Improved C(49,6,3,6)=163 record wheel
Manfred
record wheel
C(49,6,3,6)=163.
The new record wheel covers only 85.54828% of all lines with three
number
combinations. All other lines cover more than three number
combinations.
That are about 3977 lines less for three number combinations than in
the first record wheel and that means, that in about 3977 lines more
we have 4 or more right number combinations.
In my example for the new record wheel there are not two groups with
the numbers
1 to 27 and 28 to 49. I have interlocked the two wheels, so that we
have in one
group numbers from 1 to 49 (missing the numbers from the second group)
and in
the second group we have the numbers from 2 to 48 (missing the numbers
from the
first group). This is more practically, because in one drawing we have
normally
a wider spread than 22 numbers and the chance could be higher that not
three numbers will fall into the first group and three numbers into
the second group.
New improved pattern for C(27,6,3,4)=86
1 2 4 10 13 27
1 2 4 14 21 22
1 2 7 9 23 25
1 3 5 6 7 23
1 3 10 20 24 27
1 3 12 16 19 20
1 4 6 8 13 22
1 4 9 15 18 22
1 4 11 22 25 26
1 5 10 17 19 27
1 5 12 16 17 24
1 6 7 10 25 27
1 7 8 17 20 23
1 7 13 19 23 24
1 8 9 10 12 27
1 11 12 14 15 16
1 11 12 16 18 21
1 12 14 16 18 26
1 12 15 16 21 26
1 13 16 22 23 25
2 3 6 8 20 25
2 3 8 15 19 26
2 3 11 13 17 18
2 4 6 7 12 16
2 4 9 16 25 27
2 5 8 11 18 24
2 5 9 14 17 19
2 5 13 15 20 26
2 6 11 18 19 20
2 6 15 17 24 26
2 7 10 14 16 21
2 8 16 22 23 27
2 9 10 12 22 25
2 9 18 21 24 26
2 12 14 21 23 27
2 13 14 18 21 25
3 4 5 6 16 27
3 4 7 12 20 24
3 4 10 17 23 24
3 5 6 10 12 22
3 5 6 18 21 26
3 5 11 13 17 20
3 7 17 19 22 27
3 8 9 11 19 21
3 8 14 18 19 25
3 9 13 14 17 26
3 9 14 15 20 24
3 13 15 17 21 25
3 16 20 22 23 24
4 5 7 12 17 19
4 5 10 19 20 23
4 7 8 12 23 25
4 7 9 12 13 22
4 8 16 17 20 27
4 10 11 14 15 23
4 10 18 21 23 26
4 13 16 19 24 27
5 6 14 17 19 24
5 7 20 22 24 27
5 8 9 14 24 26
5 8 15 21 24 25
5 9 11 13 20 21
5 9 11 15 17 25
5 13 14 18 20 25
5 16 17 19 22 23
6 7 8 10 13 16
6 8 9 13 19 24
6 8 11 14 15 26
6 8 12 13 23 27
6 9 10 16 22 23
6 9 11 17 21 24
6 9 14 19 20 26
6 14 17 18 24 25
6 15 19 20 21 25
7 9 10 15 16 18
7 10 11 16 25 26
7 11 14 18 22 27
7 11 15 21 22 27
7 14 15 22 26 27
8 10 12 17 20 22
8 17 18 20 21 26
9 12 15 18 23 27
10 12 13 19 22 24
11 12 23 25 26 27
11 13 19 24 25 26
13 15 18 19 21 26
New improved record wheel C(27,6,3,4) + C(22,6,3,3) = C(49,6,3,6)=163
with interlocked numbers
1 4 9 18 22 42
1 4 22 26 36 49
1 4 22 29 39 45
1 4 22 31 33 38
1 4 27 29 35 38
1 5 7 30 31 47
1 5 12 16 24 41
1 5 19 27 35 41
1 7 9 29 47 49
1 7 19 24 38 47
1 7 27 31 35 49
1 7 33 41 44 47
1 9 12 27 33 35
1 12 16 18 26 39
1 12 16 18 36 45
1 12 16 19 30 44
1 12 16 26 42 45
1 12 16 36 39 42
1 16 22 38 47 49
1 24 27 30 35 44
2 3 6 8 28 32
2 3 10 13 20 25
