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# Falsification of probability

 Falsification of probability exploring possibility of falsification of random qbasic qb64 programs were created in an hour and a table using formulas = CASEBETWEEN(0;1) = IF (B3 = B2; C2 + 1; 0) = COUNTIF (C\$3: C\$55000; D2) = SUM(E2:E10) = E2 / E3 idea: fake a 50% chance results: research E green pure excel: randomly distributed naturally research 0 yellow qb 0: randomly distributed naturally research 1 in red qb 1: explicit fake equal number in a row research 2 violet qb 2: smart fake but not all programmed and skew due to algorithm Conclusion: identify fake random real Expand|Select|Wrap|Line Numbers ' 0.bas OPEN "0.txt" FOR OUTPUT AS #1 FOR s = 1 TO 50000: PRINT #1, (INT(RND * 1000) MOD 2): NEXT CLOSE Expand|Select|Wrap|Line Numbers ' 1.bas OPEN "1.txt" FOR OUTPUT AS #1 FOR d = 1 TO 5: FOR s = 1 TO 100 FOR i = 1 TO s: PRINT #1, 1: NEXT FOR i = 1 TO s: PRINT #1, 0: NEXT NEXT: NEXT: CLOSE Expand|Select|Wrap|Line Numbers ' 2.bas OPEN "2.txt" FOR OUTPUT AS #1 FOR k = 1 TO 100: FOR s = 1 TO 7 FOR d = 1 TO 2 ^ (7 - s) FOR i = 1 TO s: PRINT #1, 1: NEXT FOR i = 1 TO s: PRINT #1, 0: NEXT NEXT: NEXT: NEXT: CLOSE sequence fake shuffled turns into a random sequence and began to correspond to distributions and excel more clearly than programs but c# synthesis programs are possible online using a random synthesis program and dividing into small 0 and large 1 synthesized 55000 random and tested despite normality of number of consecutive 0...7 a larger number in a row is not possible therefore sequence is worse than usual rnd Expand|Select|Wrap|Line Numbers 'rndxx.bas OPEN "rndxxx.txt" FOR OUTPUT AS #1   FOR i = 1 TO 55555: r = Rand     IF r < 0.5 THEN PRINT #1, 0 ELSE PRINT #1, 1     'IF r <= 0.5 THEN PRINT #1, 0 ELSE PRINT #1, 1     'IF r <= 0.7 THEN PRINT #1, 0 ELSE PRINT #1, 1 NEXT: CLOSE   FUNCTION Rand: STATIC Seed x1 = (Seed * 214013 + 2531011) MOD 2 ^ 24 Seed = x1: Rand = x1 / 2 ^ 24 END FUNCTION in C# randomness is also low-power I suppose understood by people as supposedly normal Expand|Select|Wrap|Line Numbers using System;using System.Linq; using System.Collections.Generic; using System.Text.RegularExpressions; namespace Rextester { public class Program     { public static void Main(string[] args)         { Random rand = new Random(); for (int i = 1; i < 5555; i++) { var d = rand.Next(2); if (d<0.5)     Console.WriteLine("0");      else Console.WriteLine("1"); }}}} on-line compiler: https://rextester.com/WXH62544 significant reliable probability: shuffled that is: 2-sided and that is: integraly probability Program peretas.bas creates a sequence random a: 0 and 1 by manual algorithm from Internet and program creates random d: 0 ... 77777 for shuffling and sorting an array d array a is ordered and perhaps against repetition it is better to shuffle cards 1000000 Expand|Select|Wrap|Line Numbers 'peretas.bas DIM a(55555), d(55555)   OPEN "aa.txt" FOR OUTPUT AS #1: OPEN "dd.txt" FOR OUTPUT AS #2 OPEN "aaaa.txt" FOR OUTPUT AS #3: OPEN "dddd.txt" FOR OUTPUT AS #4   FOR i = 1 TO 55555: r = Rand: a(i) = INT(r * 2): PRINT #1, a(i): NEXT FOR i = 1 TO 55555: r = Rand: d(i) = INT(r * 77777): PRINT #2, d(i): NEXT   FOR i = 1 TO 55554: FOR j = i TO 55555         IF d(i) > d(j) THEN SWAP d(i), d(j): SWAP a(i), a(j) NEXT: NEXT   FOR i = 1 TO 55555: PRINT #3, a(i): PRINT #4, d(i): NEXT CLOSE   FUNCTION Rand STATIC Seed x1 = (Seed * 214013 + 2531011) MOD 2 ^ 24 Seed = x1 Rand = x1 / 2 ^ 24 END FUNCTION Theoretical values in Excel Excel via formulas =C3/2 =D3+C4 =D4*55000 show: out of 55000 for 7 steps covered 54570 numbers in their sequences and probably deviation betrays a false accident and shuffling involved 54885 close to theory Theoretical values in Excel Excel via formulas https://www.youtube.com/watch?v=YIJmgOTnkTU&t=33 Dec 28 '19 #1
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 Check for randomness of digits of number of PI Using 55,000 digits of pi first in Word translated to column by replacement Excel compiles formulas for dividing into: even \ odd and small \ big and then my tables are used at same time comparing with theoretical separation Results: average for both divisions: 0.5 and separation matches chance by true and its still possible to shuffle and its still possible to explore other constants and roots  Meaning of task: true chance for people is unnatural and it is possible to synthesize low-power human probabilities But if we are talking about overcoming chance understanding wave of probability increases reliability Probability waves increase reliability: my development of past 10th anniversary Dec 30 '19 #2
