Wheels

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lottoarchitect
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Re: Wheels

Post by lottoarchitect » Mon Dec 19, 2011 9:35 am

Hi a12ab, you could use the search function to find it, anyway here is a link discussing some design principles
viewtopic.php?f=7&t=28

As for the inability to construct, there are many more involved besides the values you see or calculated. The two principal issues are, the size of the interim computations and the time needed to evaluate the coverage of constructions of that size.

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Re: Wheels

Post by a12ab » Mon Dec 19, 2011 2:25 pm

hi lottoarchitect

can you please have it calculate the end result if pick 6 and 7 from 45, 15 groups 3 numbers each group, requesting 1 number from each group, 6 if15

you how wg calculate 593775/122million=2108 blocks and 363 blocks for pick 7

now i want to know what the theory for 45 in 15 groups, wg say invalid parameter, i just want to know the theory calculation, if i am not mistaken for pick 7 about 1440 blocks, but i rather the expert calculate this, please, this should be an easy one for you

cheers

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Re: Wheels

Post by lottoarchitect » Mon Dec 19, 2011 3:05 pm

As I said, if WG can't build this, then I can't too. You request things no program can provide at the moment. If you want theory to make t if m, by all means there is a whole bibliography on covering designs. It can't be described, it is so complex so don't expect something here - it is impossible to even begin describing how to begin constructing such things, even for the simplest cases without any groups involved. I can't help you on that.

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Re: Wheels

Post by a12ab » Thu Dec 22, 2011 7:27 pm

hi lotto architect

i try to construct pick 12 from 15 6if6 = 6 blocks, but how come number 14 and 15 not used? i mean in all 6 blocks number 14 and 15 are not used

kind regards

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Re: Wheels

Post by lottoarchitect » Fri Dec 23, 2011 1:39 pm

It picks numbers 14&15, just increase the grid size to see them, you don't see the last 2 numbers of the pick 12.

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Re: Wheels

Post by a12ab » Fri Dec 23, 2011 2:22 pm

hi lotto architect

cheers for that, any thread here that explains mother covering, i need real life example to understand it,

are you gonna be active here in forum in Christmas and new year holiday?

merry christmas and happy new year

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Re: Wheels

Post by lottoarchitect » Sat Dec 24, 2011 7:41 am

You may try to make a search for "mother", a couple of threads
viewtopic.php?f=19&t=434&p=1481
viewtopic.php?f=17&t=114&p=481

I try to be daily at the forums, even on those days. If you have questions just post them, besides me there are other users who can help if I am not around at that time.

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Re: Wheels

Post by a12ab » Thu Jan 12, 2012 7:43 pm

hi lottoarchitect

i got couple questions here:

1st: i try to construct pick 12 from 36 4if6 L=31, theory total=385,....
my theory total for 100% is 504, WG get 504=99.9%, can you help me get this to 100% at still 504? i afraid it's my lack of knowledge of bias or other features of the software that make me can't get it to 100% at 504( if not what is the minimum for 100%?)
and if stick at 385 like WG theory calculation 386 blocks do already any 4x31 times there or i really should bring this to 100%?

2nd: if let's say winning numbers are 1 4 7 9 12 30, i should able to find this 31 times in my 12's right? when 100% are reach or when theory total covered?

kind regards

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Re: Wheels

Post by lottoarchitect » Thu Jan 12, 2012 11:03 pm

Hi a12ab,

first keep in mind the theoretical displayed in WG is the general lowest minimum when we have a pack design construction. Generally we cannot approach that minimum (since 99% of the time we cannot construct a pack design) unless if it is a trivial construction and only when t=m as far as I can tell and in very few cases really. Computing exactly the real minimum requires advanced mathematics and covering design theory and such computations are not available for the majority of the coverings. So, we always give the minimum of a given covering by the means of a boundary. So, assuming we can make this c(12,36,4,6,l=31) in 504 blocks, then the real minimum is somewhere in the range 386 <= c(12,36,4,6,l=31) <= 504. This means, it may be possible to construct this in fewer than 504 blocks but no way to go below 386 (if it is possible to even approach that). Only if someone can actually make this in fewer than 504 blocks, then we have a new minimum boundary. We just don't know the exact minimum, or at least I don''t know it or how to compute it or of it is possible to compute it in first place with current theory.
EDIT: The following is valid only in t=m constructions (not t<m)
Now, in order to have the 4x31, the covering must be at 100%. If this needs 504 blocks, then if we have 503 blocks we are not guaranteed 4x31. If the block 1 4 7 9 12 30 comes out, then 4x31 means any 4 numbers of that 1 4 7 9 12 30 will show up at least 31 times each, the actual 1 4 7 9 12 30 block will appear fewer times but we don't care about that really. In general, if the draw x1, x2, x3, x4, x5, x6 comes, any 4 numbers of that draw must show up at least 31 times (that means e.g. the set x1, x2, x3, x4 will appear in at least 31 blocks of the covering, the same for x1, x3, x4, x5 etc). Actually given this is a 4if6, these x combinations are the required 6 correct numbers from your set of 36, not the actual drawn combination which has 12 numbers. Hope this answers your questions. You may send me the covering so to try and improve it if possible.

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Re: Wheels

Post by a12ab » Fri Jan 13, 2012 2:36 am

hi lottoarchitect

yes what i mean of having 4x31 is i will have any 4 from 1 4 7 9 12 30 x31 times, i need to get this to 100%, this question is answered, now what about if

pick 12 from 36 4if6 L=30(sorry i change my mind to 30 instead although 31 are prefered) i get this from wg= V12360406L30-99%-1-576, what are the 1-576 mean

i know i have 576 blocks for 99.995%, is this mean 1 possible 4 if 6 still uncovered, not necessarily any 4 from 1 4 7 9 12 30 but from any 6 right?

hope i make my question clear here:)

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