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TIGER AND

DRAGON

A COMPLETE CHESS SYSTEM

WALTER THOMAS DOWNS



Copyright©2011 by Walter Thomas Downs

The author gives the reader of this book permission to

distribute the book freely, provided that none of thecontents of this book is changed.



TABLE OF CONTENTS

FOREWORD......................................................................4

INTRODUCTION..............................................................5

CHAPTER 1: The Theory of Chess...................................6

CHAPTER 2: Eastern Martial Theory..............................11

CHAPTER 3: Algorithm of Play......................................12

CHAPTER 4: Opening Repertoire and GameAnalysis: Tiger and Dragon..............................................14

CHAPTER 5: Mind and Body..........................................30

CHAPTER 6: Your ELO Rating.......................................37

APPENDIX A: Supplemental Study.................................38

APPENDIX B: Logic and Math Used inAnalysis of the Tiger and Dragon Chess System..............39

APPENDIX C: Knowledge Base.......................................46

About the Author...............................................................60

Donations...........................................................................61



4

FOREWORD

In late 2010, I was surfing the Web, searchingfor some chess-related information, and I

happened to come upon Gary Danelishin’s

site: The Final Theory of Chess

Gary’s project was an attempt to begin

quantifying and codifying chess variations

using computers, with the twin goals of

producing interesting opening repertoires for

chess players, and attempting to answer some

age-old questions about the game, such as

who should win a game of chess given

“perfect” play? Should White or Black win, or

is it a draw?

Gary published a book with the same name as

his web-site, and has also produced a wiki-site

that gives much of his analysis of chess

openings and variations he feels are relevant

to his project.

After examining his web-site and wiki, and purchasing and studying his book, my interest

in this project was piqued.

I contacted Gary, because I was interested in

making some contributions to the wiki, and

became even more enthralled with the project

after several e-mails had been exchanged.

I found Gary to be extremely knowledgeable

about chess, especially where computers were

involved, and an intelligent, and truly humble person.

In my research and analysis that followed, I

began to formulate some questions about

chess of my own, and a plan of attack began to

form in my mind about how to approach the

project.

Gary’s approach was a “brute-force”computational method, where he used

computers to crunch through all of the

relevant openings and variations, in an effort

to build a body of chess knowledge based on

computer analyses which could be continually

added to ad-infinitum.

Still, I realized that this method would

probably take several hundred human life-

spans before we would have any resolution to

the questions the project was designed to

answer.

There is an old Chinese saying:

“When the student is truly ready, the teacher

will appear.”

In the beginning Gary was my teacher during

my assimilation of information found in the project, but now it was my turn to introduce

concepts that had not previously been

considered, and which I believed would yield

the prospect of answering the questions the

project asked, in our life-time.

I strongly recommend that all readers of this

book visit Gary Danelishin’s web-site at:

http://finaltheoryofchess.com/

I also suggest that you buy Gary’s book, The

Final Theory of Chess.

Anyone who loves chess will find the book

and web-site very interesting and informative.



5

INTRODUCTION

What constitutes a perfect game of chess?

To my mind, chess perfection would come in

a game in which I dominated the opening,

middle-game and end-game completely.

How would this be accomplished?

The answer must lie in a series of moves that

controls the structure of the game from

beginning to end. To accomplish this, the

moves must consist of maneuvers that buildtowards an attack on my opponent’s position,

and also provide prophylaxis, or preventive

measures that preclude the opponent from

doing the same to me.

Therefore, my opening must be comprised not

only of straight-forward attack, but of the

ability to accept any attack my opponent

generated, and turn it back against him.

The next question that comes to mind is:

What would constitute an optimal chess

system?

The answer to this would be, a system that

could be played either as White or Black, that

could be playable against all possible plans the

opponent might generate, and which met the

structure and move characteristics assumed

when we answered the question of what

perfect chess must be.

Thus we are led to the next question, which is:

How will we be able to judge that the

system we devise is indeed an optimal

approach?

First, we will observe Modern Chess Strategy,and Eastern Martial Theory to make sure we

are in accordance with what they consider to

be Optimal Strategy.

Then, Using my background in advanced

mathematics, and using a top-flight chess

engine, we can follow the structure of the

game in very concrete mathematical terms,

and this will allow us to draw very objective

conclusions about the structures that are

created, and what they mean.

Melding these approaches in to a cohesive

whole, we will then derive an Algorithm of

Play, that will allow us to play optimal moves

throughout the entire course of a game.

We will use these methods to generate a series

of games that should provide us with deep

insight and a complete conceptual analysis

from the opening move of a game, to the point

at which the game is determined as won, lostor drawn.

But we won’t stop there. We will also address

the mind and body relationship a player must

attain and maintain to play the best chess he

possibly can. After all, he is part of the system

too!

So, read on....

Walter T. Downs

January, 2011



6

CHAPTER 1:The Theory of Chess

By this time, the theory of chess is welladvanced, yet it seems that no one has really

taken the time to codify all of the theory in

existence in to an over-all approach that is

cohesive.

Let us start at the dawn of modern theory, and

review all of the relevant axioms so that when

I apply them later on, you will understand

where I am coming from.

First, we consider the thoughts of Wilhelm

Steintitz, Emanuel Lasker and Siegbert

Tarrasch in what I term to be the “classical”

era of chess. Note that I do not include Aron

Nimzowitsch in this group. This is because

Nimzowitsch’s concepts were so far advanced

for his time, that I really had to include them

in the axioms of modern chess theory.

We will cover none of Tarrasch’s work, as the

author shares the opinion of Lasker in his belief that Tarrasch was too dogmatic in his

approach to the game.

We will deal with the axioms of theory in

chronological order of the years in which they

first appeared.

The Axioms of Steinitz

1. A plan must have a reason.

This concept was a novelty in the time of

Steinitz. In his era, the plan in any game of

chess was simple: Attack, attack and attack

some more. Participants were honor bound to

accept gambits, and such theories as

prevention of the opponent’s plans were in the

future. Steinitz opined that one should only

attack if one was justified by the position, or in other words, if one had a concrete and

viable reason to believe an attack would

succeed.

2. The basis of a successful plan is always a

valuation of advantages and disadvantages.

Plans of attack should logically only succeed

if one held some type of advantage in the

position on the board.

3. Valuations of advantage or disadvantage

should stem from the body of chess

knowledge.

Factors such as advantages or disadvantages

in material, time and space are all relevant.

4. Don’t try to win the game out of the

opening.

Building on the previous axioms, it is simple

logic that one must build carefully from the

opening moves in to a position where a

reasonable advantage has been achieved, and

one now has the right to attack.

5. The way to a strong advantage is

through efficiently placed (optimal) pieces,

and the accumulation of many small,

seemingly insignificant, advantages.

Steinitz felt that small advantages such as

more actively placed pieces and/or a better

pawn structure, would tell in the end. From

such positions of advantage, combinations

would grow like flowers on the vine.



7

6. Economy of Defense is important.

One should play all moves necessary to the

defense of one’s position, but never more. The

minimal number of moves to establish

adequate defense is all that is required. Nomore, no less.

7. The natural end of all balanced positions

are more balanced positions, from which it

is not possible for either side to win.

Therefore, seek imbalances in the position

on the board, and seek balance in the

position in the form of compensation in

structure or material

Imbalances in structure of the opposing sides,or material imbalances such as rook + piece +

pawn versus queen, or rook + pawns versus a

pair of minor pieces, as a few examples, are

desirable, and should be actively sought when

their creation is of advantage to the player.

8. Don’t be afraid to make strange or

provocative moves.

As long as a move meets the dictates of our

axioms, in that it brings a piece to an efficient(optimal) square, performs a necessary

function of defense, or serves to provoke the

opponent in to a rash and/or precipitous act, it

is permissible.

9. Think of your and your opponent’s

position as a chain of interlocking and

complex links.

Steinitz felt that one could then discern what

moves to play based on the strength or

weaknesses of the various links (squares or

pieces). (Author’s Note: Lasker felt this

device too simplistic, but I disagree. - WTD)

The Axioms of Lasker

1. Pieces must co-operate.

“The result of co-operation, in attacking

positions is to strengthen each element of the group; in positions of defense, to protect each

other; in positions of balance, to complement

each other”

– Emanuel Lasker

2. The less distance between pieces, the

stronger and more cohesive is the whole of

the position.

