Welcome to the first program of the intermediate systems. The systems included in the "series of the natural results" involve the use of a natural stroke or without english, using the same cueing technique for all shots. As its name indicates, this series is characterized by the fact that in order to obtain the results defined by the system in many situations one has to modify the plays depending on the position of the cue ball in relation to the location of the second ball. 

The systems that establish their references using a natural stroke are not so susceptible to the different variables that can modify the outcome of each play. Although these systems also make use of the english, it is used to get before or after the established reference. The systems which establish their results using english as a primary condition, also have to resort to the "variables" not necessarily to modify a result, but to achieve the result set forth by the system.

Following the methodology applied in previous systems, this method also has averted the use of complicated mathematical operations. However, the logic of this treaty uses the same formula to find the values of the system. When playing from the long rails, the numbering of the cue ball value is the same used in some earlier systems. However, in this system a characteristic enumeration is used to define the diamond values of the other rails. 

The fourth rail return values are used to define the values of "The Universal Returns". This system also serves as the basis for the combination of systems especially in the plays of double or inverted english. 

The relationship between this method and the previous systems is clearly defined when analyzing the arrival to the immediate corner to establish the systematic value of english. One can say that this is the secondary system for excellence when implementing a play that involves the combination of systems.

Catalog # INT--BS-101
The Modified Result Series

Systems included:
Around the Table With English - The use of english depending on the position of the cueball with regard to the position of the second ball..
The Maximum Returns - The maximum return of the main positions of the system.
The Second Rail System - Based on the value of the third rail return.
The Inter-relation between Systems -

Recommended Courses: All basic systems.

Around the Table With English - This Treaty follows the same systematic procedures applied in the systems included in the basic category. In this compendium we are going to use a reference that is mostly used hitting the inner part of the first objective ball in relation to the first rail, emphasizing the results in the third and fourth rails.

If one has already memorized the rules and procedures applied in the basic systems, one can then apply them once again in this new phase. However, here you will learn the logic applied to another dimension of the game. According to what was previously said, I would say that when one says the “first dimension” one means the applications of the basic programs where the cue ball moves through the width and length of the table.

A second dimension of the game is analyzed in the systems to play around the table when the cue ball starts from one of the long rails attacking towards one of the short rails.

This new dimension is about the shots for plays "around the table" when the cue ball departs from one of the long rails towards the opposite long rail off the inside of the second ball. This means that the arrival to the first rail shall always be towards the long rail located on the same side where the second ball is contacted.

Similar to other methods categorized for plays around the table, this system can be used for banks or rail first shots and also for shots around the table, or twice around the table. In addition, it is used as the complementary system for plays of double reverse or change of english.

The steps for its implementation are slightly different from those used in the previous systems:
1) Find the exact position of the cue ball.
2) Find the exact position of the first object ball..
3) Determine if the cue ball is in the normal position of the system or whether it is before or after with respect to the position of the second object ball.
4) According to the previous paragraphs, establish the most adequate type of stroke to facilitate the scoring of the shot.

On systems without english, when the cue ball takes the path of the system after hitting the second ball, it is the second ball which determines the exact value of the cue ball, the value of the position of the third ball, and the point of attack in the first rail.

In systems with english, it is vital to know the systematic value of english. In other words, in many applications of the system is necessary to apply a specific amount of english to the cue ball to compensate for its "delayed" or "advanced" position in relation to the second ball position. Using this technique helps determine the results that may be obtained when cueing the ball in a certain place but using different techniques of execution.

This advanced technique of specifying the value of english with reference to the diamond is easier to comprehend once the student understands "the origin of english" and its value in the different sections of the table. As most systems used for shooting around the table are implemented with english, this system provides the basic principles for a better understanding of all systems using english to achieve their results.

When you apply the variations of this system in the "Link or Merging Area", be aware that this system is "linked" with the systems included in our previous programs. This relationship between the different systems facilitates their assessment and grants a variety in choice of plays.

The Maximum Returns – This system is derived from the application of the laws of the variations of this Treaty. Its main objective is to establish the results that may be obtained when playing from the main positions of the system using maximum english.  This system is also related to the Reverse systems because they are based on the maximum return of the opposite english.

The Second Rail System – As its name implies, this system is used to find the value of the second rail hit point. In contrast to the system to find the second rail (Two Rail Tikkie) included in the program for plays across the table, in this system the arrival to the second rail is determined by the expected return in the third rail.

Both systems use a very different approach in its application. The Two Rail Tikkie multiplies the value of the cue ball by the value of the desired point of contact in the second rail to find the point of attack in the first rail.

In this system the known values are the value of the arrival in the first and third rail. The unknown value is the value of the contact point in the second rail. This program uses the arrival to the third rail to find the point of contact in the second rail. It must be clear that the second rail is always one of the short rails.

This program is available in CD/ROM or by downloading it directly to your computer through our downloading section. This work includes over 200 interactive diagrams and animations with detailed explanations of each play from each of the main positions of the system. Also include a large number of videos by the best players in the world that demonstrate the techniques illustrated in the videos and described in the texts. These reinforce the knowledge acquired in the previous programs and provide a profound knowledge of the logic of the game of 3-Cushion Billiards.