Line Elimination Ideas

[Kenya649]

We know a 649 game has 13,983,816 [49C6] lines (or combinations) and every line has an equal chance of being drawn.

Incidentally you will note that certain lines do not show up regularly like others.

I have started this thread for those who think/believe certain lines are unlikely to be drawn and hence eliminate them from 13,983,816.

Your idea/contributions on how to eliminate non obvious lines is highly welcome.

To start the ball rolling, first is to generate all the possible 13,983,816 lines. For non programming guys the following code will run in Excel and generate a text file (L649.txt) on the root of c drive

Sub Generate49C6()
Open "c:\L649.txt" For Output As #1
For i1 = 1 To 49 - 5
For i2 = i1 + 1 To 49 - 4
For i3 = i2 + 1 To 49 - 3
For i4 = i3 + 1 To 49 - 2
For i5 = i4 + 1 To 49 - 1
For i6 = i5 + 1 To 49 - 0
Print #1, i1 & "," & i2 & "," & i3 & "," & i4 & "," & i5 & "," & i6
Next
Next
Next
Next
Next
Next
Close #1
End Sub

Consecutive numbers/offset >3
not many 649 game will have more than 3 consecutive/offset combination.

From our local 649 game of 282 draws it is only 15,23,24,31,32,40 line that has shown up out of 33,551 such lines in 13,983,816 lines. If you look at 15,23,24,31,32,40 it has 23-15=8,31-23=8,32-24=8 and 40-32=8. If you need the code to eliminated the consecutive/offset I can provide

Please if you have a way of eliminating such lines as described above do share with us to reduce these 13,983,816 lines and probably have a reasonable lines to choose from.

Thanks

 

[blitzed]

hiya Kenya649,

good idea to purge picks which would be symmetrical offsets, goodluck!

cheers!
blitzed

 

[Iasounis]

This is a great thread. It would be great to have a website where we could plug in picks to make sure they don't 'fit' any of these unlikely combos (i.e. runs, multiples, etc.) It's these lines that make the probability better than advertised.

 

[Flexalong]

I read somewhere on Ion Saliu's website that for example if 28 32 33 40 49 51 got drawn, 29 33 34 41 50 52 is unlikely to be drawn.

 

[GillesD]

Same offset (or Delta)

I did not check your value of 33,551 for combinations with 4 or 5 similar offsets (or Deltas as they are often named) but with 2,585 draws, the Canadian Lotto 6/49 provides a large sample for actual results.

With 4 equal Deltas, it happened 7 times (the data below is in the form: Delta, draw# and the 6 winning numbers):

01: # 1748 with numbers 38, 43, 44, 45, 46 and 47
01: # 2322 with numbers 21, 22, 23, 24, 48 and 49
03: # 1420 with numbers 16, 19, 22, 34, 37 and 40
06: # 1559 with numbers 10, 13, 16, 19, 25 and 31
09: # 1002 with numbers 12, 19, 21, 28, 30 and 39
10: # 0670 with numbers 22, 27, 32, 37, 42 and 47
13: # 0258 with numbers 07, 17, 20, 30, 33 and 43

And what is even more interesting is the fact that with draw # 670, there are also 5 equal Deltas of 5, a similar pattern to the one found in the impossible (as some will say) combination of 1, 2, 3, 4 , 5 and 6 (with a Delta of 1).

05: # 0670 with numbers 22, 27, 32, 37, 42 and 47

 

[Kenya649]

Product-Subtraction elimination

This method of elimination, targets four numbers within the six numbers and if they meet the criteria the line is eliminated e.g line 11,19,29,31,41,43. the four numbers are 19,29,41,43. The criteria is as follows
(41-29)/(29-19)=1.2
29-(19*1.2)=6.2
(41*1.2)-6.2=43 the fourth number.

NB: Out of 282 draws done locally no such a line has shown up. there are at least 13,437 such lines from the possible 49 combination 6 numbers.

Another number is 8,13,20,23,38,49 & the 4 #s are 8,20,38,49
(38-20)/(20-8)=1.5
20-(8*1.5)=8
(38*1.5)-8=49 the fourth number.

Let us try and come up with more ways of eliminating more lines.

Thanks Blitzed and Iasounis for your encouragement

 

[Kenya649]

I did not check your value of 33,551 for combinations with 4 or 5 similar offsets (or Deltas as they are often named) but with 2,585 draws, the Canadian Lotto 6/49 provides a large sample for actual results.

