My Filter Plug-Ins

[Jerzy]

Thank you Joe for explaining it to me. Pairs Odd/Even Counts filter makes sense to me now. Only the name of it is a bit misleading. In lotto games, when we consider "pairs" we usually mean the pairs of numbers, but this filter works with pairs of digits. Maybe the filter should be renamed, for example: Pairs of O/E Digits Count ?

I need to examine the results of past drawings in view of using this filter. Some experimentation with the settings would be necessary as well.

In 2 or 3 days I will describe new filters, which I believe are worth implementing.

Thank you again.

Jerzy

[Joe]

Thank you Joe for explaining it to me. Pairs Odd/Even Counts filter makes sense to me now. Only the name of it is a bit misleading. In lotto games, when we consider "pairs" we usually mean the pairs of numbers, but this filter works with pairs of digits. Maybe the filter should be renamed, for example: Pairs of O/E Digits Count ?

ok no problem,

In 2 or 3 days I will describe new filters, which I believe are worth implementing.

Thanks and will be waiting for your ideas with clear explanations.

[Jerzy]

Hi Joe,

Could you build Arithmetic Complexity Filter plugin ?

The arithmetic complexity of a combination is the count of different positive differences of its numbers, minus (r - 1). r = the count of numbers drawn.

There could be 15 differences between each of 6 numbers in 6/xx lotto, and 10 differences between each of 5 numbers in 5/xx game. If several differences have the same value, this value will be counted only once as one difference.

The arithmetic complexity of 6 number combination is within the range from 0 to 10.

For example, if the count of different (unique) differences is 15: 15 - (6 - 1) = 10

Very low arithmetic complexity is characteristic of combinations which follow arithmetic progression or are placed on the playslip panel according to certain geometric patterns.

For example: 7, 14, 21, 28, 35, 42 has AC of 0.

Combination which have low AC (from 0 to 5) could be (or should be) discarded because they are not very likely to be drawn, and if they are drawn, they produce a low payoff.

High arithmetic complexity is characteristic of randomly generated combinations (the higher, the better).

The Arithmetic Complexity filter should have 11 little boxes to allow the selection of AC values from 0 to 10 (for 6/xx lotto) and 7 boxes for 5/xx lotto (AC values from 0 to 6), and Remove & Leave buttons.

The arithmetic complexity is discussed in the book How to Win More, Strategies for Increasing a Lottery Win , Norbert Henze & Hans Riedwyl, AK Peters, Natick, Massachusetts, 1998. However, they do not have any lotto software to work on their ideas. I found only one implementation of AC filter in a lotto software. It is available on the internet and they have free demo version.

I used Excel to count AC for my lotto. If I replace the history data with tickets for the next draw, I can see the AC of those tickets and delete the unwanted ones.

I attach a copy of the Excel sheet. You can see the formulas I used.

Jerzy

[Midas]

Jerzy,

Arithmetic Complexity is very interesting, and refers to the cardinality of sequence of numbers. The formulae can be applied to any "n-ball" lottery, for example Lotto 007 has had this feature for a number of years, supplemented by geometric filters.

(1) Can you explain from your observations how AC varies with board patterns on Oz Lotto. Any figures for number of combinations reduced?.

(2) What happens to AC when patterns are either centrally located versus edge clustered on the board?.

(3) Have you considered extending the formulae for Geometric Complexity (GC) reduction, in other words consider a formuale to capture realizations of board patterns for symmetry, rotations, reflections etc...,
I have basically extended my lotto database to cover these patterns for UK national lottery, however it is too time consuming. A formulae for randomization through GC or otherwise working with AC would
really make this a unique feature of EL.

I would be interested in your views and observations.

Regards

Midas

[Joe]

[quote=Jerzy:1190478486]
Hi Joe,

Could you build Arithmetic Complexity Filter plugin ?

The arithmetic complexity of a combination is the count of different positive differences of its numbers, minus (r - 1). r = the count of numbers drawn.

There could be 15 differences between each of 6 numbers in 6/xx lotto, and 10 differences between each of 5 numbers in 5/xx game. If several differences have the same value, this value will be counted only once as one difference.

The arithmetic complexity of 6 number combination is within the range from 0 to 10.