“A defect in co-operation is often indicated by great distance between the points [that]

pieces occupy.....considering the simple

geometry of the chess-board and the laws of

motion of the pieces, distance is a

first...measure of the degree [to which pieces

co-operate.]”

– Emanuel Lasker

3. One must combine both the exploitation

and defense of weaknesses.

Whereas Steinitz and Tarrasch concentrated

mainly on the exploitation of weaknesses,

Lasker espoused the defense of weaknesses as

an integral part of the game.

4. Memorization of vast numbers of

opening variations is folly.

“[Lasker] did not believe in memorizing

...fashionable variations [that] would soon be

out of fashion...In opening theory, the only

certainty is change, flux and capricious taste.

Most players prefer to have their choice of

openings derived from dogmatic authority.”

– Fred Reinfeld



8

5. Every game of chess is unique.

“[Lasker feels that each position] ...has some

hidden aspect [that] the sceptic; the man of

resource, will unearth.”

– Fred Reinfeld

6. Avoid Dogma

“Of my fifty-seven years, I have applied at

least thirty to forgetting most of what I had

learned or read, and since I have succeeded in

this I have acquired a certain ease and cheer

which I should never again like to be

without.”

– Emanuel Lasker

7. The value of a victory often lies in its

aesthetics.

“When mind overcomes matter, we are

charmed.

In chess, the brutal force is composed of the

number, strength and mobility of the pieces,

and the difficulty of the task set. If this brutal force is bested by the few in number, the slight

in strength, in moves which [seem weak],...by

the power of the spirit, by an idea which,

seemingly absurd, is truth itself, we are

delighted.”

– Emanuel Lasker

8. At its core, chess is a matter of

mathematics.

In contrasting Tarrasch, who was admittedly

poor at mathematics, to Lasker, Fred Reinfeld

writes:

“A chess master who lacks a gift for

mathematics may very well be deficient in

specific chess qualities as well. Mathematics

requires imagination and exactitude.

Tarrasch was able to conceive great plans,

but he was inclined to be [poor] in

execution....To overcome the relatively weak

resistance of lesser players was not aninsoluble task for Tarrasch, [but] to beat

down the resistance of Lasker was...too much

for him.”

Now, we will move on to modern chess

theory. We will draw on the guiding lights of

Isaac Lipnitsky, John Watson, Mihai Suba,

R.N. Coles and Hans Berliner. Theories, ala

Nimzowitsch, are mirrored in the comments

of Watson and Lipnitsky.

Axioms of Modern Chess Theory

1. Flanking pawn moves are acceptable in

the opening, nor is the number of pawns

moved in the opening relegated to one or

two.

Concerning our pawn moves in the opening,

in the books, Questions of Modern Chess

Theory, and Secrets of Modern ChessStrategy, Isaac Lipnitsky and John Watson

write:

“There is no doubt that flank attacks as a

means of fighting for the center have a great

future.”

“Whether in closed, semi-open or open

positions, flank pawn moves are regularly

employed for a variety of reasons, e.g., the

establishment of space, [or the]

discouragement of castling by the opponent.

...the number of pawn moves in the opening

can range from one to eight or more,

depending on the requirements of the

position.”



9

2. Static strategical aims should be based

solely on the position currently on the

board.

Concerning our static strategical aims, based

on a purely pragmatic point of view, Lipnitskywrites:

“The basis for a game of chess is a purposeful

plan which, beginning in the opening, is

consistently developed in the middlegame. A

highly characteristic feature of modern

opening play is that from the very start of the

game, the players will try to predetermine the

channels in which the middlegame fight will

be conducted. “

“In the opening, you have to contend not so

much with your opponent’s individual moves

as with his ideas and plans....The masking of

your own plans, which demands flexibility in

your play, is also a very significant factor.”

These statements are the essence of modern

chess prophylaxis, which Watson says,

consists of

“...prevention of the opponent’s plans in general, and protection of key points in our

position.”

3. Dynamic strategical aims are based not

on aesthetic placement of pieces, but on the

total latent or potential activity of all pieces

and pawns.

Concerning our dynamic strategical aims, in

his book, Dynamic Chess Strategy, Mihai

Suba writes:

“As a chess player my feelings were that

dynamism was something else, not just a

temporary superiority, either numerical or

qualitative. Strange combinations sometimes

come right out of the blue. Dynamism should

should show itself not as a momentary

‘firework display’, but also as the latent or

potential activity of all pieces and pawns.”

R.N. Coles, in his book Dynamic Chess,

considers the Dynamic Revolution to be foundin the play of such players as Breyer, who:

“...instead of selecting openings where

objectives were small but clear-cut from the

outset... preferred to build up a position full of

dynamic energy - ‘malignant’ energy,

Tartakower called it - which could be released

at will at a suitable target and at a suitable

moment. In the early part of the game, during

which this energy was created and

accumulated, Breyer often made moves that were in direct conflict with the tenets of the

classical style but which were found later to

fit perfectly in to his scheme of play, when the

pent up energy was finally released. His very

odd opening moves are none-the-less in

keeping with his dynamic play, for though

contrary to Tarrasch’s teaching, he gives up

both time and space, his game thereby

acquires a certain extra hidden energy.”

Turning to a more purely quantitative view of our strategy, I refer to Hans Berliner’s book,

The System, in which he puts forth several

algorithmic formulae for determining validity

of a dynamic chess strategy.

The most important consideration is to control

the entire chessboard. Towards this end,

Berliner gives the following elements:

1. Pieces placed on optimal squares and in the

fewest number of moves.

2. Play moves that leave open the greatest

number of attractive options available to other

pieces. The piece to be moved ought to have

no more than one attractive option at its

disposal given the current position.



10

Berliner states that the strategy can be

considered successful if we are better in:

1.Optimal Pieces.

2. Piece Co-operation

3. More fixed targets4. Good defensive qualities

5. Control of more squares.



11

CHAPTER 2:Eastern Martial Theory

Although it has never been applied to chess

before, the author believes that an overview of Eastern martial arts is also of benefit to the

chess player.

According to Shaolin Martial Arts, the Tiger

vs. the Dragon is the symbol of the line

overcoming the circle and vice versa. The

tiger fights in a straightforward attack

bulldozing it's opponent. The dragon fights

using circular flexible attacks. They are

certainly worthy opponents.

Both the tiger and dragon are old Buddhist

symbols. They have come to be known as

opposite symbols - one reflecting a 'hard' style

(attacking and unrelenting) form of martial

arts, this is symbolized by the Tiger.

Conversely, the 'soft' style is represented by

the Dragon and is a form that embodies a

defensive and more fluid 'circular-attack'.

Thus, these symbols have come to be

interpreted to represent (in the same wayYin/Yang represent) duality and balance

attained through the balance of opposing

forces, etc., and are often used as symbols of

this philosophy which is found in many

Eastern cultures and practices. Many systems

of study recognize a need for both 'hard' and

'soft' styles, therefore, many systems require

training in both 'styles' in order to offer the

student a balanced base of training and

experience. The Tiger and the Dragon

represent a total balance of power.

So, how does this relate to chess? Essentially,

chess is a martial game of warfare betweentwo opposing forces, governed by the mind of

the player. Given the thousands of years of

experience gleaned in the Eastern martial arts,

it would seem to be beneficial to create strong

analogies in our play over the chessboard.

Therefore, the optimal or most efficient mode

of play is a style which is both “hard” and

“soft”; offensive and defensive. A solid

defense that is also capable of swift attack.

No doubt, you have heard of the great Chinese

military strategist, Sun Tzu. Here is what he

has to say:

“A General may defeat an adversary by

attacking when the adversary does not have

an adequate defense prepared, or by

encouraging his adversary to launch an

improperly prepared attack against his

prepared defenses.” (Paraphrased)

“In battle, there are...two methods of attack -

The direct and the indirect; yet these two in

combination, give rise to an endless series of

maneuvers...That General is skillful in attack

whose opponent does not know what to

defend; and he is skillful in defense whose

opponent does not know what to attack.”

