Quote: Originally posted by MrSteel01 on September 26, 2003

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ALL THE NUMBERS add up to 160!

No matter how they came out!

Now what?  Should we video all draws to see how they were drawn?  The numbers are on two sides equal in size & shape and weight the same in grams! +-!

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you can watch all the PB drawings on their site, but you don't need to because if you click here you can see the history in draw order (plain text, perfect for importing into excel or access or SQL etc...)

and true, the balls ARE EXACTLY the same size and weight, they also have no idea what number they have on them... think of it as a NASCAR race.... what good is it really if you sorted the top 5 finishers, it may or may not tell what the outcome of the race is...

the most frequently drawn white ball is 17... not one thru 10, that's just a result of the sorting... see for yourself...

Number	Count
1	11
2	15
3	6
4	9
5	13
6	15
7	9
8	7
9	12
10	13
11	11
12	11
13	9
14	13
15	11
16	12
17	20
18	11
19	15
20	18
21	14
22	8
23	11
24	10
25	10
26	16
27	9
28	14
29	10
30	16
31	16
32	11
33	9
34	14
35	17
36	8
37	9
38	10
39	8
40	17
41	13
42	15
43	6
44	11
45	5
46	12
47	6
48	10
49	11
50	11
51	11
52	11
53	6

also, no number has appeared in sorted position more than 11 times... the SORTING colors the results.

the above frequency list is also counting how many times each has appeared as the PB, I couldn't post the whole chart, too big...

I have been tracking our Cash 5 in Ky and the  number trends are for repeats..within every 12 draws, there is 1 or 2 draws that will repeat previously draw numbers for all 5 numbers.  The actual average for this to appear seems to be between the 6th through the 9th draw.  I don't have my PB stats caught up but I would think there was a similar relationship.   There are also trends of "hot" numbers that change from week to week.  I also  put the numbers in groups of hot, warm and cold (I set my own limits with hot being 15-20 hits for any digit, warm being 10-14 hits for any digit and anything below 10 hits for any digit being cold.)..5 numbers fell out of the hot group which had only 12 numbers in it.  I personally think that this is a good way to cut down on the amount of numbers played.  A person may not get all 5 but getting 4 seems to be easier.  Our Cash 5 is set up just like PB.  4 balls are drawn from one barrel and 1 is drawn from another.  That is the reason I am interested in the circle wheel.

If that's the case it should be even quite easy with your set up!

4 balls have some sort of repeating occurance & pb balls have to have some sort of reapeating occurance too!  Keep them seperate!

Quote: Originally posted by hypersoniq on September 26, 2003

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you can watch all the PB drawings on their site, but you don't need to because if you click here you can see the history in draw order (plain text, perfect for importing into excel or access or SQL etc...)

and true, the balls ARE EXACTLY the same size and weight, they also have no idea what number they have on them... think of it as a NASCAR race.... what good is it really if you sorted the top 5 finishers, it may or may not tell what the outcome of the race is...

the most frequently drawn white ball is 17... not one thru 10, that's just a result of the sorting... see for yourself...) 

 One thru ten was only in the drawing of numbers in a normal draw of 5/6 numbers not pb I was talking about all columns not 1 column!

Number	Count
1	11
2	15
3	6
4	9
5	13
6	15
7	9
8	7
9	12
10	13
11	11
12	11
13	9
14	13
15	11
16	12
17	20
18	11
19	15
20	18
21	14
22	8
23	11
24	10
25	10
26	16
27	9
28	14
29	10
30	16
31	16
32	11
33	9
34	14
35	17
36	8
37	9
38	10
39	8
40	17
41	13
42	15
43	6
44	11
45	5
46	12
47	6
48	10
49	11
50	11
51	11
52	11
53	6

