Tutorial - Understanding the Detailed hits analysis

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lottoarchitect
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Tutorial - Understanding the Detailed hits analysis

Post by lottoarchitect » Wed Dec 24, 2008 2:02 am

In this tutorial we will give some in-depth insight of the detailed hits and detailed filtered hits analysis of WG 1.6
As usual, this is more easily understood by the means of an example.

Let's assume we want to play the following c(10,6,4,5) = 7 covering for an 6/49 lotto. For simplicity, we also assume these are also the numbers we actually play (numbers 1 - 10).

01 02 03 04 09 10
01 02 05 06 07 10
01 03 05 06 07 10
01 04 05 07 08 09
02 03 04 06 08 09
02 03 05 07 08 10
03 04 06 08 09 10

It would be nice to know what we could win if we match 1 or 2 or 3 or more numbers from our selection of 10 numbers when compared to the actual draw. This is exactly what the detailed hits analysis shows; what we could win.
A draw with e.g. 3 matches to our numbers would be for example the draw 01 03 04 40 45 46. This draw has three numbers in common with our selection (1-10).

To obtain the relevant detailed hits analysis in WG, when we match 3 numbers, simply set the parameter "match [m] category" to 3:

Code: Select all

Details information on 3 hits
---------------------------------------------------------------------------------------------------
                 6        5        4        3        2        1        0    Total        %    Sum %
---------------------------------------------------------------------------------------------------
                 0        0        0        3        1    1 - 2    1 - 2        4    3,33%    3,33%
                 0        0        0        2    1 - 4    0 - 4    0 - 1       36   30,00%   33,33%
                 0        0        0        1    3 - 5    0 - 3    0 - 1       56   46,67%   80,00%
                 0        0        0        0        6    0 - 1    0 - 1       14   11,67%   91,67%
                 0        0        0        0        5        2        0       10    8,33%  100,00%
       0H      120      120      120       24        0        0        0      120                  
       0%  100,00%  100,00%  100,00%   20,00%    0,00%    0,00%    0,00%                           
The above analysis gives an insight of the winnings we can expect when playing this particular covering and we match 3 correct numbers. There are 120 different possibilities of draws (the last number displayed at the 0H line, under the total) that contain exactly 3 numbers compared to our selection (where xx appears is any number > 10 which of course cannot match any of our selection 1-10):

The 120 different posibilities when we match exactly 3 numbers
01 02 03 xx xx xx
01 02 04 xx xx xx
...
01 02 10 xx xx xx
01 03 04 xx xx xx
...
08 09 10 xx xx xx

Now, lets assume that the draw 01 02 10 xx xx xx comes out. If we compare this draw to our covering we can see that:
01 02 03 04 09 10 -> 3 matches
01 02 05 06 07 10 -> 3 matches
01 03 05 06 07 10 -> 2 matches
01 04 05 07 08 09 -> 1 match
02 03 04 06 08 09 -> 1 match
02 03 05 07 08 10 -> 2 matches
03 04 06 08 09 10 -> 1 match

A summary: 2x3 matches, 2x2 matches, 3x1 match. Also note that if we sum up these 2+2+3=7, it should always be equal to the total lines in our covering. In layman's terms, this means there will be 2 blocks that will offer 3 numbers, 2 blocks with 2 numbers and 3 blocks with 1 number correct.

This winning distribution corresponds to the 2nd line of the analysis:

Code: Select all

---------------------------------------------------------------------------------------------------
                 6        5        4        3        2        1        0    Total        %    Sum %
---------------------------------------------------------------------------------------------------
...
                0        0        0        2    1 - 4    0 - 4    0 - 1       36   30,00%   33,33%
...
This line tell us that there are 36 possibilities out of the 120 - or 30.00% (always assuming we will match 3 numbers) that can offer 2x3 matches, 1-4 x 2 matches, 0-4 x 1 match and the draw 01 02 10 xx xx xx is one of those 36 posibilities.
However, we might need a better insight of the 2 numbers hit category. This is where the "fold ranges at" comes in. Instead of displaying 1 - 4 (under column 2) we can expand this more. So, to expand the column 2 to its individual parts, we set the fold ranges at = 1 (which means anything above the winning division 1 will be unfolded to its individual values) as seen below:

Code: Select all

Details information on 3 hits
---------------------------------------------------------------------------------------------------
                 6        5        4        3        2        1        0    Total        %    Sum %
---------------------------------------------------------------------------------------------------
                 0        0        0        3        1    1 - 2    1 - 2        4    3,33%    3,33%
                 0        0        0        2        4        0        1        2    1,67%    5,00% <- This is the expanded version of the example above
                 0        0        0        2        3    1 - 2    0 - 1       10    8,33%   13,33% <- This is the expanded version of the example above
                 0        0        0        2        2    2 - 3    0 - 1       20   16,67%   30,00% <- This is the expanded version of the example above. This is also the line representing the hits of the draw 01 02 10 xx xx xx
                 0        0        0        2        1        4        0        4    3,33%   33,33% <- This is the expanded version of the example above
                 0        0        0        1        5        0        1        2    1,67%   35,00%
                 0        0        0        1        4    1 - 2    0 - 1       28   23,33%   58,33%
                 0        0        0        1        3        3        0       26   21,67%   80,00%
                 0        0        0        0        6    0 - 1    0 - 1       14   11,67%   91,67%
                 0        0        0        0        5        2        0       10    8,33%  100,00%
       0H      120      120      120       24        0        0        0      120                  
       0%  100,00%  100,00%  100,00%   20,00%    0,00%    0,00%    0,00%                           
Notice that all the ranges have been expanded to their individual values now under column 2, so we can have a better insight of the hits produced. If we sum up those 4 lines which are the expanded version of the line