- Sun Tzu

The Art of War



12

CHAPTER 3:Algorithm of Play

Now I will propose an algorithm of play thatis based on the axioms of classical/modern

chess theory and Eastern martial theory.

The algorithm of play gives you an entire plan

and framework on which to base your moves

in a game of chess, from the opening, to the

end of the game.

Golden Rule #1

Moves that perform both an offensive and

defensive function are highly desirable.

Golden Rule #2

Control over the entire board, and

therefore of the entire position, is highly

desirable.

Silver Rule #1

Pieces must be developed and arranged in

the form of Chains and Geometric Control.

A Chain is defined either as a series of

connected squares on which pawns or pieces

reside, or a rank, file or horizontal group of

squares on which a group of pieces line-up.

Geometric Control is defined as a group of

squares controlled by the Chains. These

constellations of squares will often take theform of a geometric shape, such as a triangle,

square, diamond, rectangle or ray.

The Chains in your position that are currently

inter-acting or connected with the Chains of

your adversary are termed Primary Chains.

Pieces or squares in your own or your adversary’s position that are either not well

defended, or in many cases, are devoid of any

defense at all, are termed Broken Links.

rdb1kgs4dpdnhp0spds0pds0

ds0sdsdssds)PdsddsHsGNdsP)Pds)P)$sdQIBdR

In this position, Black has the inter-connected

square/piece Chains, Ra8/a6, Bc8/b7/a6,

Bc8/Nd7/e6, Qd8/Nd7/d6, Bf8/Ne7/d6/c5,Bf8/g7/h6 and Rh8/h6. Of Geometric

importance, is the compact geometrical

formation of squares forming at the points, c8-

f8-f6-c6. In this connected area of 12 squares,

Black has 9 pieces. This is a very compact and

safe formation. The Primary Chain would be

the Bf8/Ne7/d6/c5 Chain, since the terminus

of the Chain at c5 interacts with the White

pawn on d4. The pawn on d6 could be termed

a Broken Link, since the pawn and the square

is momentarily not defended by anything.

Before Black had played c5, here, and with the

pawn still on c7, Black could have considered

any logical move that interacted with the

White position, such as f5, e5, d5 or c5.



13

Silver Rule #2

Moves are made by simply calculating

every move possible to you in the Primary

Chains and specifically in relation to

Broken Links. If there are no critical movesin the Primary Chains (Moves that

engender Golden Rules 1 or 2, or win

material out-right.), other moves may be

considered. Selection of the best move in

the position is governed by the Knowledge

Base (APPENDIX C).

Notes on Calculation:

Remember that you will calculate every

possible move that interacts with youropponent’s pieces. Calculate possible

captures and any moves that give check

first, followed by any move that challenges

or attacks an enemy piece next.

In general, you should have to calculate no

single move deeper than 5 moves in the

future, and often you will be able to

dispense with many of the possible moves

with just 1 or 2 moves of calculation.

If none of these moves seems particularly

strong, you may consider moves that can be

made on strictly strategical principles as

outlined in the Knowledge Base and the

Algorithm of Play’s Golden and Silver

rules.

With practice, you should be able to

complete this process in well under 2

minutes, which is the average time per

move given you in most tournament games.

Learn the Knowledge Base cold, and follow

the Golden and Silver Rules, and you will

never be without a plan or a good move!

This approach is a powerful method of play

because it assures that you will always be

afforded optimal tactical and positional

capabilities. I.e. you will always have more

tactical opportunities and resources than your

opponent, and you should never be worse positionally.

Detailed examples and use of the Algorithm

of Play will be presented in the next chapter.



14

CHAPTER 4:Opening Repertoire and Game

Analysis: Tiger and Dragon

Now, it is time to draw together Modern

Chess Theory, Eastern Martial Theory, the

Algorithm of Play and the Knowledge Base in

to a cohesive whole in order to form an

effective repertoire for both White and Black.

We will observe the operation of our theories

and structures through the eyes of Deep

Rybka 4 us ing a mathemat ica l

Fibonacci/Lucas/Fractal paradigm to confirmthe structures and make highly accurate

estimates of future results based on the

concrete math.

Bringing together all of the above, I have

determined that we should aim for two main

possible structures.

0sdp0sdp

s0phn0pd4sgqibdr

DOWNS TIGER

dpdp0sdspgphn0p04sdqibdr

UJTELKY DRAGON

The first structure I call the Downs Tiger. The

second, I call the Ujtelky Dragon, in honor of

Maximilian Ujtelky an innovative Russian

player who experimented with a similar

set-up.

We see that these two structures have adopted

opening moves that are primary to both

offensive and defensive tasks. We also see

development using the Chain method, in

which pieces are initially grouped tightly

together. In reviewing our chess axioms and

Algorithm of Play, we see that the structures

meet the requirements of both classical and

modern schools of thought and seek attributes

of both the Tiger and Dragon schools of martial systems.

There are, however some questions that I am

sure spring to mind, and that need to be

addressed:

Do the structures retard development?

Isn't this passive?

In the Tiger, aren't the bishops locked in?

In the Tiger, don't moves like a6 and h6

weaken our pawn structure?

Are there any statistics in chess databases on

these positions?

What does Deep Rybka 4 think of these

positions?



15

ANSWERS:

We have adjusted our development to gain

total control of Black’s fourth rank, rather

than attempting to play a pawn to the fifth

rank, as is the common practice. We see thatwe can quickly strike all along our front in the

Tiger with b5,c5,d5,e5,f5 or g5. We see that

the knights will be able to shift quickly to

either the king-side or queen-side with Nc6

and Nb6 or Ng6 and Nf6. In the Dragon, we

can strike with d5 or f5.We have already

attained a highly flexible and dangerous set-up

capable of exploding on any front. There is

nothing passive about these positions. We see

further, that by dominating the third rank, we

defend all major points of ingress in to our position.

Regarding the bishops in the Tiger, it is

commonly known in theory that in positions

like this, the bishops are actually well placed

on their home squares. They can be

developed, later on, to classical squares such

as c5, b4, f5, g4, e7, d7, e6, d6 or can be

developed earlier to b7 and/or g7.

In the Tiger the moves a6 and h6 serve to takethe aggressive squares of b5 and g5 away from

the opponent, we threaten g5 and b5

ourselves, along with possible major

expansions in the form of pawn "phalanxes"

on g5 and f5 or b5 and c5. Further, the moves

are provocative in nature. I.e. if the opponent

rashly tries to attack with a pawn thrust of g4

or b4, we would be able to see the attempt

from a mile away, and would have plenty of

time to react and counter, in which case our

opponent would find that he has

over-extended his position. It is also of

interest to note that these positions are so

centrally solid that Black may never have to

castle, which often gains several tempi at

some point.

Of the Tiger, there is little in the databases.

Only a correspondence player, Dieter Luebke,

experimented with a similar idea. He scored

86% with it. There are a few games in the

over-the-board bases, and Black apparently

did poorly. However on closer examination,Black lost in games where he played

passively. When Black played actively, he

won almost every game. Of the Dragon, the

initial position scored 50% in games with

players over 2200, and 61% in games with

players over 2300, mainly against English and

d4 systems, where White had played c4

(Ujtelky scored 60% with it.)

Of Deep Rybka 4, allow me to presage the

analysis games with the mathematicalstatistics produced by them, and what those

statistics mean(For general information on the

logic, math and terms used, see APPENDIX

B). In the games, using various set-ups, White

gained a maximum evaluation of + 55

centi-pawns (+ 0.55). No doubt this

evaluation was due to Rybka's over-estimation

of having more space. Yet, at no time during

the games, could the evaluation expand past

the key 62 centi-pawn level, which would

indicate a possible real advantage. In point of fact, in every case (except for our games

where White played the Tiger himself) The

evaluation eroded quickly, and Black had soon

accumulated advantages surpassing the 62

centi-pawn level, indicating that victory

was at hand.



16

Throughout the games analyzed, Deep Rybka

4's evaluations moved smoothly from one

Fibonacci/Lucas number to the next.

Fibonacci/Lucas numbers were generated

better than 95% of the time during the games.

