Optimum size for a group

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kweg
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Optimum size for a group

Post by kweg » Fri Feb 28, 2014 1:49 am

Hi Anastasios
I am using WG to construct matrix wheels and I am wondering if there is an optimum size for a group.
For example, in a local pick 6 game I recently chose 18 numbers and put them in two (2) groups of 9 and used the matrix function to wheel them asking for 3 numbers from each group. WG displayed "Th.Min 17.464" so I selected 18 games . One group actually had 3 numbers correct and the other had 2 numbers correct but in my 18 games I had 2 games of 3 out of 6 numbers correct and in each game the 3 correct numbers were made up of 2 from one group and 1 from the other.
I would have thought that if I correctly picked 3 numbers from 1 group then they would have appeared together in one game.
GAT did a great job selecting the groups of 9 numbers but somehow I have not wheeled them correctly so I would be grateful for your advice:
(1) For 18 numbers in a matrix wheel, is 2 groups of 9 optimum or is some other combination, say 3 groups of 6, better?
(2) In my example, should I have used more than 18 games? If so, how do I determine the number of games to play to maximize my results. For example, in the situation above how many games should I have played and what are the best results I can expect from 3 correct out of 9 and 2 correct out of a second group of 9.
I trust I have stated this clearly and look forward to your comments.
Thank you
Kerry Gannon

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lottoarchitect
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Re: Optimum size for a group

Post by lottoarchitect » Fri Feb 28, 2014 11:20 am

Hi kweg, several questions here, let's see what we can address.
For example, in a local pick 6 game I recently chose 18 numbers and put them in two (2) groups of 9 and used the matrix function to wheel them asking for 3 numbers from each group. WG displayed "Th.Min 17.464" so I selected 18 games
and
(2) In my example, should I have used more than 18 games? If so, how do I determine the number of games to play to maximize my results. For example, in the situation above how many games should I have played and what are the best results I can expect from 3 correct out of 9 and 2 correct out of a second group of 9.
Keep in mind, the th.min is just a theoretical estimation which really can be achieved only if t=m and basically only Steiner type systems can do that. To get a rough estimation on how many blocks are needed for any construction you attempt, set an artificially high block size and enable the auto-reduce blocks. Doing so, WG will start removing blocks whilst maintaining the desired L% coverage (I assume you have this to 100%). Then deactivate auto-reduce and remove manually some more blocks and keep optimizing till you make it at 100%. This is the preferred approach to estimate how many blocks are needed and it is especially suited when we attempt constructions with filters. A good starting value for initial blocks to use when you enable the auto-reduce is 4-5 times what the th.min indicates.
I would have thought that if I correctly picked 3 numbers from 1 group then they would have appeared together in one game.
Have you set the number groups in guide mode?
(1) For 18 numbers in a matrix wheel, is 2 groups of 9 optimum or is some other combination, say 3 groups of 6, better?
Based on this analysis here, it is best to have as few groups as possible.
viewtopic.php?f=23&t=671

hope this answers your questions.

kweg
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Re: Optimum size for a group

Post by kweg » Fri Feb 28, 2014 12:10 pm

Thank you Anastasios for your prompt and detailed response.
Your comments re the 4 to 5 times the Th. Min were most helpful and I will put this into practice the next time I wheel some numbers. I had read, some time ago , your comments on this in your post of 14 October 2013 but I had forgotten. I tend to have "seniors moments" these days. It will be interesting to see how many games above the "Th. Min" I end up with.
I think I used the "guide mode" in the "Group" / Matrix selection - I know I have to do this.
As I said in my initial post, GAT performed extremely well - picking 3 out of 3 in one of the groups and 2 out of 3 in the other. This gives me a lot of confidence in that if I get the wheeling right I could well win a substantial prize.

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Re: Optimum size for a group

Post by Rustamshah » Mon Jun 09, 2014 5:03 pm

HI LA

I just recently downloaded the WG and I am still pretty new using it, forgive my lack of knowledge, but I am still trying to figure how to construct a Matrix wheel out of my chosen numbers ? If I have a pool of numbers in mind, can I use them in matrix construction and how ?