 Invented by me at random algorithm of RNG where is trigonometry used check shows distribution is bad comparing even\odd and small\large but shuffling turns array into a normal one I came up with an algorithm Blizzard at school in last century even under old regime and in our century about same too foreign called vortex Blizzard algorithm: number 1 is random and is added random increment and control range and if necessary controlled repetition of numbers Expand|Select|Wrap|Line Numbers 'VYUGA.bas DIM a(55555) RANDOMIZE TIMER: CLS OPEN "VYUGA.txt" FOR OUTPUT AS #1 d=37 a(1) = INT(RND*d)+1 PRINT #1, a(1) FOR i = 2 TO 55555     a(i) = a(i-1) + INT(RND*3*d)+1     22 IF a(i) > d THEN a(i) = a(i)-d: GOTO 22     PRINT #1, a(i) NEXT https://ideone.com/cPYZad Expand|Select|Wrap|Line Numbers //VYUGA.cs using System;using System.Linq; using System.Collections.Generic; using System.Text.RegularExpressions; namespace VYUGA { public class Program     { static double w;      static void Main(string[] args)          { Random rand = new Random(); int d=37; double s = rand.Next(5000000); double a = Math.Round(d*s/5000000)+1; Console.WriteLine(a);   for (int i = 1; i < 255; i++) { w = rand.Next(3000000)+1; double v = Math.Round(w*d/1000000)+1; a=a+v; da: if (a>d)  { a=a-d; goto da; } Console.WriteLine(a);} Console.ReadKey(); }}} check shows distribution is good comparing even\odd and small\large and a Blizzard suddenly makes normal randomness trigonometric therefore I am looking for an algorithm of form Mersenne twister c# & qbasic Jan 4 '20 #3
 Nearest step: shuffling by weak algorithm weak randomness is randomness of normal Sequence is bad and inserted into Excel in 2 columns at a distance and to left end-to-end of 2nd column is a column of numbers in a row and columns are sorted end to end from maximum to minimum Grouped together: reverse and forward sequences and then sort both by ordering reverse sequence is shuffled simultaneously. Test shows normality of a shuffled sequences of even\odd and large\small An automatic algorithm without rnd reads array straight and immediately there is an array reverse: ... it's a computer ... Sorting reverse array shuffles forward array and it turns out sequence is normal Expand|Select|Wrap|Line Numbers 'tasov.bas DIM a(55000), d(55000) OPEN "aa.txt" FOR INPUT AS #1 OPEN "dd.txt" FOR OUTPUT AS #2   FOR i = 1 TO 55000     INPUT #1, a(i): d(55000 - i + 1) = a(i):NEXT   FOR i = 1 TO 54999: FOR j = i TO 55000         IF d(i) > d(j) THEN SWAP d(i), d(j): SWAP a(i), a(j) NEXT: NEXT   FOR i = 1 TO 55000: PRINT #2, a(i): NEXT: CLOSE Expand|Select|Wrap|Line Numbers //tasov.cs using System; using System.Linq; using System.Collections.Generic; using System.Text; using System.IO; namespace tasov { class Program     { static long[] a; static long[] d;         static void Main(string[] args)         {a = new long; d = new long;  var inpFile = new StreamReader("aa.txt"); for (int i = 1; i <= 55000; i++)  { a[i] = Convert.ToInt64(inpFile.ReadLine()); d[55000-i+1] = a[i]; }   for (int i = 1; i <= 54999; i++)  for (int j = i; j <= 55000; j++)  if (d[i] > d[j]) { var temp = d[i]; d[i] = d[j]; d[j] = temp; temp = a[i]; a[i] = a[j]; a[j] = temp; }   var outFile = new StreamWriter("vv.txt"); for (int i = 1; i <= 55000; i++)  outFile.WriteLine(a[i]); Console.ReadKey();}}} I'm testing the idea: RNG trigonometric created a bad array that doesn't pass validation binary even\odd and small\large therefore, we shuffle equally real in Excel & basic & c# just using this bad array means: sequence is weak shuffled through a sequence of weak turns into a normal sequence based on results of this topic Jan 5 '20 #4
 Developments of several years issued on new year's weekend received a state certificate of registration of computer system Research and transformation of sorting of pseudorandom sequences and formula is fixed on internet N=LOG(1-c)/LOG(1-p) Abstract includes tables and formulas and graphs therefore it is possible to publish images of pages Research and transformation of sorting of pseudorandom sequences Feb 11 '20 #5