Contrast this to "normal" openings such as theSicilian or Ruy Lopez, where analysis yielded

Fibonacci/Lucas numbers no more than 70%

of the time. Further, moves of importance in

the games generated conformed to the move

sequence 1, 2, 3, 4, 5, 7, 8, 13, 18, 21, 24, 29,

34....etc.

What does this mean? It means that in

standard openings (those openings given in

Fundamental Chess Openings, by Paul van

der Sterren), there can exist great variance inthe structures produced, thus it would be

impossible for any human to adequately

prepare against all of the structures possible.

And of course, possible predictions of future

results would hold no water. In our structures,

the numbers generated indicated that there

were only about four possible structures that

could be adopted in the positions generated.

The mathematical analysis indicated that

attempts by your opponent to deviate from the

these basic structures, leaves him in a statewhich can only hasten his demise. I.e. The

elements of the position which were negatives

for your opponent were accelerated. Also,

using the Algorithm of Play, and Playing the

Tiger and Dragon assures you that, to a high

degree of mathematical certainty, you will

consistently enjoy greater tactical

opportunities and more positional trumps.

Analysis indicates this factor to be a minimum

of 3 to 1 in your favor at all times. I.e. You

will be able to generate three tactics for every

one tactic your opponent can generate, and

you will have at least three positive positional

elements or factors for every one your

opponent has. The end result is that we can

prepare deeply for our games, often from the

opening to well in to the end-game, and in our

games, we will always enjoy the inherent

advantages mentioned. Further, the fact that

the Tiger and Dragon won these games

implies that when faced with standard

responses from our opponent (pawns on e4,

d4, c4 and/or f4, with knights on c3 and f3),we have a forced win with best play. This is

because Fractal mathematics tells us that these

self-similar structures will repeat unto infinity,

and will consistently produce the same results

.

In addition to the Rybka/Fibonacci/Lucas

analysis, we can also consider the

mathematical analysis provided by the

Shashin method (APPENDIX B). In analysis

of the initial positions in the games, we findthat, combining over-all defensive and

offensive attributes, we find that the Tiger and

Dragon have the scores, 1.237 versus 1.125

for White, indicating that, mathematically we

hold an over-all advantage in these positions.

And of course, since the structures can be

played as either White or Black, we have a

complete chess repertoire.

Don't be worried by the fact that most of thesegames ended in fairly long end-games. This is

because Rybka was able to offer the stiffest

tactical resistance possible. Statistically, up to

70% of your games will end long before the

end-game. Simply play for Chains and

Geometric square control, and be sure to

calculate all moves in the Primary Chains, and

seven times out of ten, by never missing a

tactic, you will have tactical shots that win the

game on the spot.

Note also, that at times the computer played

superfluous or seemingly redundant moves.

These moves were included in order to

examine all the possible options in the

structures.



17

We begin our analysis of games with the

structure playing itself first, and then playing

against another popular set-up, the

Hippopotamus. We consider only the Tiger, as

this is our main weapon, with the Ujtelky

Dragon used only on those occasions whenour opponent plays an early f4. This will give

us basic and valuable information as to what

moves constitute good attacking and defensive

moves when we face the more standard

responses in later games. Use a real chess-set,

and play through the games move by move, as

you read the commentary. You should also

have a pen and paper handy, as well as a

printout of the Algorithm of Play and

Knowledge Base, to refer to.

Tiger vs. Tiger

1. e3 e6 2. Ne2 Ne7 3. d3 d6 4. Nd2 Nd7 5. a3

a6 6. h3 h6

Now White makes the first thrust. He chooses

b4, building the Chain b4/a3, and planning the

move Bb2, which builds the Chain Bb2/Ra1

and controls the chain of squares on the a1-h8

diagonal.

7. b4 b6

rdb1kgs4ds0nhp0sp0s0pds0dsdsdsdss)sdsdsd)sdP)sdPsdPHN)Pd$sGQIBdR

Black responds by building the Chain

b6/c7/Qd8

8. Bb2 c5

rdb1kgs4dsdnhp0sp0s0pds0ds0sdsdss)sdsdsd)sdP)sdPsGPHN)Pd

$sdQIBdR

Black responds to Bb2 by striking at the head

of the White Primary Chain on b4,

establishing the Chains c5/b6 and

c5/d6/Ne7/Bf8. He also controls a geometric

triangle on the squares f8-c5-a7.

9.Ng3 Bb7

rds1kgs4dbdnhp0sp0s0pds0ds0sdsdss)sdsdsd

)sdP)sHPsGPHs)Pd$sdQIBdR



18

b4 is adequately defended, so following the

precepts of the Algorithm of Play(Golden

Rule #1), White plays the move that has the

greatest offensive and defensive qualities,

Ng3, adding a defender/aggressor to the

king-side, freeing the bishop on f1 andestablishing the Chains Ke1/f2/Ng3 and

Ng3/g2. Black responds with Bb7, which

seeks to control the h1-a8 chain of squares,

builds the Chain Bb7/Ra8 and Ne7/Nd7/Bb7

and allows a future Rc8. Also, developing a

knight to the third rank is in accordance with

Knowledge Base C10A.

10. c4 Ng8

rds1kgn4dbdndp0sp0s0pds0ds0sdsdss)Pdsdsd)sdP)sHPsGsHs)Pd

$sdQIBdR

White now expands the control of his Primary

Chain with the move c4, which builds the

Chain c4/e3/Bf1, establishes a geometric

triangle on the points f1-c4-b4-a3, and a pawn

phalanx on c4 and b4. Black employs the

optimal offensive/defensive move by planning

to re-deploy a knight to f6, blocking the strong

b2 bishop, developing the knight to a more

aggressive square (3rd rank knight, see

Knowledge Base C10A.) and preparing Be7

and 0-0. His move builds the Chains

Rh8/Ng8/Bf8/Ke8/Qd8 and Ng8/f7/e6. Note

that both sides are attempting to build solid

areas of dominance encompassing the breadth

of the entire board. (See Knowledge Base C3

and Algorithm of Play, Golden Rules #1 and

#2)

11. Qb3 Ngf6

rds1kgs4dbdndp0sp0s0phs0ds0sdsdss)Pdsdsd)QdP)sHPsGsHs)Pd$sdsIBdR

Remember, Algorithm of Play Silver Rule #2?

White Calculates the possible moves in his

Primary Chain, and sees that Qb3 "x-rays" the

Broken Link in Black's position: The bishop

on b7 (undefended piece) and eliminates his

Broken Link, the lone Bb2. He also creates the

Chain Bb2/Qb3/b4 and further solidifies theconnective links of the squares, pieces and

pawns on the white 3rd rank. Black sees no

immediate threat, and so continues with his

original plan, creating the Chains Nf6/Qd8

and Nf6/g7/Rh8, and building a very solid

geometric square on the points f8-f6-d6-d8.

Note that in this square, there are 8 pieces on

9 squares, a type of position which I describe

as "nuclear" in that it is capable of unleashing

tremendous force in to the position when it

unwinds.

12. e4! Be7



19

rds1kds4dbdngp0sp0s0phs0

ds0sdsdss)PdPdsd)QdPdsHPsGsHs)Pd$sdsIBdR

White looks at the relationship of his Primary

Chains to Black's Primary, and quickly

calculates that e4 offers the best in aggressionand defense, as it expands his Primary Chain

and also anticipates a possible d5 by Black.

He builds the Chains d3/e4 and e4/c4/b4.

Black answers by solidifying the center of the

geometric square mentioned previously,

building the solid Chains Nf6/Be7/Qd8,

e6/Be7/Ke8 and g7/f7/Be7/Nd7 and creating

a new, solid, piece rectangle on the points

e8-e6-d6-d8 (6 pieces on six squares).

13. Be2 O-O14. O-O Qc7

rdsds4kddb1ngp0sp0s0phs0ds0sdsdss)PdPdsd)QdPdsHPsGsHB)Pd$sdsdRIs

Note that the last few moves, both sides

complete the defense of their respective

positions and prepare future attacking

possibilities by castling (Which also

eliminates momentary Broken Links on g2

and g7). White has created the Chains c4/ d3/Be2/Rf1, Rf1/g2/h3 and Kg1/g2/Ng3. He has

also created a strong geometric defensive

square at the points f1-f3-h3-h1 (6 pieces on

nine squares). Black plays Qc7, creating the

solid Chain g7/f7/Be7/Nd7/Qc7/Bb7 and

eliminating his Broken Link of the Bb7.

