# Using filters a different way

#### Goswinus

##### Member
Yesterday, in a very nice discussion with my good friend Dennis, I remembered a "strategy" I've been thinking about before.
It's probably nothing new, but it may be interesting.

For those interested, the start of the discussion can be found under "Questions & Answers " in the thread
"Where are the DN WHEELS".

The strategy involves wheels and filters, but not in the classical way.
Filters are generally used to filter out combinations we don't like.
Wheels are used because they give us some desirable benefits like guarantees and/or balance.

My theory is to use filters not to filter combinations out, but to actually validate combinations in the wheel.
I'll give a simple example to clarify.

Check out C(12,6,3,6,1):
01 02 04 05 07 12
03 04 06 08 09 11

Let's assume we want to play with the following numbers:
01 07 08 09 13 16 19 22 27 32 35 43

When we apply the numbers in this exact same sequence to the wheel, we're looking at:
01 07 09 13 19 43
08 09 16 22 27 35

When using an odd/even-filter, the first combination is considered bad, because it has all odd numbers. This line should be filter out.
But since we don't want to limit the number of combinations, we should try something different. We'll rearrange the sequence. Just as an easy example, we take the first number and move it to the back. The actual rearranging of the sequence should actually be traversing the full 12/6 wheel.

The sequence of numbers to play becomes:
07 08 09 13 16 19 22 27 32 35 43 01

Applying this sequence to the wheel would give:
07 08 13 16 22 01
09 13 19 27 32 33

Although the first combination is now better (3 odd, 3 even), it
may still be filtered out by a high/low-filter (6 low values).
So, we should use a different sequence again.

This is of course a very small wheel, but you may get the idea:
We're using the filters to find a sequence where all combination pass the filters we're using.
Remember, the goal is to use all combinations of the wheel, so we may have to look at a lot of sequences until we have a (near to) perfect set of combinations.
In the end, we will have left the wheel intact AND have perfect combinations (according to your own personal favorite filters).

OK, I'll leave it like this (for now).

#### Dennis Bassboss

##### Member
This is very interesting indeed....re-arrangement lines in wheels that are not so good to start with could increase the number of lines that might be better or more incline to hit...
Interesting...But is-it possible to do it with any kind of wheels and never touch the garantee?

#### Nick Koutras

##### Member
Hello Goswinus and others,

What you have described is exactly what LottoDesignerXL does.

You can apply theoretical unlimited filters
and to be able to create a guarantee wheel or a percent
of it from *only* the blocks that satisfy the conditions.

And above all that, you can request multiple guarantees for
Parameter L can be satisfied as many times you indicate.

#### Dennis Bassboss

##### Member
But even with these designs...it is impossible to play many filters (reducing it substantially)and not touching the 100% garantee....

#### Nick Koutras

##### Member
Hi Dennis,

quote:
But even with these designs...it is impossible to play many filters (reducing it substantially)and not touching the 100% garantee....
------------------------------

Your statment will be true if your
settings for construction are not 6 if 6
The Design will gurantee you - or a percent of - for the
parameters *you specify*!

If you are looking for 3 if 6 then that condition is the purpose of the design.
If it is 4 if 6 then the programs looks for Tickets that will satify that condition,
and so on...

That is why the L parameter *is important*

We can increase and simulataneously satisfy our conditions.

I have to go now but tomorow I'll provide a live example of a such design so we all see it's advandeges or disandvantages.

Nick

#### Goswinus

##### Member
Dennis and Nick,

I'm still not convinced I have properly explained what I mean.

I have to stress out some things regarding this strategy:

The input is an existing wheel.
The number of lines in the wheel will remain the same.
Therefore, the wheel keeps its guarantee, no matter what happens.

There are many wizards (and/or programs) out there that can deliver wheels in any kind, shape or form. I'm not into designing wheels, I always use the already invented ones. I don't care if it's small or large. If I like it, I'll use it.

At the beginning of each "population test", we'll order the selected numbers and apply this sequence to the wheel. I call this "populating" the wheel.
Just that we're all talking about the same, I mean that when the line in the wheel says 5, we'll substitute it with the 5th number in the current sequence.

After populating the wheel, the filters come into action.
During a population test, the filters determine the actual score of the population. Again, we won't get rid of any of the lines. If we don't like the score, we will try another way of populating the wheel i.e. another sequence of the selected numbers.