With 4 equal Deltas, it happened 7 times (the data below is in the form: Delta, draw# and the 6 winning numbers):

01: # 1748 with numbers 38, 43, 44, 45, 46 and 47
01: # 2322 with numbers 21, 22, 23, 24, 48 and 49
03: # 1420 with numbers 16, 19, 22, 34, 37 and 40
06: # 1559 with numbers 10, 13, 16, 19, 25 and 31
09: # 1002 with numbers 12, 19, 21, 28, 30 and 39
10: # 0670 with numbers 22, 27, 32, 37, 42 and 47
13: # 0258 with numbers 07, 17, 20, 30, 33 and 43

And what is even more interesting is the fact that with draw # 670, there are also 5 equal Deltas of 5, a similar pattern to the one found in the impossible (as some will say) combination of 1, 2, 3, 4 , 5 and 6 (with a Delta of 1).

05: # 0670 with numbers 22, 27, 32, 37, 42 and 47

Good to hear from you GillesD,

I guess 8/2585 is a good starting point.

I have rechecked the numbers you have listed above and unfortunately they are not in my list.

Your method of isolating those eight lines is another elimination method. Please explain further how you isolated them.

My code for eliminating consecutive/Offset is as follows

Sub Conse_Off()
Dim x(6)
Open "c:\tc\Lotto\p.txt" For Input As #1
Open "c:\tc\lotto\po.txt" For Output As #2
Open "c:\tc\lotto\pv1.txt" For Output As #3
t = Now
Do While Not EOF(1)
For i = 1 To 6
Input #1, x(i)
Next

n1 = 0
For k = 1 To 15
n = 0
For i = 1 To 5
For j = i + 1 To 6
If x(j) - x(i) = k Then n = n + 1
Next
Next
If n > 3 Then
n1 = n
k1 = k
Exit For
End If
Next
If n1 > 0 Then
Print #2, x(1) & "," & x(2) & "," & x(3) & "," & x(4) & "," & x(5) & "," & x(6) & "," & n1 & "," & k1
Else
Print #3, x(1) & "," & x(2) & "," & x(3) & "," & x(4) & "," & x(5) & "," & x(6)
End If
Loop
t1 = Now
MsgBox "Process Completed" & t & "and ended " & t1
Close #1
Close #2
Close #3
End Sub

Thanks GillesD and Flexalong for your contribution to this thread

 

[stefan]

If I may add my 2 cents...
Maybe try to eliminate "low paying" combos (e.g. popular number sequences like diagonals, horizontals and verticals on lottery forms, etc...) When these drop, the amount of winners are usually high and - as a consequence - payouts are usually very low.
Good luck!
Stefan

 

[GillesD]

Patterns, patterns ???

Any pattern for 6 winning numbers in a lottery is in the eye of the viewer (and obviously any jackpot winner will see a beautiful pattern in his numbers). The combination 01-02-03-04-05-06 has a very regular pattern and most people will see it.

But for me, the 9 combinations listed below all have a very nice and regular pattern, although a few may not see it (besides starting with numbers 1 to 9):
01-03-09-27-32-47
02-05-06-15-18-45
03-09-27-32-43-47
04-10-12-30-36-41
05-13-15-37-39-45
05-06-15-18-37-45
07-14-21-28-35-42
08-11-20-23-24-33
09-27-31-32-43-47

As I said before, give me a good programmer and a powerful computer and a pattern will eventually be found for each of the 13,983,816 combinations (although when I said that, personnal computers were not as powerfull as of today).

 

[GillesD]

Getting information

...
I have rechecked the numbers you have listed above and unfortunately they are not in my list.

Your method of isolating those eight lines is another elimination method. Please explain further how you isolated them.

I was not looking for any elimination method but more for some information on the distribution of Deltas in past draws for the Lotto 6/49.

So basically, I calculated the 15 Deltas for each winning combinations and counted the frequency for values of Deltas from 1 to 25. If there was more than 3 identical Deltas, I identified the winning combination and at the end, I had 8 combinations - three with 4 identical Deltas and one with all 5 Deltas equal.

 

[Kenya649]

Number Difference

As I said I will be making reference from our local 649 game and you can compare what is posted here with your local game.