2 3 11 17 43 46
2 3 14 21 34 48
2 3 15 23 37 40
2 6 10 14 15 46
2 6 11 21 25 40
2 6 13 23 34 43
2 6 17 20 37 48
2 8 10 17 21 23
2 8 11 13 15 48
2 8 14 25 37 43
2 8 20 34 40 46
2 10 11 28 34 37
2 10 32 40 43 48
2 11 14 20 23 32
2 13 14 17 28 40
2 13 21 32 37 46
2 15 17 25 32 34
2 15 20 21 28 43
2 23 25 28 46 48
3 6 10 17 34 40
3 6 11 13 14 37
3 6 15 25 43 48
3 6 20 21 23 46
3 8 10 37 46 48
3 8 11 23 25 34
3 8 13 21 40 43
3 8 14 15 17 20
3 10 11 15 21 32
3 10 14 23 28 43
3 11 20 28 40 48
3 13 15 28 34 46
3 13 17 23 32 48
3 14 25 32 40 46
3 17 21 25 28 37
3 20 32 34 37 43
4 5 7 12 19 41
4 5 16 27 30 31
4 5 19 35 44 47
4 7 9 12 22 38
4 7 12 16 29 31
4 7 12 24 30 44
4 7 12 33 47 49
4 9 16 27 29 49
4 16 19 24 27 38
4 16 27 33 41 44
4 18 26 35 45 47
4 24 30 35 41 47
4 35 36 39 42 47
5 7 22 24 27 44
5 9 19 29 39 41
5 9 24 26 33 39
5 9 36 38 44 45
5 9 36 41 42 49
5 12 22 30 31 35
5 16 19 22 41 47
5 18 24 29 33 36
5 18 26 30 31 45
5 18 38 39 44 49
5 19 24 31 39 41
5 24 33 42 45 49
5 26 29 38 42 44
5 30 36 38 41 44
6 8 10 11 20 43
6 8 13 17 25 46
6 8 14 23 40 48
6 8 15 21 34 37
6 10 13 21 28 48
6 10 23 25 32 37
6 11 15 17 23 28
6 11 32 34 46 48
6 13 15 20 32 40
6 14 17 21 32 43
6 14 20 25 28 34
6 28 37 40 43 46
7 9 16 18 35 42
7 16 26 35 36 49
7 16 29 35 39 45
7 16 31 33 35 38
7 18 22 27 36 39
7 19 22 27 30 41
7 22 26 27 39 42
7 22 27 36 42 45
8 10 13 14 32 34
8 10 15 25 28 40
8 11 14 21 28 46
8 11 17 32 37 40
8 13 20 23 28 37
8 15 23 32 43 46
8 17 28 34 43 48
8 20 21 25 32 48
9 12 18 27 42 47
9 12 22 29 35 49
9 16 22 31 35 47
9 18 24 26 29 45
9 19 24 31 33 38
9 19 26 31 39 44
9 19 30 33 36 45
9 24 30 39 42 44
9 24 31 36 41 45
9 26 30 38 39 41
10 11 13 23 40 46
10 11 14 17 25 48
10 13 15 17 37 43
10 14 20 21 37 40
10 15 20 23 34 48
10 17 20 28 32 46
10 21 25 34 43 46
11 13 17 20 21 34
11 13 25 28 32 43
11 14 15 34 40 43
11 15 20 25 37 46
11 21 23 37 43 48
12 19 22 24 35 38
12 22 33 35 41 44
12 26 27 36 47 49
12 27 29 39 45 47
12 27 31 33 38 47
13 14 15 21 23 25
13 14 20 43 46 48
13 25 34 37 40 48
14 15 28 32 37 48
14 17 23 34 37 46
15 17 21 40 46 48
16 22 24 30 44 47
16 22 27 29 33 47
17 20 23 25 40 43
18 19 26 38 42 45
18 19 29 31 36 44
18 19 30 33 39 49
18 24 31 39 41 49
18 26 33 41 44 45
18 29 30 36 38 41
18 29 38 39 45 49
19 24 26 36 38 49
19 26 29 30 33 42
19 31 42 44 45 49
21 23 28 32 34 40
24 26 29 31 41 42
26 31 33 36 39 42
29 30 31 33 44 49
30 38 41 42 45 49
Numbers of group one: 1,4,5,7,9,12,16,18,19,22,24,26,27,
29,30,31,33,35,36,38,39,41,42,44,45,47,49. All other numbers
for group two.
Who makes a statistical research whether this splitting was better
in the past than using 1-27 and 28-49? In which group-splitting we
had less 3-3 splittings?
Manfred
Nick Koutras
Yes I agree.
This is an improved record.
From a lotto players view we can use CoverMaster to produce two reports.