In subsequent population tests we'll check the score against the "best" score. The population with the "best" score is the one all our filters like best. These are the combination you will want to play ( "SHOW ME THE MONEY!!!!" )

Applying all filters to all combinations of all populations can be a very time consuming process.
If you select 12 numbers, the maximum number of permutations is 479,001,600. Testing all of them will take forever, so you might have to limit testing to a random subset.

We should be able to determine the highest possible score of all the filters combined.
Whenever we find a population that reaches this high score, we don't have to look any further. We should have the "perfect" population of the wheel. It's the cash-.

Another way to reduce testing (and time) could be this:
If you don't want to have 6 odds or 6 evens in any of the lines, such a line is considered "invalid". While testing, we'll keep track of the "invalid" lines. During the first test we might find 6 invalid lines. If a later test reveals 7 lines, we can skip testing the rest of the combinations in this population, because it can only get worse.

Am I making sense now?

#### Dennis Bassboss

##### Member
I understand that you wouldn't cut any lines from the existing wheel Goswinus..And in some cases it is true It might work without affecting the garantee mostly like Nick is saying the 3/4,4/5,5/6 etc...
I would say that it wouldn't change the garantee depending on the ''Method of construction'' of the wheel...in some method only displacing a number from one line and put it on another will affect the garantee (Mostly for the optimized wheel)...But in some wheels using different methods of construction you might be able to displace some numbers without affecting the wheel's garantee....

#### NmbrsDude

##### Member
Gentlemen,

This sort of stuff is exactly why I actually plunk down \$10/yr Cdn to use LottoGenius. This web-site does that job for me and it's paid for itself many times over already. The best part is that it runs right in your browser so you don't need to install anything and it's very user friendly. You can save the wheels to a file once you've built them so they can become templates if you like.
The only drawback I've found so far is that the guarantees for specialized wheels are all out of 6 (e.g. 3/6, 4/6 etc) so you can't do anything fancier but it still helps me a lot. You can check it out for free for 15 days and see what you think but it may get you another step in the right direction so I think it's worth your time if you really want to explore this stuff.

ND

#### Dennis Bassboss

##### Member
NmbrsDude said:
Gentlemen,

This sort of stuff is exactly why I actually plunk down \$10/yr Cdn to use LottoGenius. This web-site does that job for me and it's paid for itself many times over already. The best part is that it runs right in your browser so you don't need to install anything and it's very user friendly. You can save the wheels to a file once you've built them so they can become templates if you like.
The only drawback I've found so far is that the guarantees for specialized wheels are all out of 6 (e.g. 3/6, 4/6 etc) so you can't do anything fancier but it still helps me a lot. You can check it out for free for 15 days and see what you think but it may get you another step in the right direction so I think it's worth your time if you really want to explore this stuff.

ND
I have been there and it is mostly interesting ...some constructions are original and mostly optimized no doubts...But as you mention I would like to see similar stuff for 4/5 , 3/4 etc...But you are absolutely right it worth looking... !

#### Nick Koutras

##### Member
Hi Goswinus and Dennis,

If I understand correct your method I can see
a big problem when you can apply the filters.
The reason is the fixed quantity of numbers
that particular wheels uses.

This fixed quantity of "wheel numbers used" V parameter
can not satisfy all the possible filters each player
wants to apply.

Example:
Let say:
1. We use the c(18,6,4,6)=42
2. Generate the wheel to cover a 49/6 Game
3. Apply filters
3a. Small Numbers 1-24=2 min to 3 max.
3b. Odd Numbers =3 min to 5 max
3c. any other filter.

Here I want to indicate that many Lotto programs
apply the filter in different ways that I use them in LottoDesigner
I use the range area for each of my filter.
These are indicated as Minimum, from that filter
to Maximum from that filter.

Anyway the point is:
That the 18 number FIXED wheel can not overlap
the two filters above in such a way to pick the winning
combination, if our filter selection is correct,
because the total numbers of the filter
exceeds the number of the FIXED wheel we are using.

There are null elements in the intersection between Wheel & Filter.

I hope that my point is on exactly what you described.

My approach is different but in general compliance with what
you have described.