Another interesting elimination is when you subtract first number from the last after you sort them. From our 649 game (last number) - (first number) <15 has zero lines i.e there has never been such a combination.

Example 10,12,19,20,21,23 (23-10<15).

There are at least 68,214 such lines in 649 combination game.

Stefan,

I will see how to eliminate what you have stated. Thank for the contribution.

Welcoming more participation

Thanks

 

[Kenya649]

Zero result

This is also an interesting pattern and it has shown only twice in our local 649 game. The pattern has at least 114,536 combinations from the possible 649 game combination.

Example 6,7,19,29,34,41
7-6=1
19-7=12
29-19=10
34-29=5
41-34=7
take the results and repeat the subtraction again
12-1=11
10-12=-2
5-10=-5
7-5=2
take the results and repeat the subtraction again
-2-11=-13
-5--2=-3
2--5=7
take the results and repeat the subtraction again
-3--13=10
7--3=10
take the results and repeat the subtraction again
10-10=0
the final result

Thanks

 

[Kenya649]

Any pattern for 6 winning numbers in a lottery is in the eye of the viewer (and obviously any jackpot winner will see a beautiful pattern in his numbers). The combination 01-02-03-04-05-06 has a very regular pattern and most people will see it.


As I said before, give me a good programmer and a powerful computer and a pattern will eventually be found for each of the 13,983,816 combinations (although when I said that, personnal computers were not as powerfull as of today).

I have no problem with any beautiful pattern that may show up but please assist in identifying such a pattern and we seen how many times it has shown up in the regional game draws.

Thanks

 

[GillesD]

A few comments

Kenya649]

A – Combinations to come out

It seems you are in a hurry for all patterns show up in your lottery. Yet you have 282 draws to analyze (or 0.002% of all possibilities). I would say that many patterns with less than 1% of the combinations are likely not to have come out yet. This could include:
- a difference of less than 15 between high and low numbers;
- a distribution for consecutive numbers of 2-2-2 or 3-3 or 4-1-1 or 4-2 or 5-1 or 6-0;
- a distribution for the last numbers (in each winning number) of 2-2-2 or 3-3 or 4-1-1 or 4-2 or 5-1 or 6-0;
- a distribution for numbers per decade of 3-3, 5-1 or 6-0.

By the way, there are 73,073 combinations with a difference of 14 or less between the high and low numbers of a combination (or 0.52%).

B – Results of 0

I have checked the data for our Lotto 6/49 with 2,586 draws; I found 31 combinations with a zero (0) result, as calculated by your method. I also found 115,944 combinations (not 114,536 as you mentioned) in the 13,983,816 possible combinations.

With 31 combinations out of 2,586 draws, this gives 1.20% while 2 combinations out of 282 give 0.71%; the theorical value would be 0.83%

C – Patterns

Generate enough patterns and eventually all 13,983,816 combinations will be covered. For example, the 9 combinations given a few posts back were all generated using the same pattern: with a starting number (like 1 to 9), multiply it by 3 and repeat to get 6 numbers. If a value is greater than 49, deduct 49 and continue. And when you get a 0 as a value, then reject that pattern.

 

[Kenya649]

C – Patterns

Generate enough patterns and eventually all 13,983,816 combinations will be covered. For example, the 9 combinations given a few posts back were all generated using the same pattern: with a starting number (like 1 to 9), multiply it by 3 and repeat to get 6 numbers. If a value is greater than 49, deduct 49 and continue. And when you get a 0 as a value, then reject that pattern.

You are absolutely right e.g the following formula

int((3^n)/49)*49)-(int(3^n)/49) 0<n<35 (n is a whole number)

will produce

1,2,3,4,5,6,9,10,12,13,15,16,17,18,22,25,26,27,29,30,31,32,34,36,37,38,40,41,43 ,44,45,46,47,48

and after analysing it with our draw it had the following results

0/6------->00.00%
1/6------->00.35%
2/6------->05.30%
3/6------->15.55%
4/6------->38.87%
5/6------->31.45%
6/6------->08.48%


Thanks GillesD.

By the way do you have a system that you use to select your numbers?

 

[fourwayflashers]

Using Excel,

would it be easy to go through the master list of 13 million combinations and pick out the lines that contain a certian number? (Ex all lines that have the number 13?)

 

[GillesD]

Cycling through all combinations

Using Excel, would it be easy to go through the master list of 13 million combinations and pick out the lines that contain a certian number? (Ex all lines that have the number 13?)

