Patent Grant
7565263
This invention is directed to a system for generating relevant statistics for games of prediction, for use in templates and presented in the form of tables. These templates show the point of equilibrium at each stage in the evolution of lottery drawings.
Over the centuries mathematicians have constructed the Theory of Probability, initially using three mathematically pure steps and then adding other ingenious ideas which have been building up over time.
The three steps were:
A—1654—Pascal—Fermat. The famous correspondence between these two established the bases of the theory of probabilities (Pascal discovered the formulas for combinatorial analysis) which is the mathematical core of the concept of risk.
B—In 1703, G. von Leibniz wrote to his friend Jacob Bernoulli, “Nature has established patterns which are the origin of the recurrence of events, but only for the most part”. After twenty years of study this led to Bernoulli's discovery of the “Law of Large Numbers” (“Ars conjectande”—The Art of Conjecturing, 1713). Jacob Bernoulli's theory for the a posteriori calculation of probabilities is empirical since it does not offer a method for organizing all the Discrete Sample Spaces mathematically and for allowing the theoretical probability of their events to be known a priori and exactly. Contrary to the popular idea, the law does not provide a method for validating observed facts, and which are nothing more than the incomplete representation of the total truth.
In essence the law states:
“In any sample the difference between the value observed and its true value will decrease proportionally as the number of observations increases”. A mathematical explanation of the law is therefore needed.
Discrete Sample Spaces—These are all the possible outcomes of an experiment.
Experiment—Experiments are those acts which, when repeated constantly under the same conditions, produce individual results, which we are unable to predict. However, after a certain number of repetitions a defined pattern or regularity will occur. This is the regularity which makes it possible to build an accurate mathematical model with which the experiment can be analyzed.
The lottery draw is a random experiment.
C—In 1773, Abraham de Moivre expounded the structure of normal distribution—“the bell-shaped curve”—and discovered the concept of “standard deviation” (“the doctrine of chances”). De Moivre's success in solving these problems is one of the most important achievements in mathematics. Eighty-three years later, when studying geodetic measurements taken in Bavaria, Gauss arrived at the same conclusion. “A Standard Deviation of 2% is accepted by the majority of statisticians”.
A simple analysis of these three steps shows that the gap which exists has to do with the knowledge of the organization of Sample Spaces, since this is what will allow us to analyze the experiment (lottery drawings) mathematically.
This process is at present carried out using statistics based on observations which have no foundation.
There are Internet sites and pamphlets distributed at Lottery Sales outlets which state, for example:
6 has been drawn 3 times with 27
17 has not appeared in the last 20 drawings
In other words, curious, interesting and casual observations.
Previous mathematical proposals are unknown.
The solution here suggested is based on a methodology which organizes “Discrete Sample Spaces” into patterns. This allows us to calculate the theoretical probability of the events, which are obeyed in the draws. If the calculations of the patterns (or templates) and the facts must coincide (respecting Standard Deviation) then it is possible to make predictions based on this information. A template is produced which represents all the games with the same behavior pattern. These games are represented by colors.
Example
If we play with the following numbers.
. . . then we are systematically playing using the same pattern or template, i.e. we always mark 2 numbers in the zero decile, 1 number in the first decile, 1 number in the second decile, 1 number in the third decile and 1 number in the fourth decile.
Each template has its own theoretical probability precisely predetermined and this is obeyed in the drawings. If the calculations and the facts must coincide (respecting Standard Deviation) we can make predictions based on the “search for the probability that an increase in the number of drawings will increase the probability that the observed mean will not deviate more than 2% from the true mean”.
The technical advantages are provided by the computer which shows the statistics of the templates and numbers in a relevant and dynamic way. In any and every lottery the Sample Spaces are dramatically simplified, so that a user need not understand statistics to identify patterns and select high probability numbers for entering in a lottery drawing.
Example
The Super Sena 6-48 type lottery, with 12,271,512 combinations (possible plays) can be represented by only 210 templates, each one with its precise theoretical probability. Therefore it is possible to manage lottery results, given that any game which is played corresponds to one of the templates.
The practical advantage of this is the rationalization of the information, allowing for calculated decisions to be taken. By using colors to represent the patterns (or templates) it is possible to manage the whole system via computer, accessible for example, by a user over the internet.
In 5 years of study and research we can state categorically that everything which exists is based on the observation of past data. This is a criterion not permitted by the law of Large Numbers since this data does not express the whole truth.