We have now reached a position where it is

possible to look far in to the future and foresee

how the game will play out. This is one of the

attributes of the Tiger and Dragon. Youalways have plenty of time to work out a plan.

White's "Big Clamp" has been successful.

Black is going to have trouble creating

counter-play. Work out the logic of the Chains

created in the rest of the game, and be sure to

practice calculating ALL moves in the

Primary Chain. Refer often to the Knowledge

Base, and record the applicable precepts. Keep

a sharp eye out for Broken Links.

15. Bc3 Rfc8 16. Rac1 Nh7 17. Rfe1 a5 18. b5

Re8 19. Qb2 Bf6

White clamps down on the queen-side,

denying Black counter-play there. Black

responds by forcing exchanges that reduces

White's pull.

20. Bxf6 Nhxf6 21. f4 Nf8 22. Ngf1 Red8 23.

g3 Re8 24. Ne3 Ng6 25. a4 Rab8 26. Bf3

Rbd8 27. Qb3 Ne7 28. Qd1 Kh7 29. Qe2 g6

30. Rf1 Rf8 31. Rf2 d5 32. e5 Ne8 33. Nb3 d4

34. Ng2 Bc8 35. Re1 Kg8 36. Nd2 Kg7 37.

Ba8 Ba6 38. Be4 Bc8 39. Nf3 Nf5 40. Kh2

Kh8 41. g4 Ne7 42. Ngh4 Ng7 43. Kg1 Rg8

44. Nd2 Rgf8 45. Nhf3 Rg8 46. Rg2 Ne8 47.

Qf2 Rg7 48. Qg3 Kg8 49. Kh1 Kf8 50. Reg1



20

Kg8 51. Qf2 Kh8 52. Qh4 Rh7 53. Qg3 Kg8

54. h4 h5 55. Ng5 Rh6 56. gxh5 Ng7 57. Nxf7

Kxf7 58. Qg5 Rdh8 59. Bxg6+ Nxg6 60.

Qf6+ Kg8 61. Rxg6 Bb7+

Note that White followed the precepts foundin the Knowledge Base C17E. I.e. with a

long-term static advantage, he denied Black

all counter-play, and built his position slowly

Note also the attribute of the Tiger found in

the Knowledge Base that states that positions

where your opponent is in a near state of

zug-zwang, will exist. For his part, Black is

following the precept of Knowledge Base

C16D. I.e. Relying on his "fortress" to hold

the position, and counting on the Tiger

attributes that state that he will always havegood squares for his pieces, and that whatever

tactics arise will never disfavor him. Note that

the combination White initiated with 57.Nxf7

lasted 5 moves, another Tiger/Dragon

attribute.

62. Ne4 Bxe4+ 63. dxe4 Rxg6 64. Qxg6 Qe7

65. Qf6 Qf7 66. h6 Qxf6 67. exf6 Rxh6 68.

Rxg7+ Kf8 69. Kg2 Rxf6 70. Rg4 Rh6 71.

Kf3 Kf7 72. e5 Rh8 73. Ke2 Rh5 74. Kd3 Rh875. Kc2 Rh5 Drawn.

Sdsdsdsddsdsdkdss0sdpdsd0P0s)sdrPdP0s)R)dsdsdsdssdKdsdsddsdsdsds

Note that in the final stage of the game, the

attributes of the Tiger came to light. The

promise to Black that resulting pawn

structures would never disfavor him, the

ability to create a fortress that White could not

penetrate, and therefore the promise fulfilled

that tactics would always be in his favor. For White's part, tactics were good to him too, as

he was able to win a pawn, although it wasn't

enough to win the game.

Tiger vs. Hippopotamus

1. e3 e6 2. d3 Ne7 3. Ne2 d6 4. Nd2 Nd7 5. h3

g6 6. a3 b6

rdb1kgs40s0nhpdps0s0pdpddsdsdsdssdsdsdsd)sdP)sdPs)PHN)Pd

$sGQIBdRConsidering the Primary Chains of Black, we

see that he is going to apply pressure to the

a1-h8 and h1-a8 diagonals. Therefore, the

move that has the greatest offensive and

defensive value is clearly g3, as we will soon

develop our bishop to contest the diagonal,

and may then castle. We build the Chain

g3/f2/Ke1.

7. g3 Bb7 8. e4 Bg7 9. Bg2 O-O 10. O-O c5



21

rds1s4kd0bdnhpgps0s0pdpd

ds0sdsdssdsdPdsd)sdPds)Ps)PHN)Bd$sGQdRIs

We have built a rock-solid Chain of c2/d3/e4

and Bg2/e4, and have built a very strong

defensive geometric square at the pointsh1-h3-f3-f1 in which our king resides. Also

note the powerful geometric triangle of

squares we control at the points h1-e4-b1.

Now, Nc3 offers the best offensive/defensive

qualities, possible defending the queen-side

and opening up squares for the queen on the

king-side. Nc3 builds the Chains Nd2/Nc3,

Nc3/b2, Bc1/c2/Nc3, and also builds a solid

geometric rectangle at the points c1-c3-d3-d1

(6 squares filled by 6 pieces). We also develop

a knight to the third rank ala Knowledge BaseC10A.

11. Nc3 Ne5

Now, the move f4 is logical, in order to

expand our Primary Chain on the king-side

and create the pawn phalanx f4 and e4.

12. f4 N5c6

rds1s4kd0bdshpgps0n0pdpd

ds0sdsdssdsdP)sd)sHPds)Ps)PHsdBd$sGQdRIs

Black is re-deploying his pieces, and intends

Nd4. It is best for us to also re-deploy and

defend against this possibility, with Ne2.

13. Ne2 d5

The move, e5 has the best offensive/defensive

value, blocking out the diagonals of Black's

dark-squared bishop, and building the Chain

g3/f4/e5.

14. e5 Qd7

It is logical to continue king-side expansionhere, with g4, building the Chains h3/g4 and

g4/Ne2/Qd1.

15. g4 a5

The move Nf3 fills the geometric center of our

Primary Chain, creating the solid Chain

Qd1/Ne2/Nf3/g4 and the Chains Rf1/Nf3/f4

and Bg2/Nf3.

16. Nf3 d4



22

Ng3 develops a knight to the third rank and

further compresses the geometric square of

h1-h4-f4-f1. Note that we have 8 pieces on 12

squares here, forming a "nuclear"

configuration. Our original defensive square

in this area of the board has now morphed into a quite ominous attacking configuration. It

is clear that our attack is going to come first,

before Black can establish any kind of

counter-play. Notice the typical Tiger attribute

that Black is suffering from zug-zwang. He

has no really good moves, but must play

something. With Ng3, we also build the Chain

Ng3/f4/e5.

17. Ng3 Nd5

rdsds4kddbdqdpgps0ndpdpd0s0n)sdssds0s)Pd)sdPdNHP

s)PdsdBd$sGQdRIs

Now, Ne4 develops a knight to the fourth rank

(Knowledge Base C10B.) and creates a solid

geometric triangle at the points g2-e4-c2. It

also builds and joins the Chains Bg2/Nf3/Ne4

and Ne4/d3/c2.

18. Ne4 f6

Black seeks to alleviate some of the pressure.

White now plays a few exchanges, and then

goes after the Broken Link on b6. Before

continuing with any other plan, he generates

play on the queen-side for a while in

accordance with Algorithm of Play GoldenRule #2.

19. exf6 Nxf6 20. Nxf6+ Bxf6 21. Nd2 Rae8

22. Nc4 Bd8 23. Qe2 b5 24. Nd2 Qc7 25. a4

b4 26. Nc4 Re7 27. Bd2 Qd7 28. Rae1 Ree8

29. b3 Bc7

sdsdr4kddbgqdsdp

sdndpdpd0s0sdsdsP0N0s)PddPdPdsdPsdPGQdBddsds$RIs

White has achieved a total domination of board. Black will now try some exchanges,

but it doesn't help.