1. I consider as a winning combinations the combination that
ALL my filters satisfy.
2. Now the search space is known and is defined by my filters
3. The program looks *only these combinations* and generates
my wheel that satisfy my parameters (18,6,3,6)
4. The L parameter comes in play here and is of a great magnitude
for the player. (SHOW ME THE MONEY! you wrote)
If L=1, which means "that if all my filters are correct"
then I want you program to guarantee me a 3 of 6 price.
That is done and indicated so by the program.
Now if L=5 then the program will search for tickets that
1. Satisfy all the filters
2. Satisfy the L=5. Which means that will guarantee us 5 such prices.
5. I want to be clear here. That the accuracy of such search is impossible
by any program today, so I use a statistical procedure which is called
"resampling" to calculate the % cover of such hypotheses as specified by
my filters and by my L parameter.

I hope that the procedure is clear

Nick Koutras

#### Goswinus

##### Member
Last attempt

...some method only displacing a number from one line and put it on another will affect the garantee...

It may be my poor english, but I'm not talking about changing numbers in the wheel at all.

Maybe I should use a different example using a wheel with letters instead of numbers.

The two combinations in an arbitrary wheel are:

A B C D E F
G H I J K L

I have 12 numbers I would like to play with:

03 08 09 12 15 23 28 31 37 39 48 49

First, I assign my numbers to the letters. I'm young, free and single, so I can arrange my numbers the way I see fit or maybe even let two dice do the trick. Here's one way of assigning them:

A=03
B=09
C=15
D=28
E=37
F=48
G=08
H=12
I=23
J=31
K=39
L=49

A little puzzling with wheel and numbers will give me the following two combinations:

03 09 15 28 37 48
08 12 23 31 39 49

In my previous message, the puzzling stage was called "populating the wheel". I've called the resulting set of combinations a "population".

Now let's assume (using filters, common sense or the input of other people) that I don't like these combinations at all. I'll just go back to my dice, and arrange my numbers differently. For example:

A=03
B=08
C=09
D=28
E=31
F=37
G=12
H=15
I=23
J=39
K=48
L=49

After puzzling, my combinations suddenly look like this:

03 08 09 28 31 37
12 15 23 39 48 49

As you can see, these are two totally different combinations. And guess what? If I don't like 'em, I'll go back to the drawing board and throw the dice again. I can repeat this until I'm satisfied.

The wheel never changes, I just use a different assignment. There's absolutely no way that assigning numbers in a different sequence violates the guarantee of the wheel. In fact, the beauty of a wheel is that it doesn't depend on numbers at all.

I know that there are wheels specifically designed so that the first number is the most important one. Is the designer going to take me to court if I swap my numbers the way I want?

Filtering

I never said that all filters should be fully satisfied. Nick is absolutely right in stating that it might be impossible. In fact, the more filters you use, the more difficult (if not impossible) it will become to find combinations that satisfy them ALL.

For instance: I would like to play 20 numbers.
I want to use two very silly filters:
Low numbers only (1..24)
Odd numbers only (...)

As you can plainly see, I've shot myself in the foot.
The combination of these filters only allow me 12 numbers to play.
I can "wheel myself silly", but I can never get to a C(20,...).

The solution is not to difficult.

A filter can give a combination a "score".
In the simplest way the score can be either 0 or 1, indicating "bad" or "good", but that seems to be a little too simple.

In a little more complex situation the score could be a number from 0 to 9, where 0 is "please throw this one out" and 9 is "you're a fool if you don't use this one".

Or maybe a percentage indicating the level of satisfaction.

In fact, the value itself is not important at all, as long as you can compare them. This rules out the values "apple" and "pear" because these two can not be compared.

If a "score" can be given to a combination, a "score" can be given to a set of combinations too.

Remember the first set? It was:

03 09 15 28 37 48
08 12 23 31 39 49

Using a combination of all kinds of arbitrary filters and averaging the scores, the "overall score" for this set is "7".

The second set:

03 08 09 28 31 37
12 15 23 39 48 49

The overall score results to "5".

If the value "7" is considered better than the value "5", I would have to say that the first set is the one we should play.

The strategy revisited

When we want to play with 12 numbers, there are 12 numbers that can be assigned to "A", leaving 11 numbers to be assigned to "B", 10 to "C", etc.
The total number of permutations is: 479001600.
In other words, there are 479001600 different "populations".

It's all a matter of finding the "best" population.

The difference between this strategy and the one Nick has described, is that "my" strategy can be applied to an existing wheel whereas Nick builds a new wheel from the found combinations.

