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 - ' 0.bas
-
OPEN "0.txt" FOR OUTPUT AS #1
-
FOR s = 1 TO 50000: PRINT #1, (INT(RND * 1000) MOD 2): NEXT
-
CLOSE
- ' 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
- ' 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 - '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 - 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 - '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 8 13472
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
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 - '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 - //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
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 - '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
- //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[55500]; d = new long[55500];
-
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
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
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 - '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: - 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
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
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
Quantum random observe principles of binomial distribution
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