The solution we intend to patent is capable of constructive operational variables since it is the result of a precise “mathematical and probabilistic model” and this begins a new phase in our knowledge of the movement of things.
It will become a central tool in any activity involving random movements, such as: genetics, finance, engineering, etc.
The discovery relates theoretical probabilities with facts, since the Law states that the mathematical regularity of an event must be obeyed, i.e., if the theoretical probability of a template is 3%, this means that this pattern should occur about 3 times every 100 draws.
In order to comply with the letter of the law the number of drawings must be the largest possible, but the theoretical probability of any pattern occurring is already sufficiently significant for it to be respected throughout the drawings.
If we compare the information available on the various probabilities of Starts, Types of Sets, Patterns and Numbers, we have a solid base and are therefore well equipped to formulate predictions as to what may happen in the future.
In this we are supported by precise and pertinent information and in accordance with the Law.
The fact that the concepts being used are classic is justification enough for leaving out bibliographic references.
Analysis
When we study any type of observed phenomenon, we have to formulate a Mathematical Model which will help us investigate this phenomenon in a precise way.
In the case of the Cn and p phenomena the challenge initially is to solve the mathematical problem, i.e. find a method which organizes Sample Spaces, whilst meeting the requirements of cause and effect.
Undoubtedly, this is the responsibility of Combinatory Analysis, since the evolution of combinations shows clearly that everything happens in deciles; that is, as basic hypotheses, combinations of deciles themselves and combinations of numbers in the same decile.
A generic solution was used which indicated all the possible combinations, given that we have combinations within combinations.
The colors reveal the forms and when we combine them in an orderly manner in predetermined spaces all the possible types of combination appear.
The resulting system is set out in the form of templates which are the synthesis of the whole natural process.
Following the precise indications given by the colors the systems come together. It is like a symphony.
After the initial harmony, the single notes come in, followed by pairs, then the trines and so forth until the final coming together of the movements.
The hypotheses are confirmed in the first movement and are repeated as in the nature of things.
Templates function as the synthesizer—the catalyst of the system. But we had to understand them in their totality.
Leibniz wrote to Bernoulli:
“Nature has established patterns which give rise to the recurrence of happenings, but only for the most part”.
Up until now there has been no methodology which organizes Sample Spaces in a causal way and which is capable of noticing, even in a simple way, the most obvious and repetitive facts in the world of experience: their patterns of behavior.
The world knows Bernoulli's Law of Large Numbers empirically. It needs an explanation.
But templates are not merely the synthesis. They also constitute the behavior patterns and the establishment of these patterns relies on the precise and a priori calculation of theoretical probabilities.
The template concept demonstrates an extreme logical coherence. Besides indicating the patterns of behavior, it shows that the causes of the occurrence of patterns are the very patterns themselves.
But sets of similar patterns of behavior are not evident in the natural evolution of combinations.
We needed to deduce them, to identify them in the natural assembly and classify them in sets in accordance with similar patterns of behavior.
In the end, the Method gave structure to the system.
Colors are used to produce the various templates, which are defined by the product of the simple combinations which they represent.
The templates rely on patterns of behavior which, when quantified, reveal the Theoretical Probabilities. And all the Sample Spaces become viable.
The basic hypotheses are the perfect answer to the need for a causal explanation (Paul L. Meyer in “Probability—Applications in Statistics”—2nd edition, Chapter 1).
Mathematical Models.
When choosing a model, we can make use of our own critical judgment. This was particularly well expressed by Prof. J. Neyman, who wrote:
“Every time we use Mathematics to study some observed phenomena, we must basically begin by constructing a mathematical model (deterministic or probabilistic) for these phenomena:
Based on this critical opinion let us examine the Model.
1 Sample Spaces are organized and reduced to groups of templates, or patterns.
2 Nothing was ignored
3 The mathematical problem has been correctly solved and the basic hypotheses are fully confirmed, since the mathematical solution of the problem allows for knowledge of all the data of the Sample Spaces
4 There was a mathematical regularity to all the perfectly obeyed consequences.
The model satisfies the above stated requirements (if a series of repetitive experiments agrees with an hypothesis, a law can be stated which governs the phenomenon by means of mathematical derivation and from experimental data).
We would add:
1 The Organization of Sample Spaces must define the behavior patterns and respond to the need for causal explanation.
2 Theoretical Probabilities must be determined both a priori and precisely.
The figures which accompany this patent are taken from the Spanish and French 6-49 type lotteries, showing the behavior of those templates (patterns) which have the same probability. Spain and France have the same type of game (6-49), and therefore the same Theoretical Probability Table.