Take a look at the following scenario:

I look in my wallet and see enough money to play 48 combinations.
I can spend a lot time thinking if I want a lot of different numbers or if I want a certain guarantee.
The most important thing is: I'm going to play 48 combinations, no more and no less.

If I use "my" strategy, I pick a wheel that satisfies my needs and I'll find the best possible "population" in accordance to my filters.

Nick, I have two questions for you.
1) Using your method, ALL filters may like combinations consisting of a total of 24 different numbers. How can you get this in a C(18,...) wheel?
2) The only other program I know that handles the "L" parameter is the cover32 program by Kari Nurmela and Patric Ostergard. This program can optimize wheels to the bare minimum. Can your program build wheels as dense as cover32?

#### Nick Koutras

##### Member
to Goswinus

Hello, and good morning,

First I'll like to indicate that my little XL
spreadsheet LT posted the other day may
come handy for you to populate ANY of your wheels.

I'm talking about the Wheel Builder & Verifier.

What you do is the following.
In the Sheet Database you enter any wheel you want to test and also parameter of the wheel as shown
by the wheels it comes with.

Now you select the Lotto Game you want to test against by altering the Lotto Game.

On the Inputs sheet Under the columns Designs to use enter the parameters of
your design you want to test.

Click the Button make random Groups
and then Click the Build Design button.

What you have done is your "population" procedure.
You can see that at "MyTickets" sheet.

The "Filters" procedure does not exit,
but may be handy as a future project.

Second Part:

You wrote:
Nick, I have two questions for you.
1) Using your method, ALL filters may like combinations consisting of a total of 24 different numbers. How can you get this in a C(18,...) wheel?
2) The only other program I know that handles the "L" parameter is the cover32 program by Kari Nurmela and Patric Ostergard. This program can optimize wheels to the bare minimum. Can your program build wheels as dense as cover32?

1) You have the ability to enter ANY kind
of Filters starting with the Minimum required to Maximum followed by the Numbers of your Filter.
Examples:
Min Max #........
1 2 01020304050607
2 4 02040608101214161820.....
0 0 3445 <== this eliminates 34,45
1 2 42434445464748
91 180 Range Sum of Ticket

Overlapped number are permitted

So ther is an unlimited number of
combinations but **you have to be correct in your filters to WIN**

2) This part I'm beta testing
Yes it does generate such compact designs.

See for an example at the rec.Gambling.Lottery

It generated the wheel below:

c(13,6,4,6,L=11)=67

LD(13,6,4,6,L=11)=67

1 2 3 4 5 6
1 2 3 4 7 8
1 2 3 9 10 11
1 2 3 5 7 9
1 2 4 8 9 12
1 2 4 6 8 10
1 2 4 7 9 10
1 2 5 7 9 11
1 2 5 7 10 11
1 2 5 8 9 13
1 2 5 6 9 13
1 2 6 8 12 13
1 2 6 8 10 11
1 3 4 7 12 13
1 3 4 10 11 12
1 3 4 8 11 13
1 3 5 6 11 13
1 3 5 7 8 12
1 3 6 7 9 13
1 3 6 8 9 11
1 3 6 7 11 12
1 4 5 10 11 13
1 4 5 8 12 13
1 4 5 6 11 12
1 4 7 8 10 11
1 5 6 10 11 12
1 5 6 9 10 12
1 5 9 10 12 13
1 6 7 9 10 13
1 6 7 8 9 13
1 7 9 10 11 12
2 3 4 9 12 13
2 3 4 9 10 12
2 3 4 6 10 13
2 3 4 6 11 12
2 3 5 8 11 12
2 3 6 7 8 10
2 3 6 10 12 13
2 3 8 10 11 13
2 4 5 6 8 9
2 4 5 7 11 13
2 4 6 7 8 10
2 5 6 7 8 12
2 5 7 8 11 13
2 5 9 11 12 13
2 6 7 11 12 13
2 6 7 9 12 13
2 7 8 10 11 12
3 4 5 10 11 13
3 4 5 6 8 12
3 4 5 7 10 13
3 4 5 6 7 13
3 5 6 9 10 13
3 5 6 7 8 13
3 5 7 9 10 12
3 5 8 9 10 11
3 6 7 8 9 11
3 7 8 9 11 12
3 8 9 10 12 13
4 5 6 9 11 12
4 5 6 9 10 13
4 5 7 8 10 11
4 6 7 9 10 11
4 6 8 9 11 13
4 7 8 10 12 13
4 7 9 11 12 13
4 8 9 10 12 13

By for now

#### Goswinus

##### Member
Nick,

First of all, I think it's great what you achieve with Excel macro's.