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Re: Optimum size for a group

Post by lottoarchitect » Mon Jun 09, 2014 11:11 pm

Hi Rustamshah, there is a detailed example with a lot of explanation at the WG's help file (at the end). Have you checked it out? Any set of numbers can be prepared as matrix, as long as you can split them in groups based on the requirement to have exactly x correct from each group. If we cannot do this split with this requirement, then matrix shouldn't be a good option. I believe the help file will answer all your questions; if you still have issues, let me know what makes it complicated.

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Re: Optimum size for a group

Post by Rustamshah » Mon Jun 30, 2014 7:41 pm

Hi LA

I have a question, regarding Th.Min, for example I have selected 25 numbers [v], where [k] is 12, expecting [t] 4 if [m] 6. It give me Th.Min of 3.554, does it mean that WG is or will give a guarantee that in approx 4 combinations I will have at least one 4 hit on given scenario ? However, when I run it, It stuck on 92.876xxx % ? what does it mean ? BTW no filters were selected !

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Re: Optimum size for a group

Post by lottoarchitect » Mon Jun 30, 2014 9:04 pm

You didn't say what was the b setting, how many blocks did you request for this covering? Th.min is just that, a theoretical minimum estimation of total blocks needed to make an 100% wheel. However, this estimation assumes the covering can be made as pack design, which means each block of the covering covers uniquely some of the required m-size combinations and no other block in the covering covers the same m-sized combinations. This situation is known as a "pack design" and only if we can construct a pack design, we can match the th.min indicated. In reality, very few t=m coverings can be constructed as pack designs and I don't know of any t<m construction that can be made as pack design. This unavoidable overlap among covering blocks is the reason we cannot approach that th.min. Thus, if you set b=4 or around there, it is reasonable to have only a 92% coverage achievement. A quick run with WG in your particular covering made it in 10 blocks; might be possible to go down to 9 blocks or even lower but no matter what we try, it is impossible to go below what that th.min indicates, even if we assume we can make that covering as pack design (it can't be done). If you look for th. min you'll find more info here.

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Re: Optimum size for a group

Post by Rustamshah » Tue Jul 01, 2014 3:01 am

Hi LA

Yes was set for 4, however, do I take it from this results that there is still 92% chance, roughly speaking that I may get 4 hit out of this scenario ?

What I am looking is to construct either two for my lotto

v=25
k=12
t=4 or 5
v=6
L=1
b=4 or 5
if it can be made with out over 90%, it would be nice.

The other one I am looking for where I m asking from WG everything same however, where k=9, of course I understand I can not have b=4 or 5 it may be more then that, if you have any previous constructions, please let me know or any tip ?

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Re: Optimum size for a group

Post by lottoarchitect » Tue Jul 01, 2014 7:54 pm

Rustamshah wrote: Yes was set for 4, however, do I take it from this results that there is still 92% chance, roughly speaking that I may get 4 hit out of this scenario ?

If your m condition is satisfied, then you'll have exactly 92% chance for a 4-hit, or whatever % indicated by WG. You may also use the detailed hits analysis to see exactly what you can expect hit-wise from that covering with 4 blocks.

There are no real tips here, just let WG construct the covering with the requested parameters. There is a small tip when the 1-block cover value (at the bottom of the progress panel) is quite high (more than 10000), you can set the bias slider to a positive setting i.e. 500, this usually makes a covering quicker but since these are small coverings, letting the engine work with the default settings is ok too. Then, when no further improvements occur, or you see the current coverage constantly higher than the current best found, simply reduce the bias.
Other small trick include adding some more blocks during optimization, let the engine reach the maximum % it can achieve (with the added blocks) and then remove them to your desired b and let it optimize as far as it can go; you can repeat that process over and over again. However these tricks are mostly useful in quite bigger wheels, in this case here I doubt you'll benefit from these tips. If you construct coverings with 50 or more blocks, this tip can give you quicker the desired results.

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