The System, which is the subject of this application, reveals by means of a simple and colored representation the complex and sophisticated working for predicting lottery outcomes.
Contrary to what might be thought, it shows that the results of the drawings follow a pattern of behavior.
It shows that each lottery has an exact number of ways of playing called the template, each of which has its own probability of being drawn.
It provides tables with up-to-date, relevant information which allows for an objective analysis and the choice of a template.
The choice of templates will be the first concern of the player.
A 5-49 lottery (meaning 5 from 49) means that 5 numbers are drawn from a group of 49. In the same way 6-48 gives us 6 numbers to be drawn from a group of 48, and so on.
Examples
The total number of possibilities for each lottery, by template in decreasing order of probability, is shown in the Theoretical Probability Table.
Lotteries like the Super Sena, Mega Sena, Quina, Canadian Lotto, German Lotto, Spanish Lottery, French Lotto, Australian Lotto, National Lottery (England) and dozens of others in the United States, have extremely well-known structures and therefore are capable of being managed.
Our aim is to show the behavior of the results in games of prediction and supply relevant information to users, preferably via a subscription service, so that rational game strategies can be formulated.
Color Convention
One of the aims of the method which is the subject of this patent is to visualize the games in a simple and efficient manner. To achieve this we created a way of representing numbers by means of colors. Each decile is associated with a color and is given a name. The denomination of each decile is defined by its initial number so for example, the numbers 01, 02 and 09 are called numbers of the zero decile (DO) and so on.
The color convention we used is shown in table 1. Examples of games using the normal representation and the representation using colors are shown in table 2.
Each game has a corresponding template; to identify it you only need to use the colors. Each template has a certain probability of happening.
Templates
A 6-48 type lottery (the Brazilian Super Sena) has a total of 12,271,512 combinations which can be represented by a mere 210 templates.
A template represents a “pattern of behavior”. See examples in table 3.
We classify the templates by types which have a common characteristic. The two first examples in table 3 show the P type templates; that is, they show the formation of a pair of numbers of the same color. The third example shows three pairs of the same color, and so it is a PPP type. The last example has a trine of the same color and is therefore a T type.
The types of current templates are shown below:
The Template Table by Order of Theoretical Probability shows each one with their respective occurrence possibilities (calculation). Each lottery has its own table.
Table of Theoretical Probability
The Table of Theoretical Probability shows the templates arranged in decreasing order of occurrence.
Theoretical Probability=Calculation
In table 4 we show a sample of the Probability Table for a 6-48 type game.
It shows for each template:
Therefore in the examples shown in this table we would expect to see, on average, nearly three occurrences of templates 1 and 2 in every 100 drawings, or put in another way, nearly 30 occurrences in every 1000 drawings. On the other hand for template 18, we would expect on average nearly 1 occurrence for every 100 drawings, or put in another way, nearly 13 occurrences in every 1000 drawings. For templates 209 and 210 the probability is around 7 occurrences in every 1,000,000 drawings.
It is important to note that the larger the number of draws the closer the mean of the numbers gets to the calculation.
The behavior of the templates over a series of drawings is shown in the Columns Table
Table of Drawings
The Table of Drawings shows in an organized way the results of all the draws. A well constructed table of draws provides important information. In our table we use:
Date of the drawing
Number of the drawing
Numbers drawn presented in color according to the color convention.
Number of the template placed in the column according to its type.
In table 5 we give a sample of the draws table from the California Fantasy 5 (5-39). This table is presented in blocks of 100 draws.
Numeric Sum of the Templates
We have seen that the templates have a theoretical probability. A further important property of templates is the numeric sum. If we know it, it can help us discover the range of bets where the chances of winning are greater. The numeric sum corresponds to the sum of all the numbers marked in a game. Therefore, a template will show maximum and minimum values of the numeric sum. The average of these two points is where we find the greater number of occurrences.
Table 6 shows template 1 for a 6-48 game.
The games with the smallest and greatest numeric sums possible in this template are shown in Table 6-B.
The average numeric sum therefore is 137. It can be easily shown that the majority of the combinations occur around the average numeric sum of the template.
Consider the example of two dice. To get a result which has the numeric sum 2 there is only one possibility: that both dice have the 1 spot face showing. The same is true for the numeric sum 12 (the dice lie with the 6 spot face showing). 7, on the other hand, which is the average of the numeric sum of the game of dice, can be obtained in six different ways (1 with 6, 2 with 5, 3 with 4, 5 with 2 and 6 with 1).
