Hi GameBelgium,

I don't understand how you would use this information. The logic way is to get all combinations of 37 drawings or 34, 35, 36, 38, 39, 40 drawings and then calculate how many numbers there are in each group.
The algorithm would be :

Go to first group of 37 drawings (drawings 1 to 37)
Calculate frequency of each number
See how many numbers have a frequency of 0 (they did not appear in this group)
If there are 6 numbers with frequency=0 then these are the numbers to play else continue with next group ( 1 to 38 without 37)
Calculate frequency of each number
See how many numbers have a frequency of 0 (they did not appear in this group)
If there are 6 numbers with frequency=0 then these are the numbers to play else continue with next group ( 1 to 39 without 37,38)
etc...

1 - It can happend that there are more than one group with 37 drawings (or others groups) that have 36 numbers. I wonder how to do then.
2- Once you have scanned all 37 groups, if you don't get your 6 numbers, you'll have to go to next group up or down. If you got 5 numbers with the 37 drawings, you'll have to go down to the 36 drawings group. If you have more than 6 numbers in the 37 group, you'll have to go to the 38 group.

As exemples, these are the first 20 groups of 37 drawings :

1- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
2- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 38
3- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 39
4- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 40
5- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 41
6- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 42
7- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 43
8- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 44
9- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 45
10- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 46
11- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 47
12- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 48
13- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 49
14- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 50
15- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 51
16- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 52
17- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 53
18- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 54
19- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 55
20- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 56

Now, as I said, there are probably anothers methods to do the job. If I take all the combinations of the 6/42 lotto : 5.245.786 combinations, the usefullness of this information is to find which combinations have not yet popped up but it would let us with a huge number of combinations.

taaroa

Hi Taaroa,

I don't understand why you have numbers up to 56? I thought we are playing6/42 lotto.

Flex

Hi Flex,

We are searching all combinations of 37 drawings in 100 drawings. And among them, we select the one group if exist which contains 36 numbers.

The examples I gave is about drawings. We have 100 drawings and in the group 20 for example, you have :

20 : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 56

Here, you count the first 36 drawings then you replace drawing 55 with drawing 56. It's about combinations of 37 drawings in 100 drawings.

Next group, you'll have drawing 57 and so on ...untill you reach drawing 100. Then you continue.

I hope I'm clear enough.

By the way, this is the simple program I wrote to do that. It lists all combinations for groups of 37 drawings, if you are courageous to do that. Here, I stopped at group 20.

rem this program generates all combinations of 37 in 100 drawings.

print time$()

count=0

for a=1 to 64
for b=a+1 to 65
for c=b+1 to 66
for d=c+1 to 67
for e=d+1 to 68
for f=e+1 to 69
for g=f+1 to 70
for h=g+1 to 71
for i=h+1 to 72
for j=i+1 to 73
for k=j+1 to 74
for l=k+1 to 75
for m=l+1 to 76
for n=m+1 to 77
for o=n+1 to 78
for p=o+1 to 79
for q=p+1 to 80
for r=q+1 to 81
for s=r+1 to 82
for t=s+1 to 83
for u=t+1 to 84
for v=u+1 to 85
for w=v+1 to 86
for x=w+1 to 87
for y=x+1 to 88
for z=y+1 to 89
for a1=z+1 to 90
for b1=a1+1 to 91
for c1=b1+1 to 92
for d1=c1+1 to 93
for e1=d1+1 to 94
for f1=e1+1 to 95
for g1=f1+1 to 96
for h1=g1+1 to 97
for i1=h1+1 to 98
for j1=i1+1 to 99
for k1=j1+1 to 100

The following 2 lines are only for test. Here, I ask the program to print the time when he reach the 20th group and then stop. By taking note of the time at the beginning and at the end of the process, you know how much time it took.

'if count = 20 then print time$()
'if count = 20 then end)

count=count+1

print count;"-";" ";a;" ";b;" ";c;" ";d;" ";e;" ";f;" ";g;" ";h;" ";i;" ";j;" ";k;" ";l;" ";m;" ";n;" ";o;" ";p;" ";q;" ";r;" ";s;" ";t;" ";u;" ";v;" ";w;" ";x;" ";y;" ";z;" ";a1;" ";b1;" ";c1;" ";d1;" ";e1;" ";f1;" ";g1;" ";h1;" ";i1;" ";j1;" ";k1

next k1
next j1
next i1
next h1
next g1
next f1
next e1
next d1
next c1
next b1
next a1
next z
next y
next x
next w
next v
next u
next t
next s
next r
next q
next p
next o
next n
next m
next l
next k
next j
next i
next h
next g
next f
next e
next d
next c
next b
next a

print count
print time$()
print " Finished the job, my friend! Good luck!"


end

I use the LibertyBasic program. There is a free version on their site.


taaroa

Hi,

This is my explanation again said another way :

Group 1 : I take the first 37 drawings in 100 drawings.
Group 2 : I replace drawing 37 with drawing 38
Group 3 : I replace drawing 38 with drawing 39
Group 2 : I replace drawing 39 with drawing 40
Group 2 : I replace drawing 40 with drawing 41
Group 2 : I replace drawing 41 with drawing 42
Group 2 : I replace drawing 42 with drawing 43
Group 2 : I replace drawing 43 with drawing 44

etc...



1- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
2- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 38
3- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 39
4- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 40
5- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 41
6- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 42
7- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 43
8- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 44

When you reach the group #64 you will be at the bottom of the list of 100 drawings. See 64 below. Then you continue with group 65 but this time there is not drawing 36. And so on...

64- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 100
65- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 37 38
66- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 37 39
67- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 37 40
68- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 37 41

That's all about combinatorics.

taaroa

Hi Gandalf,

I counted the frequency for each number in the 33 drawings you gave. These are the results :

Dernier tirage enregistré :24/01/2009
Ordre-#-Freq - Loto test Belge
1 36 10
2 23 9
3 33 9
4 12 8
5 35 8
6 24 7
7 19 7
8 38 7
9 31 7
10 27 7
11 18 7
12 28 6
13 1 6
14 7 6
15 11 6
16 37 6
17 9 6
18 41 6
19 22 5
20 3 5
21 42 5
22 6 5
23 39 5
24 4 5
25 13 5
26 21 4
27 34 4
28 17 4
29 29 4
30 25 4
31 40 4
32 14 3
33 26 3
34 15 3
35 32 2
36 20 0
37 5 0
38 16 0
39 30 0
40 10 0
41 2 0
42 8 0

This group of 33 drawings have 7 numbers not 6 with frequency 0 :
2-5-8-10-16-20-30. I'm wrong?

taaroa

Thanks for the clarification, Taaroa.

I see what you mean and that is just displaying billions and billions of combinations of draws. I wonder how long more it will take to actually count the numbers in them and return the groups that have more than 6 missing numbers.

"Thanks for the clarification, Taaroa.

I see what you mean and that is just displaying billions and billions of combinations of draws. I wonder how long more it will take to actually count the numbers in them and return the groups that have more than 6 missing numbers."

Flex"

Yes, it will be a very long time. And if you must resume the count for another group than 37, 36 for example, you can imagine the time it will take. For the Belgium 6/42, you'll have three days to do that because the drawings are Wednesday and Saturday.

So, the algorithm to do the job is not a difficult one but the program must be written by a good programmer knowing fast language and he must have a very fast computer. These are the keys. There is not another way to do that from my point of view. As Ganalf said, we can also calculate by choosing the 37 drawings at random. It is one solution. You would be happy to find the good group in one hour or two.
Now, it depends how they pay for the jackpot. I don't have found this information. If the jackpot is good enough, it will be worth calculating one whole day or more! Then, when you have won, you buy better computers and dispatch the work on these. Another way is to borrow NASA computers!

taaroa

I've been trying some random combinations to see how many drawings within the last 100 have 30+ missing. Not surprisingly, almost ALL of them do!

The last drawing of the Belgian Lotto was:
02 05 08 10 16 20
In 33 of the last 100 drawings, none of these numbers did occur.

Now, if I change the values of the last drawing to random combinations:
01 02 03 04 05 06: 41 of the L100
12 14 16 18 20 22: 33 of the L100
18 19 20 21 22 23: 32 of the L100
36 37 38 39 40 41: 36 of the L100
05 12 13 24 34 35: 31 of the L100
...
(I went on for a while, ALL combinations having more or less the same result)

Having said that, even if you'd find a programmer to search for all combinations from the last 100 drawings not containing a six number combination for 37 times (which is how this thread started), you'd come up with thousands and thousands of combinations.

As I said before, if you find the programmer the second key problem will be to find a high speed computer. It's a material problem. We know how to do it but we need just the good programmer and the good computer. They'll do the job. The problem is that it will be difficult to get the computer, but NASA computers can do it easily.

So, we can conclude that we will not have the right computer and for this reason, we must search another way.

I think that we must look at the random method. I think that Excel can do that :
- list last 100 drawings in 6 colums
- Add a column with random() formula for a number between 1 and 100
- Sort the lines on that column
- Count the frequency of each number for the first 37 numbers

I'm not an Excel expert so, if somebody could help us on that point, it would be a good point.

I'm programming the same thing with LibertyBasic. Will be slow as I'm just a self-made programmer.

taaroa

Hi Taaroa,

I think GameBelgium is refering to the problem you mentioned in a previous post and I quote "It can happend that there are more than one group with 37 drawings (or others groups) that have 36 numbers. I wonder how to do then."

He is getting thousands of such groups with 36 numbers.

Which makes me think that using 100 draws may be too much.

Hi Flex,

I was speaking of groups of 37 drawings which have 36 numbers. I don't think there will be thousands of these groups with 36 numbers. Now, we can also look at the number of last drawings to use. I keep on Gandalf original idea of 100 drawings. I don't know why he use 100 drawings. Using less drawings say 42 drawings will cut the number of 37 drawings combinations a lot. We must test that. There will be 850668 combinations of groups of 37 drawings.

taaroa

Indeed Taaroa and best of luck.

Hi,

I just analysed 300 groups of 20, 33 and 37 drawings with an Excel sheet.
I shuffled (at random) the last 100 drawings then calculate the frequency of groups of 20, 33 and 37 drawings.
I noticed that the group of 37 drawings had one missing number sometimes.
The group of 33 drawings have one number missing sometimes and 2 numbers missing rarely.
The group of 20 drawings had some 6 numbers missing and once eight numbers missing.

To calculate the frequency, I took the first 20 drawings, then the first 33 drawings (20+13), then the first 37 drawings (33+4). The calculation was made at the same time. Then I shuffled the 100 drawings again and the groups were analysed again.

My conclusion is that 6 numbers missing in 33 to 37 drawings is a rare occurence if you limit your search to a small number of groups.
The group of 20 drawings do have some 6 numbers missing but it that case there are too many numbers to choose.

Just for information, these are the 6 numbers I found for Wednesday drawing:

1-14-17-27-32-37
1-11-30-34-38-40
2-9-10-14-25-26
20-21-25-30-31-34
4-9-14-17-19-25-26-34 (8 numbers)

taaroa

For what lottery is that Taaroa? I'm really curious to follow-up on these results.

Hi GameBelgium

Ek neem aan dat jy my kan lees en verstaan, ek gaan vir jou 'n file oplaai vir Saterdag, dan moet jy my met die nommers help asb.

BlouBul