Tutorial - Understanding the Detailed hits analysis
Posted: 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:
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:
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:
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
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]
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 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%
...
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%
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%
...
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]