30. h4 Nd8 31. Bxb7 Nxb7 32. Qg2 Nd8

33. f5



23

sdshr4kddsgqdsdpsdsdpdpd

0s0sdPdsP0N0sdP)dPdPdsdssdPGsdQddsds$RIs

At this point, Rybka's evaluation of the

position exceeded the 62 centi-pawn mark,

and we can probably conclude that White hasa strategically won game. In the rest of the

game, it is clear that the white pieces clearly

dominate the black pieces. White tucks his

king away safely, and then goes to work on

the incredibly weak black king-side. Carefully

play through the rest of this game, noting the

ease with which White converts his

advantage.

33...exf5 34. Rxe8 Qxe8 35. gxf5 Kh8 36.

fxg6 Rxf1+ 37. Kxf1 hxg6 38. Qf2 Ne6 39.Ke2 Kg7 40. Kd1 Qa8 41. Kc1 Qd5 42. Qf1

Kg8 43. Kb2 Kg7 44. Qf2 Kg8 45. Qe2 Bd8

46. Qg4 Kg7 47. Bf4 Nxf4 48. Qxf4 Kh7 49.

Ka2 Qe6 50. Qf3 Kg7 51. h5 Qf6 52. Qd5

Qg5 53. h6+ Kh7 54. Qxg5 Bxg5 55. Nxa5

Bf4 56. Nc6 g5 57. a5 g4 58. a6 g3 59. a7 g2

60. A8=Q g1=Q 61. Qa7+ Kxh6 62. Qxc5

Bd2 63. Nxd4 Kh7 64. Qc7+ Kh8 65. Nf3

Qc1 66. Nxd2 Qxd2 67. Qc5 Kg7 68. d4 Kf6

69. d5 Kg5 70. Kb2 Kg6 71. d6 Kf6 72. Ka2

Kg6 73. Qc7 Qf4 74. Qc6 Qf6 75. Qd5 Qd8

76. Qe6+ Kg7 77. Kb2 Qh4 78. d7 Qd4+ 79.

Kc1 Qg1+ 80. Kd2 Qg2+ 81. Ke3 Qg3+ 82.

Kd4 Qf4+ 83. Kd3 Qg3+ 84. Kc4 Qf4+ 85.

Kd5 Qd2+ 86. Kc6 Qxc2+ 87. Kb7 Qg2+ 88.

Kc7 Qc2+ 89. Qc6 Qh2+ 90. Qd6 Qc2+ 91.

Kb8 1-0

From these two games, we can construct the

basic plan of the Tiger, which is attacking

with the pawn thrusts (as White or Black)

g4/g5, f4/f5, b4/b5 and c4/c5. We also see that

it is important to maneuver with the knights,

probing at whatever structure our opponentsets up. The central pawn thrusts such as e4/e5

or d4/d5 are possible, but usually held in

reserve until later, although they do play a key

role in the Ujtelky Dragon, which we will

analyze later.

Tiger vs. Standard Set-up

1. e4 e6 2. d4 Ne7 3. Nf3 d6 4. Nc3 Nd7

5. Be2 h6 6. Be3 a6 7. O-O

Since White has castled while our position is

still very flexible, one approach is to embark

on a plan of king-side expansion. g5 creates

the Chain h6/g5 and intends to develop the

king's bishop to g7, collecting the square

Chain a1-h8.

7...g5 8. Ne1

Ng6 is the logical continuation of our plan. It

creates the Chains h6/Ng6, g5/Ng6 and

Ng6/f7/Ke8. I also develops a knight to the

third rank. (Knowledge Base C10A.)

8...Ng6 9. Nd3 Bg7 10. f4

rdb1kds4dp0ndpgspds0pdn0dsdsds0ssds)P)sddsHNGsdsP)PdBdP)$sdQdRIs



24

White plays a threatening move, yet here we

follow Algorithm of Play Golden Rule #2 and

play Nb6, expanding on the queen-side. It is

the promise of the Tiger, that we will always

have adequate tactical resources. Now,

11.fxg5 hxg5 would accelerate our king-sideattacking chances, and is clearly bad. The

aggressive 11.f5?! is no problem, as evidenced

by the following line:

11. f5?! exf5 12. exf5 Nh4 13. Bg4 O-O 14.

g3 Qe7 15. Qc1 Re8 16. f6 Qxe3+ 17. Qxe3

Rxe3 18. Bxc8 Rxc8 19. gxh4 Bf8 20. hxg5

hxg5 21. Rf5 Bh6 When Black has a better

pawn structure and more active pieces, and is

therefore better in this end-game.

10...Nb6 11. Kh1 Nc4 12. Bg1 O-O 13. Qc1

Here, Black continues to expand on the

queen-side with b5. However there are always

plenty of viable options with the Tiger.

Another plan might be 13...f5 14.exf5 exf5

15.b3 Nb6 16.Bh5 Kh7 18.Bf2 g4 19.h3

gxh3....etc.

13...b5 14. a4 Bb7 15. b3

rds1s4kddb0sdpgspds0pdn0dpdsds0sPdn)P)sddPHNdsds

sdPdBdP)$s!sdRGK

Here we simply retreat the knight with Na5,

but to show the tremendous tactical ability of

the Tiger, also possible was 15...c5!? 16.bxc4

cxd4 17.fxg5 hxg5 18.axb5 dxc3 19.Qe3 axb5

20.cxb5 Ra5....etc.

15...Na5 16. fxg5 hxg5 17. axb5 axb5 18.

Nxb5 Bxe4 19. Qe3 Bb7 20. Bf3 Nc6 21. Bf2

rds1s4kddb0sd0gssdn0pdnd

dNdsds0ssds)sdsddPdN!BdssdPdsGP)$sdsdRdK

Always be sure to calculate all moves possible

in relation to the Primary Chains, especially

where they intersect with the enemy. Wequickly find the very interesting g4!?

21...g4!? 22. Bxg4 Ba6! 23. Rxa6 (23.Nc3

Nxd4 when Black is better.)

23...Rxa6 24. Qd2 Qe7 25. Re1 Rfa8



25

rdsdsdkdds0s1pgsrdn0pdnd

dNdsdsdssds)sdBddPdNdsdssdP!sGP)dsds$sdK

Per Knowledge Base B., "Winning the

Exchange", we know that since White still has

the bishop pair, we gain about 1.15 for theexchange which makes the material balance

only slightly in our favor. Yet here, we must

consider that Black's pieces are much more

active, and therefore, we hold a clear

advantage at this point.

26. Bf3 Qd7 27. h4 Ra1 28. h5 Rxe1+ 29.

Nxe1 Nge7 30. g4 Ra1 31. Kg1 d5 32. Kh2

Nd8 33. h6 Bf8 34. c4 c6

sdshsgkddsdqhpdssdpdpds)dNdpdsdssdP)sdPddPdsdBdssds!sGsI4sdsHsds

Black has a strategically won game here. This

is because of his incredibly dangerous central

pawn mass which will be unstoppable. Study

the technique in the rest of the game that

follows. Black crushes White with ease.

35. Nc3 f6 36. Kg2 Nf7 37. Na4 Qd6 38. h7+

Kh8 39. Nc5 e5 40. cxd5 cxd5 41. Qb2 Ra8

42. Bd1 Nc6 43. dxe5 Nfxe5 44. b4 Nc4 45.

Qb1 Ra7 46. Nf3 Rxh7 47. Nh4 f5 48. Qa1+Kg8 49. Qc1 f4 50. Nd3 N6e5 51. Nxe5 Qxe5

52. Nf3 Ne3+ 53. Bxe3 Qxe3 54. Qxe3 fxe3

55. Bb3 Bxb4 56. Bxd5+ Kg7 57. Bc4 Ba5

58. Be2 Rh8 59. Nd4 Kf6 60. Bd3 Bb6 61.

Ne2 Kg5 62. Bf5 Bc7 63. Kf3 Rh3+ 64. Ke4

Bb6 65. Kd3 Rh2 66. Be6 Rh7 67. Ke4 Rh6

68. Bf5 Rh2 69. Kd3 Rf2 70. Be6 Rf8 71. Ke4

Re8 72. Ke5 Ba7 73. Kd5 Kf6 74. g5+ Kxg5

75. Ke5 Bb8+ 76. Kd5 Kh4 77. Bf7 Rf8 78.

Bg6 Kg4 79. Bd3 Kf3 80. Nd4+ Kf2

White must give up a piece to stop Black from

queening, and is totally lost.