For example, if the count of different (unique) differences is 15: 15 - (6 - 1) = 10

Very low arithmetic complexity is characteristic of combinations which follow arithmetic progression or are placed on the playslip panel according to certain geometric patterns.

For example: 7, 14, 21, 28, 35, 42 has AC of 0.

Combination which have low AC (from 0 to 5) could be (or should be) discarded because they are not very likely to be drawn, and if they are drawn, they produce a low payoff.

High arithmetic complexity is characteristic of randomly generated combinations (the higher, the better).

The Arithmetic Complexity filter should have 11 little boxes to allow the selection of AC values from 0 to 10 (for 6/xx lotto) and 7 boxes for 5/xx lotto (AC values from 0 to 6), and Remove & Leave buttons.

The arithmetic complexity is discussed in the book How to Win More, Strategies for Increasing a Lottery Win , Norbert Henze & Hans Riedwyl, AK Peters, Natick, Massachusetts, 1998. However, they do not have any lotto software to work on their ideas. I found only one implementation of AC filter in a lotto software. It is available on the internet and they have free demo version.

I used Excel to count AC for my lotto. If I replace the history data with tickets for the next draw, I can see the AC of those tickets and delete the unwanted ones.

I attach a copy of the Excel sheet. You can see the formulas I used.

Jerzy
[/quote]

Well and good, we can expect this feature within couple of days jerzy,

Thanks,

[Jerzy]

Midas,

I have to read about the Geometric Complexity. Do you know of a Web page which presents or discusses this issue in easy to understand way?

I experimented with filtering combinations according to their location on the panel, for example dividing 45 numbers into 2 groups of 22 and 23 numbers, but there was nothing surprising in it. Almost always 1 to 5 numbers were drawn from each of these groups. 0 or 6 numbers from 22 or 23 are uncommon and are drawn uncommonly.

Certain geometric patterns have low arithmetic patterns and will be removed by AC filter.

However, certain geometric patterns despite its high or relatively high arithmetic complexity are still rare and unlikely to be drawn. These patterns in most cases can be removed, but we need a different tool for it.

For your information, I will present an idea of a Cluster filter.

And I hope that Joe will find it useful and be able to build such a filter.

Thank you for bringing these issues to my attention.

Regards

Jerzy

[Joe]

hi,

Here is the plug-in "Arithmetic Complexity" Jerzy asked for,

please download the jar file, and give a try,

please let me know if any modifications needed, thanks,

good Luck,

[CSenior]

[quote=Joe]
hi,

Here is the plug-in "Arithmetic Complexity" Jerzy asked for,

please download the jar file, and give a try,

please let me know if any modifications needed, thanks,

good Luck,
[/quote]

Hi Joe,

Thanks for the plugin but I am getting an error. Could you please assist in correcting it. Thanks!


*** Error Mon Sep 24 05:37:33 EDT 2007
*** App Version: 4.2.1 Build: 956
*** Java Version: 1.4.2_06
*** OS Version: Windows XP 5.1
*** Lottery: Florida Lottery
*** Message: com/expertlotto/ArithmeticComplexity/ArithmeticComplexityPlugin (Unsupported major.minor version 49.0)
*** Stack:
java.lang.UnsupportedClassVersionError: com/expertlotto/ArithmeticComplexity/ArithmeticComplexityPlugin (Unsupported major.minor version 49.0)
at java.lang.ClassLoader.defineClass0(Native Method)
at java.lang.ClassLoader.defineClass(Unknown Source)
at java.security.SecureClassLoader.defineClass(Unknown Source)
at java.net.URLClassLoader.defineClass(Unknown Source)
at java.net.URLClassLoader.access$100(Unknown Source)
at java.net.URLClassLoader$1.run(Unknown Source)
at java.security.AccessController.doPrivileged(Native Method)
at java.net.URLClassLoader.findClass(Unknown Source)
at java.lang.ClassLoader.loadClass(Unknown Source)
at java.lang.ClassLoader.loadClass(Unknown Source)
at com.expertlotto.plugin.PluginManager.loadPlugins(PluginManager.java:106)
at com.expertlotto.Main.run(Main.java:42)
at java.lang.Thread.run(Unknown Source)
*******************************************************

[Joe]

[quote=CSenior]
[quote=Joe]
hi,

Here is the plug-in "Arithmetic Complexity" Jerzy asked for,

please download the jar file, and give a try,

please let me know if any modifications needed, thanks,

good Luck,
[/quote]

Hi Joe,

Thanks for the plugin but I am getting an error. Could you please assist in correcting it. Thanks!


