DEV Community: AndreyDanilin

Waves of probability increase reliability. Priority of Russia

AndreyDanilin — Sat, 09 May 2020 12:15:37 +0000

Waves of probability increase reliability. Priority of Russia

Theory and Practice "0 and 1"

Mathematical laws are valid in all probabilities and it
is important to know a dozen of mismatch limits in a row.

Investigating logarithm is obtained:
formula including logarithm follows from calculation
probabilities of guessing consecutive events

For example, simplest: 0.7*0.7*0.7 = 0.7^3 = 0.343
degree to which it is necessary to build 0.7 to get 0.343
N = LOG(0.343)/LOG(0.7) = 3
and corresponding formula for not guessing

Multiplication of constant probabilities C+p^N=1
and in 20th century formula was restored by
Andrey Danilin: N = LOG(1-C)/LOG(1-p)
C — probability of winning guaranteed
p — probability of winning event.

Example task: number of mismatches in a row
with a probability of 99% for a probability of 48.65%
= LOG(1-0,99)/LOG(1-0,4865) = 7
and that means about 50% probability
easy to guess 7 times in a row

Easily possible to count:
formula was discovered by Andrey Danilin: N=7+(5*(1/x-2))
and for example, x=0.1 N=47 is normal and x=0.78 N=4 is normal.

same formulas are valid for probabilities above 50%.

Geometric progression contained in condition or in solution
meaning of “degree to which it is necessary to build”
is solved through logarithm

Start

Using mismatch limit in a row in tables
a wave or a period of guessing of 2 types is detected:

1st type: wave or period — as probability itself
through number of runs and where probability is 1/3
there is a wave or guessing period after 3 runs;

2nd type: wave or period — as limit of discrepancies in a row
and where probability is 1/3 there is a wave or guessing period
in 12 draws and possibly several bets on signal

Rates

Virtually raise stakes when you lose
and lower stakes when winning to minimum bet

Really set only observing Quadrat Economy Danilins

Practice

We synthesize 50 numbers 0 and 1 controlling amount of 25

case: 00111000000011111101010011111000001010111010000111
specially assigned 7 consecutive losses 0000000

we get 4 results of form:
assumed a win / loss and guessed / failed to guess:

A — guess win — 1-1 — participation and win
E — guess loss — 0-0 — non-participation
I — not won — 0-1 — non-participation
U — loosing — 1-0 — participation and loss

Practice: 001

idea: missing a few ex
and missed only former would be winning

notation: "!" = signal and "." = waiting

case: 00111000000011111101010011111000001010111010000111
code: ..!A........!A..........!A........!U...........!A.

isolate codes A&U = AAAUA = advantageous: A>U
no rate increase and 2 consecutive bids possible
after signal and loss and stop when winning

Practice: 1st wave

comparable to perfect distribution

idea: 01010101010101010101010101010101010101010101010101
case: 00111000000011111101010011111000001010111010000111
code: EUIAIUEUEUEUEAIAIAEAEAEUIAIAIUEUEUIUIUIAIUIUEUEAIA

isolate codes A&U = UUUUUAAAAAUAAUUUUUAUUUA

see 5 losses in a row and balance is intact
because according to simplest system of betting on losing
7 consecutive losses are required until balance is reset
starting with minimum rate of 1%: = 2^7 = 128 percent of balance

ideas are completely identical signs will repeat
picture of coincidence with same number of mismatches in a row

idea: 00110011001100110011001100110011001100110011001101
case: 00111000000011111101010011111000001010111010000111
code: EEAAIEUUEEUUIIAAIIUAEIUUIIAAIEUUEEAUIEAAIEAUEEUAIA

isolate codes A&U = AAUUUUAAUAUUAUAUUAUAAAUUAA
see 5 consecutive losses and balance is intact

Practice: 2nd wave

notation: "!" = signal and "." = waiting

idea: skip 7 consecutive as 0000000
and put a maximum of 2 in a row or before winning

case: 00111000000011111101010011111000001010111010000111
code: ...........!A.....................................

in example there could be a loss and see 1 win rare
therefore it is important to monitor all signs

Idea: simply skip 4 in a row like 0000
and put a maximum of 2 in a row or before winning
same formula including logarithm and reliability below

case: 00111000000011111101010011111000001010111010000111
code: ........!U......................!UA...........!A..

isolate codes A&U = UUAA
see 3 consecutive losses and balance is intact
but skipping 3 in a row as 000 would be more risk