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KY C/5

Fri Sep 26 '03	7 - 12 - 13 - 32 - Cashball: 3
Thu Sep 25 '03	8 - 12 - 25 - 30 - Cashball: 7
Fri Sep 26 '03	7 - 12 - 13 - 32 - Cashball: 3
Thu Sep 25 '03	8 - 12 - 25 - 30 - Cashball: 7
Wed Sep 24 '03	2 - 24 - 26 - 27 - Cashball: 5
Tue Sep 23 '03	2 - 8 - 14 - 32 - Cashball: 19
Mon Sep 22 '03	10 - 14 - 17 - 26 - Cashball: 24
Sat Sep 20 '03	13 - 15 - 17 - 30 - Cashball: 25
Fri Sep 19 '03	6 - 15 - 21 - 32 - Cashball: 31
Thu Sep 18 '03	3 - 4 - 9 - 32 - Cashball: 26
Wed Sep 17 '03	6 - 7 - 10 - 22 - Cashball: 23
Tue Sep 16 '03	1 - 3 - 21 - 32 - Cashball: 12
Mon Sep 15 '03	9 - 19 - 27 - 28 - Cashball: 26
Sat Sep 13 '03	5 - 14 - 19 - 29 - Cashball: 24
Fri Sep 12 '03	3 - 13 - 16 - 28 - Cashball: 9
Thu Sep 11 '03	9 - 16 - 20 - 28 - Cashball: 30
Wed Sep 10 '03	1 - 10 - 19 - 30 - Cashball: 19
Tue Sep 9 '03	6 - 8 - 9 - 29 - Cashball: 9
Mon Sep 8 '03	6 - 11 - 13 - 28 - Cashball: 5
Sat Sep 6 '03	1 - 3 - 14 - 23 - Cashball: 3
Fri Sep 5 '03	4 - 11 - 23 - 24 - Cashball: 7
Thu Sep 4 '03	2 - 3 - 9 - 20 - Cashball: 12
Wed Sep 3 '03	7 - 8 - 16 - 19 - Cashball: 26
Tue Sep 2 '03	16 - 17 - 19 - 25 - Cashball: 26
Mon Sep 1 '03	12 - 24 - 26 - 33 - Cashball: 16
Sat Aug 30 '03	8 - 19 - 23 - 33 - Cashball: 31
Fri Aug 29 '03	21 - 27 - 28 - 31 - Cashball: 26
Thu Aug 28 '03	1 - 2 - 13 - 20 - Cashball: 10
Wed Aug 27 '03	27 - 29 - 30 - 32 - Cashball: 13
Tue Aug 26 '03	4 - 17 - 23 - 27 - Cashball: 6
Mon Aug 25 '03	1 - 6 - 20 - 32 - Cashball: 24
Sat Aug 23 '03	1 - 9 - 12 - 25 - Cashball: 28
Fri Aug 22 '03	8 - 16 - 20 - 33 - Cashball: 12
Thu Aug 21 '03	9 - 14 - 26 - 29 - Cashball: 8
Wed Aug 20 '03	5 - 9 - 17 - 24 - Cashball: 4
Tue Aug 19 '03	17 - 24 - 26 - 30 - Cashball: 4
Mon Aug 18 '03	14 - 16 - 22 - 28 - Cashball: 23
Sat Aug 16 '03	14 - 19 - 22 - 24 - Cashball: 11
Fri Aug 15 '03	5 - 10 - 15 - 32 - Cashball: 16
Thu Aug 14 '03	4 - 12 - 18 - 23 - Cashball: 22
Wed Aug 13 '03	12 - 14 - 16 - 24 - Cashball: 30
Tue Aug 12 '03	2 - 9 - 16 - 31 - Cashball: 22
Mon Aug 11 '03	5 - 10 - 25 - 32 - Cashball: 25
Sat Aug 9 '03	6 - 18 - 22 - 28 - Cashball: 26
Fri Aug 8 '03	13 - 21 - 28 - 31 - Cashball: 30
Thu Aug 7 '03	19 - 21 - 23 - 29 - Cashball: 30
Wed Aug 6 '03	8 - 15 - 26 - 28 - Cashball: 11
Tue Aug 5 '03	11 - 12 - 18 - 20 - Cashball: 14
Mon Aug 4 '03	5 - 11 - 16 - 30 - Cashball: 14
Sat Aug 2 '03	1 - 16 - 28 - 31 - Cashball: 31
Fri Aug 1 '03	3 - 25 - 26 - 27 - Cashball: 20
Thu Jul 31 '03	7 - 10 - 16 - 19 - Cashball: 17
Wed Jul 30 '03	3 - 23 - 29 - 30 - Cashball: 26