0-1

For the sake of completeness, allow me to

show two other possible game continuations

where Black drew with ease.

7... c5 8. a3 Qc7 9. Qd2 Ng6 10. d5 e5 11. h3

Be7 12. a4 b6 13. Rfe1 O-O 14. Rab1 Re8 15. b3 Qd8 16. Rb2 Nh4 17. Nxh4 Bxh4 18. Ra1

Rb8 19. Rab1 Qc7 20. Bc4 Be7 21. Qe2 Qb7

22. Bd3 Qa7 23. Na2 f5!

A typical example of the explosive tactics the

Tiger offers, out of seemingly quiet and stable

positions.

24. exf5 e4 25. Bxe4 Bf6 26. Qf3 Bxb2 27.

Rxb2 Ne5 28. Qg3 Qf7 29. Bxh6 Kf8 30. Bc1

Bxf5 31. Bxf5 Qxf5 32. Qf4 Qxf4 33. Bxf4

b5 34. axb5 Rxb5 35. Rb1 c4 36. Nc3 ½ - ½

White must shuffle the knight from a2 to c3

acquiescing to a draw by perpetual if Black

moves the rook back and forth.



26

9... e5 10. dxe5 11. Qd2 Nf6 12. f3 Bd6 13.

Rfd1 Rg8 14. Kh1 Nf4 15. Na4 Bd7 16. Nac5

Bc6 17. c4 Qe7 18. Nb3 Qe6 19. Bxf4 gxf4

20. Na5 Nxe4 21. fxe4 Bxe4 22. Bf3 Bxf3 23.

gxf3 O-O-O 24. c5 Bxc5 25. Nxc5 Rxd2 26.

Nxe6 Rxb2 27. Rab1 Rxb1 28. Rxb1 fxe6 29. Nxb7 e4 30. fxe4 Rg5 31. h4 Re5 32. Kg2

Rxe4 33. Nc5 Re2+ 34. Kf3 Rxa2 35. Rg1

Kb8 36. Rg8+ Ka7 37. Rh8 Kb6 38. Nxe6 A5

39. Rxh6 A4 40. Nxf4+ Kb5 41. Ne2 Ra3+

42. Kg4 Re3 43. Nd4+ Kc5 44. Nc2 Rc3 45.

Ne1 Rc4+ 46. Kg5 Kb5 47. Rh8 A3 48. Ra8

Rc5+ 49. Kg4 Rc4+ 50. Kg3 Rc1 51. Nf3 Kb4

52. h5 Rh1 53. Nh2 Rg1+ 54. Kh4 Rh1 55.

Kh3 Re1 56. h6 Re7 57. Kg4 Kb3 58. Nf3 a2

59. Ng5 Kb2 60. h7 Rxh7 61. Nxh7 a1=Q 62.

Rxa1 Kxa1 ½ - ½

Next, we will examine two possible plans of

play when your opponent assumes an

Auerbach structure with pawns on e4, d4 and

c4. You will see that there is nothing to fear

here at all. Remember that having some space

in the opening does not mean you have an

advantage (Knowledge Base C1.).

Tiger vs. Auerbach # 1

In this game, Black adopts the early g5 plan

and blows White away. I offer the game with

very little comment. Remember to Study the

Chains and Geometric that are developed, and

to calculate all moves in the Primary Chains.

Don't forget to look for Broken Links. Study

the whole game and the techniques used,

carefully. Black is a pawn up in the end-game,

but of key importance is the superior activity

of his pieces.

1. d4 e6 2. c4 Ne7 3. Nc3 d6 4. Nf3 Nd7 5. e4

a6 6. Be2 h6 7. Be3 b6 8. O-O g5 9. d5 e5 10.

h4 g4 11. Ne1 h5 12. Nd3 Ng6 13. Bg5 Be7

14. Bxe7 Qxe7 15. g3 Nxh4! 16. gxh4 Qxh4

17. Ne1 Rg8 18. Ng2 Qh3 19. Qd2 Bb7 20.

Rae1 O-O-O 21. Bd1 g3 22. fxg3 Rxg3 23.

Re2 Rdg8 24. Rxf7 R3g4

sdkdsdrddb0ndRds

p0s0sdsddsdP0sdpsdPdPdrddsHsdsdqP)s!RdNddsdBdsIs

It is move 24, and Black already has astrategically won game! The rest is nothing

but torture for White. Study carefully how

Black uses his superior pieces, and how he is

careful to squash any type of white

counter-play.

25. Ref2 Rh4 26. Kf1 Qh1+ 27. Ke2 Rxg2 28.

Rxg2 Qxg2+ 29. Kd3 Nc5+ 30. Kc2 Qxd2+

31. Kxd2 Kb8 32. Ke3 A5 33. A3 Bc8 34. b4

axb4 35. axb4 Na6 36. Nb5 Rh3+ 37. Kf2 h4

38. Bf3 Rg3 39. Rh7 Nxb4 40. Rxh4 Rg7 41.Ke3 Na6 42. Rh2 Nc5 43. Rg2 Rh7 44. Rg1

Bd7 45. Rh1 Rg7 46. Nc3 Nb3 47. Kf2 Nd2

48. Be2 Bg4 49. Bd3 Rf7+ 50. Ke3 Nb3 51.

Rf1 Rh7 52. Rf8+ Kb7 53. Bf1 Rh1 54. Rf7

Nc5 55. Rg7 Rxf1 56. Rxg4 Rh1 57. Nb5

Rh3+ 58. Kd2 Rh2+ 59. Ke3 Rh7 60. Rg3

Ka6 61. Rg8 Ka5 62. Rc8 Kb4 63. Nxc7 Rh4

64. Ne8 Rxe4+ 65. Kf3 Rf4+ 66. Ke2 Kxc4

67. Nxd6+ Kxd5 68. Nb5 Re4+ 69. Kd2 Rh4

70. Re8 Rh3 71. Kc2 Kc4 72. Nd6+ Kd4 73.

Nf5+ Kd5 74. Kd2 Rd3+ 75. Ke2 Ke4 76.

Nh6 Rb3 77. Nf7 Rb2+ 78. Kd1 Nd3 79.

Nd6+ Kd4 80. Rf8 Nc5 81. Nf5+ Kc4 82. Rc8

e4 83. Ng3 e3 84. Ke1 Kc3 85. Kf1 Kd4 86.

Ne2+ Ke5 87. Rg8 Ne6 88. Rg3 Rb1+ 89.

Kg2 Nf4+ 90. Kf3 Nxe2 91. Kxe2 Rb2+ 92.

Ke1 Kf4 93. Rg7 b5 94. Re7 b4 95. Re8 Rc2



27

96. Rf8+ Ke4 97. Re8+ Kd4 98. Kf1 b3 99.

Rd8+ Kc3 100. Ke1 Kb2 101. Rb8 Ka2 102.

Kf1 b2 103. Ra8+ Kb1 104. Ra3 Kc1 105.

Rxe3 b1=Q

0-1

Tiger vs. Auerbach # 2

In this game Black adopts a plan with the c5

advance. Note the board-wide and swift attack

on all fronts. The Tiger is NOT a passive

opening.

1. d4 e6 2. c4 d6 3. Nc3 Nd7 4. Nf3 Ne7 5. e4

h6 6. Be3 a6 7. Bd3 c5 8. d5 exd5 9. exd5 g5

10. Qc2 Bg7 11. h3 b5 12. cxb5 axb5 13.Bxb5 Bb7 14. h4 g4 15. Nh2 f5 16. Rd1 O-O

17. O-O f4

rds1s4kddbdnhsgssds0sds0dB0Pdsds

sdsds0p)dsHsGsdsP)Qds)PHdsdRdRIs

The once proud white position is in shambles,

and Black’s attack rages across the board.

18. Bc1 Ne5 19. g3 fxg3 20. fxg3 Rxf1+ 21.Rxf1 Kh8 22. Rd1 Qg8 23. Qe4 Bc8 24. a4

Bf5 25. Qe2 Bg6 26. Bf4 Nf5 27. Bc6 Ra7 28.