Practice: 2nd waves

matches on 2nd wave from previous match
we add a step as a calculated limit of mismatches in a row

notation: "!" = signal and "." = waiting

case: 00111000000011111101010011111000001010111010000111
code: ...123456!U......123456!A...123456!U..............
code: ....123456!U......123456!A...123456!A.............
code: .....123456!A.......123456!A.......123456!A.......
code: .............123456!U.123456!U.......123456!U.....
code: ..............123456!A...123456!U......123456!U...
code: ...............123456!U...123456!U......123456!A..
code: ................123456!U...123456!A..... 123456!A.

isolate codes A&U = UUAUAUUAAAUUUAAUAUUAA
see 3 consecutive losses and balance is intact

Practice: 2 waves and more waves

idea 001: missing some ex would be losing
and missed only former would be winning

notation: "!" = signal and "." = waiting

case1: 00111000000011111101010011111000001010111010000111
code1: ..!U........!A..........!A........!U...........!A.

case2: 11100001011101010000011111001010111111000000011100
code2: .......!U...........!A......!U...............!A...

where case2 is reverse sequence from case1 for experiment

isolate codes A&U = UUAAAUUAA = advantageous: A>U
no rate increase and 2 consecutive bids possible
after signal and loss and stop when winning

see 2 consecutive losses and balance is intact

let us assume that all possible situations are independent:

case3: 0001000010000110000011
code3: ...!U...!U...!A.....!A

case4: 0001000011000100000011
code4: ...!U...!A...!U.....!A

at same time: UU / UA / AU / AA
so were: 1 win and 1 loss and 2 return

probability of winning 1/4 = 25 %
probability of losing 1/4 = 25 %
probability of return 1/2 = 50 %

everything with target: division not coincidence in row
and also same for 3 or more independent signs
and for ideas about a step over limit of mismatch in a row

Conclusion

Waves of probability increase reliability

Nobel Prize will not receive itself

Guess number: 1-line C# & qbasic learning algorithm. Priority of Russia

AndreyDanilin — Wed, 01 Apr 2020 06:38:30 +0000

Guess number: 1-line C# & qbasic learning algorithm. Priority of Russia

A few months ago reading a USA forum and seeing a competition:
create a program "guess number" shorter and I overtook americans
1-m by inventing a 1-line algorithm implemented in 2 languages

    1 IF Russia = 0 THEN Russia = 2222: RANDOMIZE TIMER: num = INT(RND * 100) + 1: GOTO 1 ELSE IF Russia <> 0 THEN INPUT n: IF n < num THEN PRINT «MORE»: GOTO 1 ELSE IF n > num THEN PRINT «less»: GOTO 1 ELSE IF n = num THEN PRINT «da»: END ELSE GOTO 1 'DANILIN Russia 9-9-2019 guessnum.bas

I post originals

    using System; using System.Text;namespace GURU { class Program { static void Main(string[] args) { Random rand = new Random(); int Russia = 0; int n = 0; int num = 0; dav: if(Russia == 0) {Russia = 2222; num = rand.Next(100)+1; goto dav; }else if (Russia != 0) {Console.Write("? "); n = Convert.ToInt32(Console.ReadLine());} if (n < num) { Console.WriteLine(«MORE»); goto dav;}else if (n > num) { Console.WriteLine(«less»); goto dav;}else if (n == num) {Console.Write(«da»); Console.ReadKey(); }else goto dav;}}}// DANILIN Russia 9-9-2019 guessnum.cs

and hope readers will write their programs
strictly 1-line algorithms in other programming languages

My algorithm guesses a number up to a billion 10^9 in a logarithmic number of steps

    //milliard.cs
using System;
using System.Text;
namespace DAV 
{ class Program
 { static void Main(string[] args) 
 { int h2 = 1000000000;//or 500
int h1 = 0; int t = 0;
Random rand = new Random();
int c = rand.Next(h2); //computer
int h = rand.Next(h2); //human or h2/2; 

dav: 
t++;
Console.WriteLine(); Console.Write(t);
Console.Write("  "); Console.Write(c);
Console.Write("  "); Console.Write(h);
Console.Write("  ");

if(h < c)
 { Console.Write("MORE");
 int a=h; h=(h+h2)/2; h1=a; goto dav;
 }
else if(h > c)
 { Console.Write("less");
 int a=h; h=(h1+h)/2; h2=a; goto dav;
 }
Console.Write("win by "); Console.Write(t);
Console.Write(" steps"); Console.ReadKey();
}}}

Results:

1  69682914  543648564  less
2  69682914  271824282  less
3  69682914  135912141  less
4  69682914  67956070  MORE
5  69682914  101934105  less
6  69682914  84945087  less
7  69682914  76450578  less
8  69682914  72203324  less
9  69682914  70079697  less
10  69682914  69017883  MORE
11  69682914  69548790  MORE
12  69682914  69814243  less
13  69682914  69681516  MORE
14  69682914  69747879  less
15  69682914  69714697  less
16  69682914  69698106  less
17  69682914  69689811  less
18  69682914  69685663  less
19  69682914  69683589  less
20  69682914  69682552  MORE
21  69682914  69683070  less
22  69682914  69682811  MORE
23  69682914  69682940  less
24  69682914  69682875  MORE
25  69682914  69682907  MORE
26  69682914  69682923  less
27  69682914  69682915  less
28  69682914  69682911  MORE
29  69682914  69682913  MORE
30  69682914  69682914  win by 30 steps

For Excel:

=log(10^9;2)
=29,89
=30

Q.E.D.
What we needed to prove

Falsification of randomness and transformation by sorting of pseudorandom sequences. Priority of Russia

AndreyDanilin — Fri, 27 Mar 2020 15:55:10 +0000

Falsification of randomness and transformation by sorting of pseudorandom sequences. Priority of Russia

Objective: to prove possibility of falsification of chance and reality of overcoming rigged chance.

Accident natural, divided by integral of logarithmic spectra, predictable shows short range of repetitions and distance of repeats massively long absent, but sorting sequences results in spectra separation in view of theoretical.

Gap of Education of Russia and USSR and CIS: integral and logarithm in lower grades do not study and subsequently consider simplest ostensibly difficult.

Designations should be understood literally: randomness is natural — natural, created without a computer.

Program "Fake accident 1"

In sequence increases number of same in a row.

    ' dafalse11.bas qbasic
    OPEN "da11.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

Column G shows absurd distribution with average 0.5.
Column A – name of experiment;
B1 =average(C1:C50000) is mean value of sequence;
Columns C...F – study of quantities in succession;
Column J – random permutations;
Column K – sequence after rearrangement;
M1 =average(N1:N50000) is mean value of sequence;
Columns N...R – study number in a row.

Exploring other criteria — it is possible to use other formulas, but illuminated technique available for understanding in elementary school.

Up 500 cells before permutation of cells: unsatisfactory

Up 500 cells after permutation of cells: normal.

Conclusion: identified an obvious forgery of form: equal to number of same in a row and converted.

Program "False randomness 2"

In sequence increases number of same in a row, especially given algorithm validation.

    ' dafalse22.bas qbasic
    OPEN "da22.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

Up 500 cells before permutation of cells: unsatisfactory

Up 500 cells after permutation of cells: normal

Conclusion: it was found a clever fake, it's not programmed all possible options and see bias because of synthesis algorithm.

False shuffled sequence becomes a sequence of random.

Conclusion: to identify a fake sequence really.

Programs datasov.bas and datasov.cs is a permutation of elements of original array by sorting array inverted.

Program changes in language qbasic

    ' datasov.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

Program permutations in C#

    // datasov.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();}}}

Algorithm without built-in RNG reads array from source and creates array inverted and then sort reverse array shuffles original array and result is a normal sequence.

Conclusion: reliable accident – a 2-sided integral accident.

My original formula N=LOG(1-C)/LOG(1-p)
is too difficult so many years ago
I found a simple formula
for a reliability c=0.99=99% N=7+(5*(1/p-2))
confirmed graphically

What we wanted to prove.

Research and transformation by sorting pseudo-random sequences. Priority of Russia

AndreyDanilin — Thu, 19 Mar 2020 12:00:34 +0000

Research and transformation by sorting pseudo-random sequences. Priority of Russia

Objective: To set up algorithms in C# and qbasic languages and table Excel compatible th, etc. it is possible to examine pseudo-random sequence for randomness and capable of determining sequence of a non-random or bad.

Graphical shell: Excel table compatible for researching by over 50 thousand elements of 2 types:

Study of a sequence of numbers;
Examination of sequence of digits 0 and 1. Investigation sequence of numbers : t b le defines binary attributes, such as less\more and even\oddness.

Excel Shell compatible graphical table uses formulas:

Number of consecutive matches is calculated by formula:
N=log(1-C)/log(1-P), where N is step or spectrum,
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.

Column A is name of sequence;
Column B - sequence;
Column D - 1st distribution less / more;
Columns E, F - definition of identical ones in a row;
Columns G, H - counting number of signs identical in a row;
Column J - 2nd distribution even / odd;
Columns K, L - definition of signs identical in a row;
Columns M, N - counting number of signs identical in a row.