Tue Jul 29 '03	12 - 13 - 24 - 30 - Cashball: 16
Mon Jul 28 '03	3 - 9 - 10 - 31 - Cashball: 22
Sat Jul 26 '03	3 - 21 - 27 - 31 - Cashball: 7
Fri Jul 25 '03	6 - 8 - 9 - 15 - Cashball: 7
Thu Jul 24 '03	7 - 19 - 20 - 28 - Cashball: 15
Wed Jul 23 '03	10 - 18 - 22 - 26 - Cashball: 18
Tue Jul 22 '03	7 - 8 - 17 - 27 - Cashball: 24
Mon Jul 21 '03	1 - 2 - 5 - 19 - Cashball: 21
Sat Jul 19 '03	4 - 27 - 29 - 30 - Cashball: 16
Fri Jul 18 '03	2 - 5 - 19 - 23 - Cashball: 27
Thu Jul 17 '03	4 - 22 - 25 - 29 - Cashball: 17
Wed Jul 16 '03	4 - 18 - 30 - 33 - Cashball: 4
Tue Jul 15 '03	8 - 11 - 25 - 27 - Cashball: 24
Mon Jul 14 '03	7 - 19 - 26 - 27 - Cashball: 7
Sat Jul 12 '03	6 - 20 - 22 - 23 - Cashball: 24
Fri Jul 11 '03	2 - 8 - 10 - 25 - Cashball: 16
Thu Jul 10 '03	11 - 14 - 26 - 32 - Cashball: 31
Wed Jul 9 '03	8 - 21 - 28 - 31 - Cashball: 16
Tue Jul 8 '03	5 - 12 - 29 - 31 - Cashball: 17
Mon Jul 7 '03	10 - 19 - 21 - 30 - Cashball: 29
Sat Jul 5 '03	11 - 22 - 28 - 30 - Cashball: 24
Fri Jul 4 '03	9 - 12 - 13 - 22 - Cashball: 25
Thu Jul 3 '03	23 - 28 - 30 - 32 - Cashball: 18
Wed Jul 2 '03	9 - 13 - 24 - 33 - Cashball: 17
Tue Jul 1 '03	8 - 25 - 30 - 31 - Cashball: 17
Mon Jun 30 '03	3 - 18 - 24 - 29 - Cashball: 19
Sat Jun 28 '03	4 - 18 - 27 - 31 - Cashball: 23
Fri Jun 27 '03	1 - 5 - 14 - 19 - Cashball: 23
Thu Jun 26 '03	2 - 9 - 16 - 29 - Cashball: 17
Wed Jun 25 '03	12 - 27 - 29 - 32 - Cashball: 27
Tue Jun 24 '03	7 - 20 - 30 - 32 - Cashball: 14
Mon Jun 23 '03	10 - 20 - 25 - 26 - Cashball: 12
Sat Jun 21 '03	4 - 24 - 26 - 31 - Cashball: 19
Fri Jun 20 '03	3 - 7 - 12 - 14 - Cashball: 4
Thu Jun 19 '03	1 - 5 - 6 - 31 - Cashball: 18
Wed Jun 18 '03	5 - 13 - 17 - 21 - Cashball: 29
Tue Jun 17 '03	15 - 19 - 26 - 31 - Cashball: 24
Mon Jun 16 '03	2 - 4 - 8 - 23 - Cashball: 1
Sat Jun 14 '03	5 - 18 - 22 - 24 - Cashball: 16
Fri Jun 13 '03	2 - 13 - 18 - 28 - Cashball: 26
Thu Jun 12 '03	8 - 24 - 26 - 27 - Cashball: 4
Wed Jun 11 '03	21 - 22 - 25 - 26 - Cashball: 26
Tue Jun 10 '03	7 - 9 - 12 - 20 - Cashball: 13
Mon Jun 9 '03	10 - 13 - 15 - 25 - Cashball: 19
Sat Jun 7 '03	2 - 6 - 8 - 30 - Cashball: 30
Fri Jun 6 '03	4 - 20 - 25 - 29 - Cashball: 4
Thu Jun 5 '03	5 - 15 - 24 - 29 - Cashball: 4
Wed Jun 4 '03	8 - 18 - 29 - 32 - Cashball: 11
Tue Jun 3 '03	10 - 24 - 26 - 33 - Cashball: 30
Mon Jun 2 '03	1 - 12 - 13 - 17 - Cashball: 23
Sat May 31 '03	15 - 18 - 21 - 26 - Cashball: 6
Fri May 30 '03	6 - 8 - 24 - 29 - Cashball: 4
Thu May 29 '03	5 - 11 - 13 - 25 - Cashball: 4
Wed May 28 '03	8 - 19 - 22 - 33 - Cashball: 14
Tue May 27 '03	3 - 13 - 20 - 27 - Cashball: 14