Code: Select all

---------------------------------------------------------------------------------------------------
                 6        5        4        3        2        1        0    Total        %    Sum %
---------------------------------------------------------------------------------------------------
...
                0        0        0        2    1 - 4    0 - 4    0 - 1       36   30,00%   33,33%
...
it should be again 36. Indeed, 2 + 10 + 20 + 4 = 36
Similarly works any other line which will be expanded up to the hits specified by the "fold ranges at" option.
We can also see that this particular wins distribution will come out 30% of the time, when we match 3 correct numbers. That means, 30% of the time we will have 2 x 3 matches, 1-4 x 2 matches etc. when we have 3 correct numbers in our selection 1-10 compared to the actual draw. The sum % column adds the % of all the above lines and up to that line it is displayed. The last line of course should always add to 100%.

The last two lines (0H and 0%) simply show how many of those 120 possibilities will not offer a particular win division. For example, under column 3, we can see at the 0H row the number 24. This means 24 out of the 120 possibilities (when we match 3 numbers) will not offer any block with 3 matches and above (4,5 or 6 numbers). The 0% is just the percentage of the 0H row.

[This tutorial will be expanded more to include information for the filtered coverings hits analysis]

kweg
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Re: Tutorial - Understanding the Detailed hits analysis

Post by kweg » Sun Aug 04, 2013 1:12 am

Hi LA
I use all three of your programs ( LA for stats, GAT to select numbers and WG to wheel) and I am still on a learning curve.
I am trying to understand the Detailed Hits Analysis. I have read your tutorial and and noted your post about the typo which cleared up a point for me. However, I cannot understand the 3 hits analysis and the table relating to it in the Tutorial.
You state - "There are 120 different possibilities of draws (the last number displayed at the 0H line, under the total) that contain exactly 3 numbers compared to our selection" . Looking at the table, numbers appear under the "3" column in only the first 3 lines ( Giving a total of 96). There are no numbers in the 3 column in the last 2 lines ( a total of 24). Why are the last 2 lines therefore included in the total count to give 120.
I would be grateful if you could clarify this for me.
Thank you
Kerry

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Re: Tutorial - Understanding the Detailed hits analysis

Post by lottoarchitect » Sun Aug 04, 2013 3:37 pm

Hi kweg, that's the whole point of this hits analysis, to show you that there is also the possibility to have 3 correct numbers in your selection and still however you don't get the 3-hit win. A recap, if you match 3 correct numbers to your selection (regardless of how you play these numbers), this translates as there are 120 ways this can occur. These are the 120 ways:

1) 01 02 03 xx xx xx
2) 01 02 04 xx xx xx
...
8) 01 02 10 xx xx xx
9) 01 03 04 xx xx xx
...
120) 08 09 10 xx xx xx

Now, the analysis states 24 ways (14+10 under the column total) out of those 120 do not produce a 3-hit when you play that particular wheel, even if you have 3 correct numbers in your selection. 14 ways of those 120 produce 6 times a 2-hit and another 10 ways produce 5 times a 2-hit but none produces 3-hits. Those 24 ways are those illustrated by the 2 rows

Code: Select all

   6        5        4        3        2        1        0    Total        %    Sum %

   0        0        0        0        6    0 - 1    0 - 1       14   11,67%   91,67%
   0        0        0        0        5        2        0       10    8,33%  100,00%
So, this hit analysis says in simple words, if you match 3 correct numbers to your selection of 10 numbers which translates as 120 different ways to have 3 correct numbers, when playing that particular wheel, you can expect 96 ways to give you the 3-hit and another 24 not to give that 3-win. Indeed 96+24=120 which covers all the possibilities of 3 correct numbers to your selection of 10 numbers that can be drawn and the given wheel can cover 96 out of 120 possibilities to give you the 3-win.
Actually, if you evaluate this wheel as a 3if3, you'll see the coverage equal to 96/120 or 80% coverage to produce a 3 win when you have 3 correct numbers in your selection. The hits analysis is the detailed view of this coverage achievement.

kweg
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Re: Tutorial - Understanding the Detailed hits analysis

Post by kweg » Sun Aug 04, 2013 11:54 pm

Thanks LA for your quick and detailed response.
I had misinterpreted the phrase - "There are 120 different possibilities of draws (the last number displayed at the 0H line, under the total) that contain exactly 3 numbers compared to our selection" to relate wholly to winning numbers.
Regards
Kerry

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