Old cover c(27,6,3,4)=27
T if M Tested Covered % Uncovered %
-----------------------------------------------------------------
- 2 On 2 : 351 351 100.00000 0 0.00000
- 2 On 3 : 2,925 2,925 100.00000 0 0.00000
- 2 On 4 : 17,550 17,550 100.00000 0 0.00000
- 2 On 5 : 80,730 80,730 100.00000 0 0.00000
- 2 On 6 : 296,010 296,010 100.00000 0 0.00000
1,458 3 On 3 : 2,925 1,467 50.15385 1,458 49.84615
- 3 On 4 : 17,550 17,550 100.00000 0 0.00000
- 3 On 5 : 80,730 80,730 100.00000 0 0.00000
- 3 On 6 : 296,010 296,010 100.00000 0 0.00000
16,277 4 On 4 : 17,550 1,273 7.25356 16,277 92.74644
56,324 4 On 5 : 80,730 24,406 30.23164 56,324 69.76836
99,068 4 On 6 : 296,010 196,942 66.53221 99,068 33.46779
80,214 5 On 5 : 80,730 516 0.63917 80,214 99.36083
285,148 5 On 6 : 296,010 10,862 3.66947 285,148
96.33053
538,489 <-- = uncovered
Your new instance:
T if M Tested Covered % Uncovered %
-----------------------------------------------------------------
2 On 2 : 351 351 100.00000 0 0.00000 -
2 On 3 : 2,925 2,925 100.00000 0 0.00000 -
2 On 4 : 17,550 17,550 100.00000 0 0.00000 -
2 On 5 : 80,730 80,730 100.00000 0 0.00000 -
2 On 6 : 296,010 296,010 100.00000 0 0.00000 -
3 On 3 : 2,925 1,475 50.42735 1,450 49.57265
1,450
3 On 4 : 17,550 17,550 100.00000 0 0.00000 -
3 On 5 : 80,730 80,730 100.00000 0 0.00000 -
3 On 6 : 296,010 296,010 100.00000 0 0.00000 -
4 On 4 : 17,550 1,276 7.27066 16,274 92.72934
16,274
4 On 5 : 80,730 24,525 30.37904 56,205 69.62096
56,205
4 On 6 : 296,010 197,608 66.75720 98,402 33.24280
98,402
5 On 5 : 80,730 516 0.63917 80,214 99.36083
80,214
5 On 6 : 296,010 10,871 3.67251 285,139 96.32749
285,139
537,684 <-- Uncovered
<<<< Better by 805 >>>
Thanks
Manfred wrote:
--
Nick Koutras
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Lotto DesignerXL: http://LottoDesigner.5u.com/index.htm
Features : http://LottoDesigner.5u.com/features/index.htm
Download : http://LottoDesigner.5u.com/download/index.htm
Lotto Designs : http://LottoDesigner.5u.com/designs/index.htm
E-mail : mailto:tl...@hotmail.com
Technical Papers: http://LottoDesigns.50megs.com/index.htm
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Franc Jose
If I had a method to select 22 numbers that use to hit 6 numbers more often
than the odds while the other 27 numbers group, got the same characteristic
(6 hits >>> than the odds) ... it would be easy for me to try the
49_6_3_6_=163 wheel.
This doesn't want to minimize the research you and others are making ... but
if there's no research in the predictive area the wheel cannot value the
risk of playing 163 lines.
If someone knows how to select a 22 numbers group that beat the odds in 6 or
5 hits but is equal to the odds in the 0 and 1 hits he must play the 22
numbers and reject to play the 27 complementar numbers.
So, have someone an efficient method to make the 6 or 5 hitting more in
these two complementar groups (22+27=49).
Frank
"Manfred" <sm...@gmx.de> wrote in message
news:72aa15be.02021...@posting.google.com...
Robert Perkis
Is the new wheel actually one wheel where almost every number
comes in contact with every other in at least one combination?
Or are they still two totally independent wheels, merged with
a random overlay over the pointer number template? As a user
of CoverMaster might do by importing the wheel and clicking on
[randomize] or exchanging their numbers for pointer numbers in
such an order?
Is there a link to where this new wheel will be on display?
Thank you.
Robert Perkis / http://www.lotto-logix.com/wheellinks.html
Manfred
the new wheel is no one wheel. It consists
of the two wheels (in pallel). Therefore I posted also the new part
C(27,6,3,4).
The other part C(22,6,3,3) is well known and both are totally
independent.
I merged them by hand with the posted numbers with Covermaster's
function
Tools - Transpose - swap... with... - Apply , but I could have done it
also
randomly with Covermaster. But then I would not have got the numbers
split
which I wanted for the two wheels.
I have a homepage, but not yet filled with content.
I think, the progress of the new wheel is minimal and it's no worth
to consist on
a Copyright and everybody may show the improved wheels C(27,6,3,4)=86
and
C(49,6,3,6)=163 on his home page.
If you load the wheel into Covermaster, then set the right settings
for match and hits.
Then goto: Tools - Reports - Charts - Dependency. All columns with
34428
represent the numbers from the wheel C(22,6,3,3)=77. You may sort
them
into one block if you use first: Tools - Sort - Dependency.
Manfred
Robert Perkis <rob...@icdus.com> wrote in message news:<3C7569D1...@icdus.com>...
Michał Piechowski
I've been checking this problem recently and friend pointed me to your solution. I've verified that indeed that set of 163 "tickets" is enough, so I send my respect for your achievement. Anyway, I have a question because in this thread the word "improved" appears many times but word "optimal" was not mentioned even once. During my tries I've came to the point where my set had size less than 400 but it was not a problem (just a bit CPU intensive task) to make it smaller since in multiple tickets I could replace some numbers with "0" and still such set would cover all cases. I've used my algorithm on your 163 record and there is not even a one number that could be removed from any of those tickets, so in my eyes this is optimal solution which can't be improved further. Am I missing something?
BR,
Michal