Mon May 26 '03	5 - 19 - 30 - 31 - Cashball: 18
Sat May 24 '03	4 - 5 - 9 - 15 - Cashball: 25
Fri May 23 '03	14 - 18 - 21 - 30 - Cashball: 3
Thu May 22 '03	13 - 18 - 22 - 27 - Cashball: 5
Wed May 21 '03	3 - 11 - 14 - 24 - Cashball: 28
Tue May 20 '03	1 - 4 - 23 - 28 - Cashball: 6
Mon May 19 '03	12 - 23 - 25 - 33 - Cashball: 15
Sat May 17 '03	8 - 17 - 21 - 23 - Cashball: 26
Fri May 16 '03	5 - 6 - 8 - 12 - Cashball: 10
Thu May 15 '03	4 - 12 - 28 - 29 - Cashball: 11
Wed May 14 '03	4 - 7 - 22 - 28 - Cashball: 28
Tue May 13 '03	13 - 14 - 16 - 30 - Cashball: 4
Mon May 12 '03	2 - 17 - 31 - 32 - Cashball 11
Sat May 10 '03	3 - 21 - 23 - 29 - Cashball: 11
Fri May 9 '03	1 - 2 - 10 - 27 - Cashball: 2
Wed May 7 '03	4 - 18 - 20 - 27 - Cashball: 28
Tue May 6 '03	9 - 13 - 14 - 26 - Cashball: 27
Mon May 5 '03	1 - 2 - 7 - 28 - Cashball: 8
Sat May 3 '03	12 - 15 - 16 - 26 - Cashball: 9
Thu May 1 '03	1 - 11 - 25 - 33 - Cashball: 11
Wed Apr 30 '03	6 - 15 - 31 - 33 - Cashball: 1
Tue Apr 29 '03	12 - 20 - 25 - 32 - Cashball: 11
Mon Apr 28 '03	15 - 22 - 27 - 33 - Cashball: 16
Sat Apr 26 '03	4 - 24 - 26 - 30 - Cashball: 20
Fri Apr 25 '03	16 - 17 - 25 - 27 - Cashball: 2
Thu Apr 24 '03	15 - 24 - 30 - 32 - Cashball: 12
Wed Apr 23 '03	8 - 16 - 29 - 30 - Cashball: 23
Tue Apr 22 '03	10 - 12 - 15 - 24 - Cashball: 2
Mon Apr 21 '03	10 - 17 - 23 - 32 - Cashball: 23
Sat Apr 19 '03	1 - 4 - 18 - 33 - Cashball: 16
Fri Apr 18 '03	8 - 17 - 21 - 25 - Cashball: 16
Thu Apr 17 '03	9 - 12 - 13 - 28 - Cashball: 3
Wed Apr 16 '03	15 - 18 - 20 - 26 - Cashball: 19
Tue Apr 15 '03	7 - 16 - 25 - 31 - Cashball: 22
Mon Apr 14 '03	14 - 23 - 25 - 29 - Cashball: 18
Sat Apr 12 '03	3 - 4 - 7 - 27 - Cashball: 27
Fri Apr 11 '03	1 - 11 - 15 - 27 - Cashball: 5
Thu Apr 10 '03	6 - 9 - 11 - 25 - Cashball: 14
Wed Apr 9 '03	6 - 7 - 12 - 15 - Cashball: 8
Tue Apr 8 '03	5 - 12 - 13 - 17 - Cashball: 16
Mon Apr 7 '03	9 - 22 - 24 - 31 - Cashball: 31
Sat Apr 5 '03	8 - 16 - 31 - 32 - Cashball: 6
Fri Apr 4 '03	9 - 15 - 18 - 28 - Cashball: 20
Thu Apr 3 '03	1 - 6 - 7 - 28 - Cashball: 30
Wed Apr 2 '03	8 - 10 - 27 - 30 - Cashball: 19
Tue Apr 1 '03	11 - 18 - 21 - 32 - Cashball: 12
Mon Mar 31 '03	2 - 22 - 26 - 28 - Cashball 22
Sat Mar 29 '03	5 - 7 - 12 - 13 - Cashball: 16
Fri Mar 28 '03	7 - 17 - 22 - 23 - Cashball: 27
Thu Mar 27 '03	19 - 21 - 22 - 27 - Cashball: 5
Wed Mar 26 '03	13 - 14 - 17 - 21 - Cashball: 24
Tue Mar 25 '03	15 - 19 - 25 - 29 - Cashball: 15
Mon Mar 24 '03	4 - 7 - 8 - 31 - Cashball: 24
Sat Mar 22 '03	2 - 8 - 28 - 31 - Cashball: 10