Yes, very easy, the following macro cycles through all 13,983,816 combinations:

Option Explicit

Dim A As Integer, B As Integer, C As Integer
Dim D As Integer, E As Integer, F As Integer

Sub Cycle_All()
' Go through all possible combinations
For A = 1 To 44
For B = A + 1 To 45
For C = B + 1 To 46
For D = C + 1 To 47
For E = D + 1 To 48
For F = E + 1 To 49
' Insert statements to do whatever you want on each combination
...
Next F
Next E
Next D
Next C
Next B
Next A
End Sub

You then have to insert statements at the place indicated to evaluate each combination and take appropriate action.

If you want to find how many combinations have the number 13 as one of the 6 numbers, then:
- declare a variable to store the number of combinations such as "Dim N as Double" (it has to be declared as DOUBLE in case there are more than 32,767 combinations) at the top with other declarations
- set the variable N to 0 with the line "N=0" at the top of the macro
- then add the line "If A = 13 Or B = 13 Or C = 13 Or D = 13 Or E = 13 Or F = 13 Then N = N + 1" where indicated
- the last line of the macro (before the End Sub statement) could something like "Range("A1").Value=N" to display the value obtained in cell A1.

And by the way, there are only 1,712,304 combinations with the number 13 in it.

 

[hopefull]

I like the number 13,and I like numerical order even better.
12-Nov-1983 . 01 02 07 13 22 31
05-Feb-1994 .01 02 13 17 31 41
24-Dec-1983 .01 02 13 21 42 48
22-Feb-1997 .01 03 07 13 39 46
12-Jun-1993 .01 03 13 21 32 45
12-Aug-1987 .01 04 13 16 30 31
30-May-1998 .01 05 12 13 16 21
27-Jul-2002 .01 05 13 22 28 43
30-Jan-1993 .01 06 13 14 19 34
03-Sep-1983 .01 06 13 15 22 27
25-Dec-1993 .01 07 13 24 40 46
12-Jan-2002 .01 07 13 30 34 36
23-Oct-2004 .01 08 13 24 27 43
16-Jul-1988 .01 08 13 28 31 44
15-Jan-1986 .01 10 13 19 25 33
31-Mar-2001 .01 12 13 28 32 44
04-Jan-1989 .01 13 14 45 46 48
30-Dec-1987 .01 13 17 18 45 48
30-Jan-1991 .01 13 17 23 30 40
24-Mar-2007 .01 13 19 26 32 46
14-Nov-1987 .01 13 19 32 33 38
20-Sep-1989 .01 13 21 31 36 48
12-Jan-2005 .01 13 21 34 36 42
12-Apr-2008 .01 13 23 35 38 42
17-May-2000 .01 13 23 36 37 48
20-Oct-2004 . 02 03 13 14 31 36
13-Sep-1995 . 02 03 13 16 22 48
20-Jun-2001 . 02 03 13 17 23 32
21-Sep-1996 . 02 03 13 17 23 42
22-Dec-1990 . 02 03 13 26 36 38
07-Sep-1994 . 02 03 13 27 30 49
28-Jun-1989 . 02 04 13 16 17 40
07-Sep-1988 . 02 05 13 23 35 45
01-Aug-1990 . 02 08 13 23 27 44
30-Apr-1986 . 02 09 13 18 20 29
17-Oct-1992 . 02 13 15 24 33 35
15-Oct-1988 . 02 13 27 29 35 38
25-May-1988 . 02 13 28 40 41 43
07-May-1983 . 02 13 41 42 44 47.
this was just a tiny example.
on my home computer, I am sorting all previously drawn combinations in a numerical order to see where the hits are congregating the most.yes statistics.

 

[GillesD]

Numerical order

Using the lexographic value as the index key and you will find even more quickly that

- lowest set is #883, on 08/07/92 with 01, 02, 03, 04, 13 and 48;

- highest set is #1748 on 21/10/00 with 38, 43, 44, 45, 46 and 47

 

[Flexalong]

Hi GilesD,

I would like to seek your help on this. I would like to remove combinations with numbers that multiply to make a third number in them for example 1 6 8 48 50 52 has 6 x 8 = 48.

In this case I won't be removing combinations from all possible combinations but just a group of maybe thousand plus combinations.

Hope you can help me with an excel macro or formulas for this.

Thanks in advance.