Formulas used in table:
Cell Formula Explanation
C1 = AVERAGE(D1: D55000) average value of sequence numbers
C2 = AVERAGE(B1: B55000) Distribution Average 1
D1 = IF(B1<C$2; 0; 1) If number is less than its unit, then 0, otherwise 1
D2 = IF(B2<C$2; 0; 1) If number is less cf. ., then 0, otherwise 1, etc.
E2 = IF(D2=D1; E1+1; 0) If signs of distribution are same, then counter of same in a row is +1, otherwise counter is reset to zero
F2 = IF(E3=0; E2; "") If counter is reset to zero g n, largest fixed counter
G2-G19 0 ... 7 Numbers in order to compare
H1 = SUM(H2:H10) Sum of comparisons
H2 = COUNTIF(F$1: F$55000; G2) Number of signs 1 in a row
H3 = COUNTIF(F$1: F$55000; G3) Number of signs 2 in a row, etc.
H12 = H2/H3 ratio of amounts of nearest straight iznako in
I12 = AVERAGE(H12:H19) average value of relationship
I13 = AVERAGE(N12:N19) average value of relationships, etc.
I1 = AVERAGE(J1:J55000) Distribution Average 2
J1 = IF(B1/2 = WHOLE(B1/2); 0; 1) If number is even, then 0, otherwise 1
J2 = IF(B2/2 = WHOLE(B2/2); 0; 1) If number is even, then 0, otherwise 1, etc.
K2 = IF(J2=J1; K1+1; 0) If signs of distribution are same, then counter of same in a row is +1, otherwise counter is reset to zero
L2 = IF(K3=0; K2; "") If counter is reset to zero g n, largest fixed counter
M2-M19 0 ... 7 Numbers in order to compare
N1 = SUM(N2: N10) Sum of comparisons
N2 = COUNTIF(L$1: L$ 55000; M2) Number of signs 1 in a row
N3 = COUNTIF(L$1: L$ 55000; M3) Number of signs 2 in a row, etc.
N12 = H2/H3 ratio of nearest number of signs

Other monitoring functions can be programmed in table.
In table it is possible to create graphs of values of any cells.

Continuation of table explores random permutation sequence

Column Q - random for permutation : integers up to 10^6,

to minimize repeat random ;
Column R - initially copy column B and then edited enenny ;

Columns T ... AE - same as columns of C of N ... .

Cell Formula Explanation
Q1 = CASEBETWEEN(0; 1000000) Random to rearrange
Q2 = CASEBETWEEN(0; 1000000) Random for permutation, etc.

Permutation is performed by sorting 2 columns Q and R:
column Q is master and column R is slave.

Result: permutations of column R and a new sequence.

RNG - random number generator: natural or pseudo.
Research on built-in RNG shows normality of algorithm.

Before reshuffling 500 cells:

After reshuffling 500 cells:

Check shows a good distribution by comparing attributes: small/large and even/odd.

Table explores trigonometric RNG using digits after decimal point of trigonometric functions, standard RNG not using.

    'rndsin.bas
    OPEN "rndsin.txt" FOR OUTPUT AS #1
    c = 0: a = SIN(TIMER) * 100 + 200
    PRINT #1, "a= ", a

    FOR k = 1 TO 10 ^ 3 + a * 10 ^ 3: NEXT

    FOR i = 1 TO 100
        FOR j = 1 TO a
            x = SIN(TIMER) * 1000 + 2000
            b = COS(x): c = c + b
            LOCATE 1, 1: PRINT j
        NEXT

        d = (ABS(c)) - INT(ABS(c))
        PRINT #1, d
        FOR k = 1 TO 10000 + a * b * c * 10 ^ 2: NEXT
    NEXT

Before reshuffling 500 cells: unsatisfactory

Obviously, distribution is poor, detecting frequency and spread of values, comparing signs: small/large and even/odd.

After reshuffling 500 cells: normal

Goal: eliminate built-in RNG.

Permutation method: original sequence is sorted, and same sequence is accepted as random for permutation, inverted or inverted in any way.

For example, in Excel, 2 copies of sequence columns are created at a distance, and one column has a leading row 1...55000 rows and 2 columns are sorted from maximum to minimum, inverting original data.

Next, 2 columns of sequence are mapped side by side and sorted, where master column is reverse and slave column is initial.

Before reshuffling 500 cells: unsatisfactory

After 500 permutations of cells: normal

Result: sequence became normal without built-in RNG.

Conclusions: true randomness is unnatural for people and it is possible to synthesize sequences that are low-power or fake, which are taken by people and computers as random sequences.