COPY/PASTE info!

Here's the Visual Basic algorithm I've come up with for finding the combinatorial index of a combination for N items taken R at a time. Those of you who know VB, know what to do. Those of you who know another programming language and VB should know what to do.

 

 

 

Global Counter(1 To R) As Integer 'R must be assigned some value before program run.

'The program can handle anything R or less when

' when assigned.

'note: This global array must be put in the declarations part of the function module or

'some other module.

 

Function Fact(N) As Double 'The factorial function, Fact(N)= N!

If (N < 1) Then 'This is a recursive calling function, means it calls

' itself multiple times.

Fact = 1 'If your BASIC language dose not support recursive

' calling, then this function needs to be changed to meet

Else ' the function of:

' N! = N * (N - 1) * (N - 2) * (N - 3) * ... * 3 * 2 * 1

Fact = N * Fact(N - 1) ' where 0! = 1 and N < 0 is undefined.

End If

End Function

 

 

Function Perm(N, R) As Double 'This is the permutational function of N items taken R at

' a time.

If (N < R) Then

Perm = 0

Else

Perm = Fact(N) / Fact(N - R)

End If

End Function

 

 

Function Comb(N, R) As Double 'This is the combinatorial function of N items taken R at

' a time.

If (N < R) Then

Comb = 0

Else

Comb = Perm(N, R) / Fact(R)

End If

End Function

 

 

Function Cdist(N, R, C, Z) As Double 'This is the column distribution function of N

' items taken R at a time in column C for item Z.