With the templates the behavior is the same. The greatest occurrence possibility happens around the average of the numeric sum.
The information is shown in the Numeric Sum Table, Table 6-B.
Map of Drawings
The history of drawings by template is shown in a table which we call the “drawings map”. This map shows all the draws of each one with the date, drawing number, numbers drawn and the average numeric sum shown at the head of the table.
In Table 7 we present a sample of the “Drawings Map” from template 1 of the Super Sena.
Using the method of the invention, users can take advantage of the system for determining higher probability plays in particular lotteries by subscribing, over the internet or otherwise, to have access to various levels of the templates and associated mathematical information in accordance with a subscription payment plan.
In the “Basic” subscription plan, the drawings map does not show information about the numeric sum. This information is available in the “Intermediate” plan, at a higher subscription rate. Generally, a user would subscribe to the system, to have access to the statistical information developed, generated by computer and accessible in the form of the templates. A subscription type service is appropriate as the data is continually updated as lottery drawing results are generated over time which of course affects the information generated.
In essence, the invention is a method for generating statistical information related to predicting the outcome of a lottery drawing, organizing the data, preparing templates and optionally tables useful in predicting the outcome of a lottery, and providing game players access to the generated data for assisting the players in selecting numbers to play in the lottery. The system is computer based and includes at least one database of data for storing the game outcome historical data for generating the templates and tables, and for supporting access by users, possibly via the internet on a subscription basis, to the system. The method further includes color coding the templates so as to simplify the selection process by a user who is unfamiliar with statistical analysis and probability predictions.
Columns Table
The purpose of the columns table is to show the behavior of each template over the period of the drawings, which are divided into blocks of 100.
It shows in a dynamic way the swings of the templates by always referring the calculation back to the facts.
In Table 8 shows a sample of this table.
Description: On the left hand side it shows the templates with their respective theoretical probability and with their actual occurrence. On the right there are three columns which show the total of the facts divided into blocks of 100 draws. At the top on the right there are links which allow for navigation around the blocks.
We can see that template 3 appeared twice in the first 100 draws, once in the next 100 and five times in draws 201 to 300. This produces a theoretical probability of occurrence of 2.97% and it is showing 3.02% for 300 draws. Template 75 never appeared, but as its theoretical probability is 0.4% it should occur nearly four times in every 1000 draws.
We can see that despite oscillating, in accordance with the Law of Large Numbers, we can state that:
This table is an important tool for formulating game strategies.
The Statistics of the Numbers
The statistics always refer to numbers, pairs, trines, etc. for each decile.
The positional statistic shows the total of the occurrences of the numbers, pairs, trines, etc. per decile in each possible position.
Examples of the occurrences of pairs in decile 1 (P1) in accordance with their occurrence per column (only the deciles beginning with 10 are shown) are set out in Tables 9, 9-A, 9-B, 9-C, 9-D and 9-E.
The positional statistic is very useful for analyzing a template. Therefore if we were to play using the template shown in Table 10, we ought to refer to the following statistics:
The correct evaluation test for probabilities is when, on average, the calculation agrees with the facts. Therefore, the evaluation has to be done using a group of templates with the same probability.
An example of the analysis for 1000 drawings:
So the facts are presenting on average
The calculation is=29.70 (rounded up) 30 draws
Average of the facts=31.66 (rounded up) 32 draws.
Analysis:
Templates 1, 2 and 3 should present 30 draws, but they are presenting on average 32.
This table shows the ranking of each template within its own group.
In Table 11 we show the similar behavior of the first 35 templates in a 6-49 lottery (France and Spain).
Positional Table Per Start
The Theoretical Probability Table shows the templates in order of probability. A reorganization of this table, grouping the templates with the same initial colors gives the Positional Table per Start.
Take a 6-48 (Super Sena) game. Any template of this game has to start in one of the ways shown in Table 12.
The Start Table shows a very rapid convergence of the facts for the calculations. It is a great analysis tool for formulating game strategies, since it shows in a fairly succinct way where the drawings are ahead or behind, relative to the calculated position.
Table 13 shows a sample of the Start Table of the Super Sena in accordance with the results up to draw 517 of 21/07/2001.
We can see for each type of possible start the theoretical probability (% calculation) and the percentage of the actual occurrence (% facts) of the starts. The two final columns show the links to the Columns and Drawings Table for the start selected.
In the example in Table 13 we can see that start 1 has a 9.68% theoretical probability and is showing 9.26%, based on facts, up to the draw of 21/07/2001. In Table 14 and 15 there are samples of the Columns and Drawings Tables for this start.