*** Error Mon Sep 24 05:37:33 EDT 2007
*** App Version: 4.2.1 Build: 956
*** Java Version: 1.4.2_06
*** OS Version: Windows XP 5.1
*** Lottery: Florida Lottery
*** Message: com/expertlotto/ArithmeticComplexity/ArithmeticComplexityPlugin (Unsupported major.minor version 49.0)
*** Stack:
java.lang.UnsupportedClassVersionError: com/expertlotto/ArithmeticComplexity/ArithmeticComplexityPlugin (Unsupported major.minor version 49.0)
at java.lang.ClassLoader.defineClass0(Native Method)
at java.lang.ClassLoader.defineClass(Unknown Source)
at java.security.SecureClassLoader.defineClass(Unknown Source)
at java.net.URLClassLoader.defineClass(Unknown Source)
at java.net.URLClassLoader.access$100(Unknown Source)
at java.net.URLClassLoader$1.run(Unknown Source)
at java.security.AccessController.doPrivileged(Native Method)
at java.net.URLClassLoader.findClass(Unknown Source)
at java.lang.ClassLoader.loadClass(Unknown Source)
at java.lang.ClassLoader.loadClass(Unknown Source)
at com.expertlotto.plugin.PluginManager.loadPlugins(PluginManager.java:106)
at com.expertlotto.Main.run(Main.java:42)
at java.lang.Thread.run(Unknown Source)
*******************************************************
[/quote]

This is Java version problem, please use the upgraded version 1.6.

thanks,

[Midas]

Jerzy,

Reference the book "How to win more strategies for increasing a lottery win", by Norbert Heinz and Hans Riedwyl, I would like to add that this is the first book written by mathematicians which is packed with useful ideas backed with plenty of statistical proof. The problem is converting the concepts into reality.

(1) Geometric Complexity is a new concept which I introduced, but the authors have touched on in Chapters 5 (5.6) and 7((7.1) and Appendix 8.9. You will note the approach is to program the geometric patterns into one's exisitng lotto database. Therefore you end up with a much larger database with common patterns. My suggestion is to capture these patterns through an analytical formulae which can be programmed as a filter to capture the various player patterns. Otherwise you are left with the weekly predicament of tuning a large database with perhaps over 10K reduction lines.

(2) Edge Numbers or Cluster Numbers are explained in Chapters 7.3 and 7.4. If you experiment you will quickly realise a useful algorithm using existing panel and group filters!.

(3) AC filter reduction under Appendix 8.9 Table (8.4) provides the number of lines reduced for AC filter reduction as follows for Lotto (6/49).

AC No of Lines

0 216
1 1027
2 10147
3 34495
4 141271
5 3358768
6 1219724
7 4542028
8 2871100
9 2871100
10 3078578

So if we follow the recommendations and play AC(6 to 10), we only reduce ~3.5 Million lines, clearly a useful reduction however, it is still missing the geometric or randomization filters which provides the ultimate reduction.

(4) lotto 007 XP uses a crude implementation of the AC value with only some simple filters, the key being "width". EL has far more in the repertoire to make effective filter reductions.

http://www.lotto-007.com/images/Lotto007_Filter.JPG

The key is to this is an analytical formulae for geometric randomization, I believe Stan and Bobes are conducting this research.

(5) Have you checked Joe's program implementation against the various test patterns?.

Regards
Midas

[Jerzy]

Midas,

I find your ideas very interesting. To develop them further or to convert them into practical, real things, I need to read and think more about it.

I know AC filter is available in Lotto007 and Lotto PowerPlayer Pro. Both applications have probably the same author(s).

I am happy with Joe's implementation of filters, particularly AC filter. However, I need more time to find the settings for some of his filters which could be the most appropriate for my lottery.

Thank you.

Jerzy

[Jerzy]

Joe,

Thank you Joe for the AC filter. Excellent job!

The filter is user friedly and everything in it seems to work correctly.