Any sequences can be synthesized in programming languages and in Excel-compatible tables.

Problem of overcoming randomness is solved by recognizing normal or false randomness in an Excel table with graphs.

Which was exactly what I needed to prove.

PI and randomness of digits after decimal point. Priority of Russia

AndreyDanilin — Sat, 14 Mar 2020 06:56:03 +0000

PI and randomness of digits after decimal point. Priority of Russia

On March 14, on day "3.14", PI celebrates its day

Importance of topic: research on distribution of PI digits and irrational numbers opens up possibility of studying continuous data in real time,
when incoming data is counted without pauses for a separate input of data array

Understanding patterns of distributions human and natural and fake and machine actually apply results of 4 types of research:

Creation of randomness
Overcoming randomness
Falsification of randomness
Overcoming falsification of randomness

Gap of Education in Russia and CIS and USSR:
we don't study logarithm and integral in lower grades
and later consider simplest allegedly difficult
as well as algorithms for fast calculations are not studied

In addition fast computing algorithms are not taught in school,
although algorithms are clear in many programming languages
without use of quantum computers

But this work highlights public pyramid
spectral integral logarithmic binomial criterion

Using 55,000 digits of PI after decimal point,
first in a Word compatible program replace special characters
numbers are translated into a column and then in an Excel compatible
program digits are divided into binary attributes:
small \ large and even \ odd

Results: average for both binary distributions: about 0.5
and binary divisions correspond to theoretical probability

Table is applied:

Where are main formulas:
Cell-Formula-Explanation

C1 =AVERAGE(D1:D55000)
Average value of sequence numbers

C2 =AVERAGE(B1:B55000)
Average distribution value 1

D1 =IF(B1<C$2;0;1)
If number is less than average, then 0, otherwise 1

D2 =IF(B2<C$2;0;1)
If number is less than 1, then 0, otherwise 1, and so on.

E2 =IF(D2=D1;E1+1;0)
If distribution features are same, then counter of same attributes is +1,
otherwise counter is reset to zero

F2 =IF(E3=0;E2;" ")
If counter is reset to zero, largest counter is fixed

H2 =COUNTIF(F$1:F$55000;G2)
Number of signs 1 in a row and so on

H12 =H2/H3
Ratio of nearest number of attributes

J1 =IF(B1/2=ROUND(B1/2);0;1)
If number is even, then 0, otherwise 1

J2 =IF(B2/2=ROUND(B2/2);0;1)
If number is even, then 0, otherwise 1, etc

K2 =IF(J2=J1;K1+1;0)
If distribution features are same, then counter of same attributes is +1,
otherwise counter is reset to zero

L2 =IF(K3=0;K2;" ")
If counter is reset to zero, largest counter is fixed

N2 =COUNTIF(L$1:L$55000;M2)
Number of signs 1 in a row and so on

N12 =H2/H3
Ratio of nearest number of attributes

Other control functions can be programmed in table
You can create graphs of values of any cells in table

Continuation of table explores random permutations of sequence

Column Q - for a random permutation of integers up to 10^6,
to avoid repeating random events;
Column R - initially a copy of column B, later modified;
Columns T...AE - same as C...N columns"

Cell-Formula-Explanation

Q1 =RANDBETWEEN(0;1000000)
For a random permutation

Q2 =RANDBETWEEN(0;1000000)
Random for permutation, etc.

Preliminary conclusions: predominance of spectrum of repetitive features is found, what is typical for natural sequences, for example, by typing manually 3000 digits, 1st spectrum of repeated features will be higher than theoretical value

Using capabilities table for a permutation of elements of sequence and shuffled, spectra take on theoretical values as would be synthesized by RNG and CSPRNG and CPRNG

Spectra follow formula of Danilin: N = LOG(1-c)/LOG(1-p) by principle:
when C=P=0.5; N = 1 = log0.5/log0.5 = log(1-1/2)/log(1-1/2) = 1
for C=0.25; P=0.5; N = 2 = log0.75/log0.5 = log(1-1/4)/log(1-1/2) = 2, etc

Program for distribution spectra of random number
of consecutive identical features less \ more and even \ odd

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

'dablip.bas

RANDOMIZE TIMER
tb = TIMER: s = 0
OPEN "dablip.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

Feature of program: index of indixes p(f(i)) & q(m(i))

Results:

40 second 139'555 in second
5'600'000 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

I think random have problems with parity:
parity of random changes too sharply

For self-study:

Uniformity of each of digits of PI
Methods for approximate calculation of PI
Learn 8 digits of PI after decimal point
Find formulas for calculating digits of PI
Remember circle length formulas