 Program for distribution spectra of random number of consecutive identical features less \ more and even \ odd number of numbers depends on seconds and counts 10 ^ 5 elements per second and I imagine what will happen in fast languages Expand|Select|Wrap|Line Numbers 'datable99.bas   RANDOMIZE TIMER tb = TIMER: s = 0 OPEN "zz99.txt" FOR OUTPUT AS #2 n = VAL(MID\$(TIME\$, 7, 2)) * 10 ^ 5 DIM b(n), d(n), e(n), f(n) DIM j(n), k(n), m(n), p(16), q(16) LOCATE 1, 1: PRINT " THEORY        Average       BIG           EVEN "   FOR i = 2 TO n - 1     b(i) = INT(RND * 900) + 100: s = s + b(i): m = s / i       IF b(i) < m THEN d(i) = 0 ELSE d(i) = 1     IF (b(i) MOD 2) = 0 THEN j(i) = 0 ELSE j(i) = 1       IF d(i) = d(i - 1) THEN e(i) = e(i - 1) + 1 ELSE e(i) = 0     IF e(i) = 0 THEN f(i) = e(i - 1) ELSE f(i) = 12     IF f(i) > 12 THEN f(i) = 12       IF j(i) = j(i - 1) THEN k(i) = k(i - 1) + 1 ELSE k(i) = 0     IF k(i) = 0 THEN m(i) = k(i - 1) ELSE m(i) = 12     IF m(i) > 12 THEN m(i) = 12       p(f(i)) = p(f(i)) + 1: q(m(i)) = q(m(i)) + 1       IF (i MOD 1000) = 0 THEN LOCATE 3, 1: PRINT i, " from ", n, INT(100 * i / n); " %",  NEXT   LOCATE 3, 1: FOR t = 1 TO 12     PRINT INT(n / (2 ^ (t + 1))), INT((p(t - 1) + q(t - 1)) / 2), p(t - 1), q(t - 1) NEXT   te = TIMER PRINT: PRINT te - tb; "second", INT(n / (te - tb)); " in second  " PRINT n, " elements ",   PRINT #2, te - tb; "second", INT(n / (te - tb)); " in second  " PRINT #2, n, " elements ",: PRINT #2,   PRINT #2,: PRINT #2, " THEORY        Average       BIG           EVEN ": PRINT #2, FOR t = 1 TO 12     PRINT #2, INT(n / (2 ^ (t + 1))), INT((p(t - 1) + q(t - 1)) / 2), p(t - 1), q(t - 1) NEXT Results: Expand|Select|Wrap|Line Numbers  40 second             139555  in second    5600000       elements         THEORY        Average       BIG           EVEN     1400000       1400610       1399595       1401625   700000        700026        700122        699931   350000        349716        349508        349925   175000        174823        174892        174755   87500         87424         87564         87285   43750         43837         43931         43744   21875         22028         21983         22074   10937         10850         10865         10835   5468          5481          5496          5466   2734          2755          2732          2778   1367          1388          1396          1380   687           687           687           687  Practical distributions correspond to theoretical ones so random sequence is qualitative and it is possible to study patterns of different sequences Binomial Logarithmic Integral Pyramidal Distribution BLIP distribution of Random numbers Feature of program: index of indixes p(f(i)) & q(m(i)) I think random have problems with parity: parity of random changes too sharply Mar 5 '20 #6
 Number of consecutive matches is calculated by formula N = log(1-C)/log(1-P), where N is step, P is probability, C is reliability of probability. Substituting C and P: N = log(1-0.99)/log(1-0.5) = 6.7 = natural value 7, that means that 7th step of distribution should include about 1% of half data, due to counting repetitions and 0 and 1, in amount of 100%. Distribution step number: at C = P = 0.5; N = 1 = log0.5/log0.5 = log(1-1/2)/log(1-1/2) = 1 at C = 0.25; P = 0.5; N = 2 = log0.75/log0.5 = log(1-1/4)/log(1-1/2) = 2, etc. Multiplication of constant probabilities c+p^n = 1 personifies reliability of probability and creates a formula N = log(1-c)/log(1-p) c - probability of winning guaranteed p - probability of winning event. for example: with a probability of 99% for a probability of 48.65% number of mismatches in a row n = log(1-0,99)/log(1-0,4865) = 7 and that means about 50% probability is easy to guess 7 times in a row. it is simpler to calculate by formula N=7+(5*(1/p-2)) for example p = 0.1 N = 47 is normal and p = 0.78 N = 4 is normal and same formulas are valid for probabilities above 50%.  what I was required to prove Mar 30 '20 #7
 Checking in Wolframalpha Reliability win and lose both probability of winning and losing create 4 combinations: C+p^N=1 (1-C)+p^N=1 C+(1-p)^N=1 (1-C)+(1-p)^N=1 Everything is interchangeable: C=1-c c=1-C P=1-p p=1-P Artificial intelligence of Wolframalpha knows logarithm: solve C+(1-p)^N=1 for N https://wolframalpha.com/input/?i=so...%5EN%3D1+for+N Apr 6 '20 #8

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