numbers in sequence from left to right, split the interval in half and each time choose one of the parts of the next interval (if a 0 comes up, then the left one, if a 1 comes up, then the right one). Thus, you can get to any point in the interval, as accurately as you like. So, 1 : the interval is divided in half and , the right half is selected, the interval is narrowed: . Next number 0 : the interval is divided in half and , the left half is selected, the interval is narrowed: . Next number 0 : the interval is divided in half and , the left half is selected, the interval is narrowed: . Next number 1 : the interval is divided in half and , the right half is selected, the interval is narrowed: . According to the accuracy condition of the problem, a solution has been found: it is any number from the interval, for example, 0.625. In principle, if we take a strict approach, then the division of intervals must be continued until the left and right boundaries of the found interval COINCIDE with an accuracy of the third decimal place. That is, from the point of view of accuracy, the generated number will no longer be distinguishable from any number from the interval in which it is located.
The second way to solve the problem
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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.
| Table 22.1. Random numbers. Evenly random numbers distributed from 0 to 1 |
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| Random numbers | Evenly distributed 0 to 1 random numbers |
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| 9 | 2 | 9 | 2 | 0 | 4 | 2 | 6 | 0.929 |
| 9 | 5 | 7 | 3 | 4 | 9 | 0 | 3 | 0.204 |
| 5 | 9 | 1 | 6 | 6 | 5 | 7 | 6 | 0.269 |
Dignity this method is that it produces truly random numbers since the table contains verified uncorrelated numbers. Disadvantages of the method: for storage large quantity numbers require a lot of memory; There are great difficulties in generating and checking this kind of tables; repetitions when using a table no longer guarantee the randomness of the numerical 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 added to the left. This fact is reflected as in Fig. 22.6, and in subsequent similar figures.
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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 (in best case scenario), 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 presented in binary system number, 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).
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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 cell contents to the left by 1/4 of the cell length, we get 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).
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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”, the 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 the 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).
in case of checking it for frequency test
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 (total of 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 generated numbers).
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 uniform distribution, or p is the probability that the experimental value of χ 2 exp..
| will be less than the tabulated (theoretical) χ 2 theor. or equal to it |
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| Table 22.2. | Some percentage points of the χ 2 distribution | p = 1% | p = 5% | p = 25% | p = 50% | p = 75% | |
| ν = 1 | 0.00016 | 0.00393 | 0.1015 | 0.4549 | 1.323 | 3.841 | 6.635 |
| ν = 2 | 0.02010 | 0.1026 | 0.5754 | 1.386 | 2.773 | 5.991 | 9.210 |
| ν = 3 | 0.1148 | 0.3518 | 1.213 | 2.366 | 4.108 | 7.815 | 11.34 |
| ν = 4 | 0.2971 | 0.7107 | 1.923 | 3.357 | 5.385 | 9.488 | 13.28 |
| ν = 5 | 0.5543 | 1.1455 | 2.675 | 4.351 | 6.626 | 11.07 | 15.09 |
| ν = 6 | 0.8721 | 1.635 | 3.455 | 5.348 | 7.841 | 12.59 | 16.81 |
| ν = 7 | 1.239 | 2.167 | 4.255 | 6.346 | 9.037 | 14.07 | 18.48 |
| ν = 8 | 1.646 | 2.733 | 5.071 | 7.344 | 10.22 | 15.51 | 20.09 |
| ν = 9 | 2.088 | 3.325 | 5.899 | 8.343 | 11.39 | 16.92 | 21.67 |
| ν = 10 | 2.558 | 3.940 | 6.737 | 9.342 | 12.55 | 18.31 | 23.21 |
| ν = 11 | 3.053 | 4.575 | 7.584 | 10.34 | 13.70 | 19.68 | 24.72 |
| ν = 12 | 3.571 | 5.226 | 8.438 | 11.34 | 14.85 | 21.03 | 26.22 |
| ν = 15 | 5.229 | 7.261 | 11.04 | 14.34 | 18.25 | 25.00 | 30.58 |
| ν = 20 | 8.260 | 10.85 | 15.45 | 19.34 | 23.83 | 31.41 | 37.57 |
| ν = 30 | 14.95 | 18.49 | 24.48 | 29.34 | 34.80 | 43.77 | 50.89 |
| ν = 50 | 29.71 | 34.76 | 42.94 | 49.33 | 56.33 | 67.50 | 76.15 |
| ν > 30 | ν p = 95% ν ) · x p p = 99% x 2 p+ sqrt(2 + 2/3 · 2/3 + ν )) | ||||||
| x p = | O | (1/sqrt( | 2.33 | 0.00 | 0.674 | 1.64 | 2.33 |
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
Even D. Knuth in his book “The Art of Programming” noted that having χ 2 exp.
for small ones, in general, it’s also not good, although this seems, at first glance, to be 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. p will be practically zero, but you are unlikely to recognize them as random. If χ 2 exp. If χ 2 exp. n i much less than χ 2 theory. p i · N (that is
small), then the generator p the requirement of a random uniform distribution, since the observed values p too close to theoretical
and cannot be considered random. p i · N But if χ 2 exp.
lies in a certain range between two values of χ 2 theor. , which correspond, for example,
= 25% and
= 50%, then we can assume that the random number values generated by the sensor are completely random.
In addition, it should be borne in mind that all values
must be large enough, for example more than 5 (found out empirically). Only then (with a sufficiently large statistical sample) can the experimental conditions be considered satisfactory. p i So, the verification procedure is as follows. i 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. n It is clear that the theoretical probability loss It is clear that the theoretical probability The th digit (from 0 to 9) is equal to 0.1. It is clear that the theoretical probability 2) Checking the appearance of series of identical numbers m Let us denote by m L
number of series of identical digits in a row of length n. Everything needs to be checked n 3 = 2 .
from 1 to It is clear that the theoretical probability, Where p It is clear that the theoretical probability this is a user-specified number: the maximum occurring number of identical digits in a series. It is clear that the theoretical probability In the example “24633899915467766618” 2 series of length 2 (33 and 77) were found, that is p 2 = 2 and 2 series of length 3 (999 and 666), that is p The probability of occurrence of a series of length p is equal to:
= 9 10 p It is clear that the theoretical probability= 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.
The frequency of occurrence of series is calculated using the chi-square formula we previously discussed using the values p It is clear that the theoretical probability .
Note: The generator can be tested multiple times, but the tests are not complete and do not guarantee that the generator produces random numbers. For example, a generator that produces the sequence 12345678912345 will be considered ideal during tests, which is obviously not entirely true.
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 criteria randomness, as well as converting uniformly distributed random numbers to other types random variables. More than two hundred pages are devoted to the presentation of this material.
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