The Columns Table shows, on the left hand side, the templates for the selected start (start 1 in this example) in order of theoretical probability. On the right we have three columns divided into blocks of 100 drawings. On the right hand side at the top, there are the links which allow for navigation through the blocks.
From what we have described so far it is obvious that the subject matter of this patent, a System of Relevant Statistics for Games of Prediction using Templates and presented in the form of Tables, provides totally new characteristics in this field, which merit the granting of an Invention patent.
The invention system makes it possible to view comparisons between what is expected (the average probability of a pattern to be drawn) and what actually occurs (real results of lottery drawings). The knowledge can help build a game strategy, by choosing the patterns with a better chance of occurrence. The system provides for a user theoretical tables that show what is expected to occur with the patterns (average probability), result tables that show actual results of each pattern in actual drawings, and control panels which cross expected results with actual ones. In order to simplify decision-making and visualize the results, the colored patterns have been divided into two basic groups, the “types” and the “starts”. Types classify patterns according to the number of color occurrences (pair of one color, trine of one color, etc.) as described above. The grouping of patterns according to their type was shown in the respective table of theoretical probability. For example, in a 6/48 lottery, the patterns type PP (two pairs of distinctive colors) have 38.27% chances coming out. Therefore, there would be around 38 occurrences of this type in every 100 drawings.
Starts are the start of a pattern, determined by its initial ten (color) and by the number of times it appears. The grouping of patterns by start is shown in its specific table. Start 0 of a lottery 6/49 has a theoretical probability of occurrence of 42.23%. This means that there would be about 42 occurrences in every 100 drawings. The simplest and most effective way to define a game strategy is by finding out which groups of patterns (start and type) have a wider difference in comparison with the expected results. One strategy is the advanced strategy where a player would play on groups which occur more frequently than expected while another is the delayed strategy where a player chooses groups which were drawn less times than expected. After defining a strategy, the player looks for the best patterns of the chosen group.
The system provides the user with tools to help plan a selection for a game, providing means to search groups with greatest divergence in relation to theoretical results, to view pattern statistics and see the consolidated position of starts and types, providing control panels to observe the behavior of the starts and types through time, and providing drawing tables to view the groups behavior at the latest drawings
The system also provides generated search pattern statistics to find the best patterns within the chosen start and type, and allowing a user to use the drawings to identify patterns that aren't usually repeated within a short space of time.
The comprehensive system additionally has a random play analyzer, numbers combiner and results checker, all available to a user having the higher level subscription service.
As described above, winning a lottery is not merely a matter of luck. By having access to the templates, tools and tables generated by a computer, which are constantly updated, a person may create a game stately related to the behavior pattern of the lottery drawings, based on mathematics and probabilities, presented in a format that visualizes the patterns and selections so one having no familiarity with mathematics or probabilities can easily use the tools for selecting numbers for a lottery drawing. By subscribing to the inventive system, a user has access to the tables with behavior patterns for the specific lottery, patterns of games with their respective drawing probabilities and updated information in accordance with drawing results. Preferably, a user would subscribe for a time period, for example 6 months, for a single lottery, with all the tools available for that time period related to that lottery. A basic subscription may provide access, for example, to the theoretical tables of probability, of the patterns, of the types and of the starts, a drawing results table and drawing results map, a control panel of starts, of the types and of the patterns, and statistics, simple as well as positional and pattern statistics. Optional features of a higher level subscription may include a random play theoretical table, numbers combiner and results checker.
While preferred embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes or modifications may be made without varying from the scope of the invention.
| Number | Date | Country | Kind |
|---|---|---|---|
| 0107513 | Oct 2001 | BR | national |
| Number | Name | Date | Kind |
|---|---|---|---|
| 5197736 | Backus et al. | Mar 1993 | A |
| 5199709 | Lumpp et al. | Apr 1993 | A |
| 6017032 | Grippo et al. | Jan 2000 | A |
| 6371482 | Hall, Jr. | Apr 2002 | B1 |
| 6783456 | White | Aug 2004 | B2 |
| 20040053657 | Fiden et al. | Mar 2004 | A1 |
| Number | Date | Country |
|---|---|---|
| 2001017633 | Jan 2001 | JP |
| 2003271776 | Sep 2003 | JP |
| 2004164257 | Jun 2004 | JP |
| Number | Date | Country | |
|---|---|---|---|
| 20030200053 A1 | Oct 2003 | US |