If (Z < C) Or (Z > (N - R + C)) Or (Z > N) Or (C > R) Or (N < 1) Or (R < 1) Or (C < 1) Or (Z < 1) Then

Cdist = 0

Else

Cdist = Comb(Z - 1, C - 1) * Comb(N - Z, R - C)

End If

End Function

 

 

Function fColumnSum(N, R, Z) As Double 'This function performs a column count for N

' items taken R at a time for item Z.

If Z < 1 Then

fColumnSum = 0

ElseIf (Z >= 1) And (Z < N - R + 1) Then

col_sum = 0

For a = 1 To Z

col_sum = col_sum + Cdist(N, R, 1, a)

Next a

fColumnSum = col_sum

ElseIf Z >= N - R + 1 Then

fColumnSum = Comb(N, R)

End If

End Function

 

 

 

Function Comb_Count(N, R) As Double 'This is the combinatorial index for a combination

' in N items taken R at a time and R must not be

' larger than the Counter() array size R.

fsum = fColumnSum(N, R, Counter(1) - 1) + 1

'Counter() is an array containing the combination.

'The Counter() array must be globally dimensioned

' outside the function and must be the size of R.

'Also, numbers (item index) must be assigned

' in ascending order; Counter(1)is the minimum

' number through Counter(R) is the maximum number.

For a = 2 To R

fsum = fsum + fColumnSum(N - Counter(a - 1), R - a + 1, Counter(a) - Counter(a - 1) - 1)

Next a

Comb_Count = fsum

End Function

 

 

 

 

 

 

After putting the functions in the appropriate module and putting the Counter array in the declarations section of the main program module, all that needs to be done is assign the combination to the Counter array and call the Comb_Count function. It would look something like this: (i.e. for a 6/49 lottery with a combination of (06, 10, 17, 37, 40, 49)

 

Sub Some_subroutine_of_the_main_program()

Counter(1) = 6

Counter(2) = 10

Counter(3) = 17

Counter(4) = 37

Counter(5) = 40

Counter(6) = 49

CombinIndex = Comb_Count(49, 6)

'CombinIndex now contains the combinatorial index of that combination.

 

End Sub

The combinatorial index of (06, 10, 17, 37, 40, 49) in 49 numbers taken 6 at a time is 7,275,389.

How you want to assign the combination values is up to you. The way I shown here is just an example. Also, this only works with single combinations like a 6/49 or 5/35. Powerball or Mega Millions are not single combos. They are a multiple combos, a pick 5 part and a pick 1 part. This algorithm only works on the pick 5 part or the pick 1 part.

You may need to text format some of the code here, however, it will work.

 

Nice work!

Thank you. It would be interesting to see what the VC translation would be. VB is my native language. I've done a little study in C, but never really got the hang of it.

Jade,

Wow, it's bee

Actually, I've always been here...  I like to watch and learn... plus, working on my home and working in general is taking up most of my time.

Quote: O

By the way, those are some nice functions you posted.  I'm a huge fan of recursion - I think you can generate some of the most elegant coding through recursion.  Thanks for posting.

There has been some questions about the recursive calling factorial function.

Here is a possible solution to the factorial function:

Function Fact(N) As Double 'The factorial function, Fact(N) = N! = N * (N-1) * (N-2) * (N-3) * ... * 3 * 2 * 1

If (N < 1) Then

Fact = 1 

Else 

F = 1

For a = 1 To N

F = F * a

Next a

Fact = F

End If

End Function

why are you concerned with cpu cycles? You spent all that money on the latest cpu and unless you are doing something like you are trying to do you will only consume on average 2-5% of cpu. So let it rip and see how long it taqkles to produce result.

I have done something similar and it takes about 10 minutes to go through several million iterations. I have also tried using MSAcess and the results are fast.

You are doing a form of data mining ...to yield some insight ..to hell with cpu time.......go for it.