Jerzy

[Jerzy]

Joe,

The next filter idea that is worth implementing is a Cluster Filter.

When you look at the marked panels on the playslip, you can see that on some panels the ticket numbers are separated (or isolated) from each other, on other panels they are clustered into groups (or a group) of 2, 3, 4, 5, or maybe 6 numbers, and on certain panels there could be a combination of separated numbers and clusters. Numbers in a small cluster are adjacent to each other vertically, horizontally or diagonally, but in a large cluster some of them are connected with others through the adjacent numbers.

We can calculate a cluster number, which is the count of isolated numbers plus the count of groups of numbers connected in clusters.
The cluster number range can be from 1 to 6.

Or, we can find cluster pattern, a composition of clusters (noticing their sizes) and separated numbers. The second option makes more sense if you want to build a good filter. The cluster number can be the same for certain patterns which have different occurrences and some of them could not be safely removed but some of them could be. For example: the cluster patterns 2-2-2, 3-2-1, and 4-1-1 have the cluster number 3, but they differ considerably in their occurrrences in the history data and in the full package of tickets.

The cluster number and cluster patterns depend very much on the total pool of numbers in the game and on the shape of the game board.
Expert Lotto is already configured for total count of numbers in the game, count of numbers drawn at each drawing, and the shape of the game board. It uses this configuration when working with existing filters, like Panel Filter or Number Filter (the shape of the game board is clearly displayed at certain filters and you can select numbers on it). So probably implementation of Cluster Pattern Filter in Expert Lotto is possible and might be even easy.

The following cluster patterns are possible:

1-1-1-1-1-1
2-1-1-1-1
2-2-1-1
2-2
3-1-1-1
3-2-1
3-3
4-1-1
4-2
5-1
6

I used Excel to do statistical analysis of cluster patterns in the history of my game.

I placed past winning numbers in the columns B, C, D, E, F, G, H (in column A the date) and in the next 45 columns I counted the occurrence of each number in the combination if it appeared of the game board as a separate number. Conceptualization of the formulas for counting the occurrences of separate numbers and clusters of 2 numbers took me some time.

Next, I identified all clusters of 2 numbers that are possible, as they appear on the panel. To be sure, I just marked them with a pencil on the play slips. After that I entered the pairs of numbers which form clusters as the headers of colums (pairs from 1-2 to 44-45). I calculated the occurrences of these pairs in a given combination if they appeared on the game board as a cluster.

I have not calculated directly the occurrences of clusters larger than 2 numbers because Excel has not enough columns for that.

I calculated total count of separate numbers and total count of clusters of 2 numbers in a combination, and arrived at the correct cluster pattern in a combination by a simple process of deduction.

5-1 if there are no clusters of 2 nrs and there is 1 separate number.

4-2 if there is only one cluster of 2 nrs and no separate number.

4-1-1 if there are no clusters of 2 nrs and there are 2 separate numbers.

3-3 & 6 if there are no clusters of 2 and no isolated numbers. Unfortunately, because I could not count the occurences of clusters of 3 directly, I had to consider both groups jointly. As both groups have very low occurrences and both are good candidates to be filtered out, it does not really matter. But if you do paterns of 3-3 and 6 separately it will be an elegant solution.

3-2-1 if 1 cluster of 2 nrs and 1 separate number present.

3-1-1-1 if no clusters of 2 nrs but 3 separate numbers present.

2-2-2 if 3 clusters of 2 present.

2-2-1-1 if 2 clusters of 2 and 2 separate numbers.

2-1-1-1-1 if 1 cluster of 2 and 4 separate numbers.

1-1-1-1-1-1 if all numbers are separate.

To help you understand this better, I attach the copy of the Excel sheet that I used for calculation of cluster pattern statistics. If I replaced the history data with combinations from the package, I could delete the combinations with cluster paterns which have low occurrence. But this method of filtering is not good enough. I hope you will create something better.

If you need any additional information, let me know.

Jerzy

[CSenior]

Thanks Joe! The upgrade worked great!

[Joe]

[quote=Jerzy]
Joe,

Thank you Joe for the AC filter. Excellent job!

The filter is user friedly and everything in it seems to work correctly.

Jerzy
[/quote]

Thanks and will be waiting for more filters to implement,