...What you have done is your "population" procedure.
You can see that at "MyTickets" sheet.
...

This is nice.

The "Filters" procedure does not exit,
but may be handy as a future project.
...

Well, actually... The "Filters" procedure is not just handy.
It's vital to the strategy I'm talking about, since the steps in the strategy are:
a) populate
b) filter
c) evaluate (check if result is better than the "best so far")
d) goto a)

If you can make this last part tick I think you would have a great tool!

Regards,
Goswinus

#### Nick Koutras

##### Member
Hi Goswinus,

You wrote:

a) populate
b) filter
c) evaluate (check if result is better than the "best so far")
d) goto a)

===========

For me to proceed, I have to understand
2. How to define "Best so Far"

If you could provide such info I'll be glad to
give it a try completing the project.

Nick

#### Goswinus

##### Member
Nick,

Filter definitions are rather personal. Everybody likes them differently I suppose. I can give you a an example.

Odd/Even
How many odd and even numbers in a set?
There are two possibilities. You can work with the theoretical distribution or you can select the actual distribution.
As an example, we'll take a look at the actual distribution.
It's based on the first 1906 draws (because I had that data file available):

0-6 0.84%
1-5 7.66%
2-4 22.98%
3-3 32.06%
4-2 25.29%
5-1 10.28%
6-0 0.89%

When you check out a set in a population you check out in which distribution group the set belongs. When it's a "3-3" set, you give the set 32.06 points. Repeat this for all sets, and take the average number of points as the "population score".

Other filters
For example, these filters can work the same.
- High/Low
- Sum
- Width
- Repeaters
...

The population with the highest score is the "best".

This should give you an idea.
But if you have another/better way and/or more/other filters, that's great too.
It's the strategy that counts.
The actual implementation of the strategy is not that important.

Regards,
Goswinus

#### Dennis Bassboss

##### Member
To Nick!

How do you applied the resampling on your population ?...There are many ways of doing this resampling....What criterias did you use ?
Your program is very nice! I had a look at it this morning!

#### Dennis Bassboss

##### Member
To Goswinus!!

I think that basically we are saying the same thing but when I mentionned ...(When changing a number from the wheel and therefore changing the garantee...)''mostly in the optimized wheels'' I meant by that the wheels that are replicating some numbers more than others right from the start...
Buddy when you quoted me that sentence from my original post mysteriously dissapeared .... So I will say it again in some cases displacing only one number from the wheel might change the garantee and that mostly in the optimized wheel....

#### Goswinus

##### Member
I have to apologize to Dennis.
Please allow me to correct my mistake.
Dennis' original statement was:

Dennis Bassboss said:
I understand that you wouldn't cut any lines from the existing wheel Goswinus..And in some cases it is true It might work without affecting the garantee mostly like Nick is saying the 3/4,4/5,5/6 etc...
I would say that it wouldn't change the garantee depending on the ''Method of construction'' of the wheel...in some method only displacing a number from one line and put it on another will affect the garantee (Mostly for the optimized wheel)...But in some wheels using different methods of construction you might be able to displace some numbers without affecting the wheel's garantee....

Indeed it is strange that sometimes parts of previous statements mysteriously disappear.

But Dennis, you are in fact right, the type of wheels, where the position of the number in the population sequence is important, are not suitable for this strategy.

Is it fair to say that it might very well work on the as-small-as-possible-and-preferably-with-a-lot-of-different-number wheels? A nice example that comes to mind is the world-record C(49,6,3,6)=163 by Dragan Stojiljkovic & Rade Belic.

I think I'll just go ahead and write a program that does the trick.
Maybe that's the only way to find out if it works.

Oh by the way Nick:
I have found a C(13,6,4,6,11)=66.
Do you want me to post it?

#### Dennis Bassboss

##### Member
I can't wait to see what you are going to come with...(RE:the 163 wheels)coming from the Grandmaster that you are...It is going to be good...no doubts here...

#### Dennis Bassboss

##### Member
And thanks for underlining the quote....