Nb5 Re7 29. Qd2 Qd8

sds1sdsidsds4sgssdB0sdb0

dN0PhndsPdsdsGp)dsdsds)ss)s!sdsHdsdRdsIs

Black has a strategically won game here.

White will not be able to stop the Black piece

invasion. Black's bishop pair are ragingmonsters (though we have sacrificed a pawn,

we gain at least a ½ pawn back for this

(Knowledge Base B. "Valuation of

Imbalances/Bishop Pair") and ALL of Black's

pieces are aggressive and mobile. We are

winning...

30. b3 h5 31. A5 Qc8 32. Bxe5 Bxe5 33. Nf1

Kh7 34. Re1 Rf7 35.Rxe5

Total desperation.

35...dxe5 36. Qe1 Nd4 37. Nxd4 exd4 38. Bb5

Qf8 39. Bc4 d3 40. d6 Rd7 41. Qe5 Qxd6 42.

Qxd6 Rxd6 43. Nd2 Rd7 44. Bb5 Re7 45. Kf1

Kg7 46. a6 Kf6 47. Bc6 Ra7 48. Bb7 Ke5 49.

Kf2 Kd4 50. Nc4 Kc3 51. Ke3 Kxb3 52. Ne5

Kc3 53. Nxg6 d2 54. Ke2 Kc2

0-1



28

In our final game, we examine the Ujtelky

Dragon. In addition to the Tiger, the Dragon

can be played against systems where White

plays c4 English set-ups, Auerbach set-ups or

queen-pawn set-ups of d4 and c4. The main

use of the Dragon is in structures where White plays an early f4. In these cases, the Dragon is

often best.

Dragon vs. Broad Front

1. e4 e6 2. d4 Ne7 3. f4 d6 4. Nf3 Nd7 5. c4

g6 6. Nc3 Bg7 7. Be2 O-O 8. O-O

rdb1s4kd

0p0nhpgpsds0pdpddsdsdsdssdP)P)sddsHsdNdsP)sdBdP)$sGQdRIs

White’s position looks impressive. However,

according to the Shashin method of

mathematical position estimation, Black is

better! Observe how Black swiftly dismantles

the white position.

8...d5 9. cxd5 exd5 10. e5 a6 11. a3 b5 12.

Be3 c6 13. b3 a5 14. Qd2 Rb8 15. Bf2 Nb6

16. Bh4 Be6 17. Rfc1 Qd7 18. a4 bxa4 19.

Nxa4 Nxa4 20. bxa4 Bh6 21. Bf6 Rb4 22. g3Rfb8 23. Bxe7 Qxe7 24. Rxc6 Bg4 25. Qe3

Bf8 26. Bd1 Rb2 27. Rc2 Qb4 28. Ne1 Rb3

29. Nd3 Bf5 30. Be2 Qe7 31. Rd2 Qd7 32.

Bf3 Rc3 33. Qe2 Rbb3 34. Rad1 h5

sdsdsgkddsdqdpdssdsdsdpd

0sdp)bdpPds)s)sddr4NdB)sssds$Qds)dsdRdsIs

It is move 34, and White is strategically lost.

The rook pawn is going to fall, and then our

outside passed pawn will tell (See KnowledgeBase C17E, C17F, C17H, C17J and C17T.)

35. Bg2 Bg4 36. Bf3 Be6 37. Ra1 Bf5 38.

Rad1 Ra3 39. Bg2 Qc6 40. Nf2 Rxa4 41. Bh3

Bxh3 42. Nxh3 h4 43. Qg4 hxg3 44. hxg3

Raa3 45. Rg2 Rc1 46. Rxc1 Qxc1+ 47. Kh2

Ra1 48. Nf2 A4 49. Qd7 Qe1 50. Qe8 Qe2 51.

Nh3 Qf1 52. Nf2 Re1 53. f5 gxf5 54. Qd7

Qa6 55. Qxf5 Qg6 56. Qxg6+ fxg6 57. Ng4

Be7 58. Rb2 A3 59. Rb8+ Kg7 60. Ra8 Re4

61. Ra7 Kf8 62. Ra8+ Kf7 63. Nh6+ Kg7 64.Ra7 Kxh6 65. Rxe7 Re2+ 66. Kh3 a2 67. Ra7

Kg5 68. e6 Kf5 69. e7 g5 70. g4+ Kf4 71.

Rxa2 Re3+ 72. Kg2 Rxe7 73. Ra5 Ke4 74.

Ra4 Ke3 75. Kg3 Re4 76. Ra7 Rxd4 77. Rd7

Ke2 78. Rd6 Rd3+ 79. Kg2 Ke3 80. Ra6 d4

81. Ra4 Rc3 82. Ra1 Rc2+ 83. Kg3 d3 84.

Re1+ Re2 85. Rg1 d2 86. Ra1 Re1 87. Ra3+

Ke2 88. Ra2 Rg1+ 89. Kh2 Rb1 90. Kg2 Ke1

0-1

The Tiger and Dragon leave a powerful

impression. White never really seemed to have

a chance at all.



29

Study these games over and over, until you

understand the techniques thoroughly.

According to concrete mathematical analysis

you will face similar themes in every game

you play.

Now, if you study the Algorithm of Play and

the Knowledge Base, until you have them

down cold, and can site them "chapter and

verse", I see no reason why you should ever

lose a game of chess again.

If you get bored, or you want to change things

up a bit, the system is very flexible. Possible

are: e6 and Ne7 followed by an early d5 or f5,

d6 and Nd7 followed by an early c5 or e5, or

if you want to play a super-positional game,e6, Ne7, g6 and d5. If White plays e5, seeding

you the f5 square for your knight then h5 and

Nf5. If White doesn't advance the e pawn,

then dxe4, and after he captures back with a

piece, then h5 and Nf5. This is the super-solid

Gurgenidze set-up, and it is a tough nut to

crack.

Another pleasant attribute of the Algorithm of

Play, is that you will be able to find moves

quite rapidly, so you should always be aheadon the clock. You should be able to play out

your games to completion in quite a bit less

than 2 hours (The standard time control in

most tournaments.)

Finally, the Tiger and Dragon can also be

played as White, so you now have a complete

and very dangerous chess repertoire!

A Note on early Advances and Move

Orders

early advances by the opponent such as an

early e5 or d5 do not impress. You have the

choice of either capturing, if advantageous toyou, or stepping past the pawn, which often

closes the center for a long time to come, and

gives good play and squares to your knights.

In general, the first six moves of the game can

be played on auto-pilot, and you can choose

any move order you like that reaches the

Tiger or Dragon. It is usually advisable to play

out the two center pawns first, followed by the

knights or bishop, and then the a6/h6

advances.



30

CHAPTER 5:MIND AND BODY

Of course, our games are not played by

computers, but by us. We as humans can tend

to be a bit fragile physically and/or

psychologically, and thus, our game may

suffer.

The Body Connection

First, we will consider the physical body, as

basic physical well-being is required to play

chess optimally.

Daily Exercise Quota

Always get at least 8 hours of sleep per night.

A 20 minute brisk walk, or if your not

capable, a 40 minute, more leisurely walk, is

recommended.

Daily Diet

1 cup of Ginko/Green Tea decaffeinated teataken any time during the day, or with meals

if stomach sensitive. (I recommend the Triple

Leaf brand, which can be gotten at

http://www.vitacost.com/ A 6 month supply

will cost you about $40.00)

Drink eight, 8 ounce glasses of water per day,

or as much as you can possibly stand.

Eat three moderate meals per day.

Breakfast

1 cup of fruit.

1 slice whole-wheat plain toast or 1 cup

granola or other sugar-free, high fiber cereal,

with fat-free milk or apple-juice.

Lunch and Dinner

3 ounces of broiled skinless chicken, fish or

lean beef.

Lots of brightly colored steamed vegetables,

especially any green vegetable.

½ a baked potato (with non-fat, cholesterol

free-margarine and imitation fat-free bacon

bits if you must).

OR

Brown non-processed rice.

If you feel this is too stringent, once every

week, take one day and eat what-ever you

want.

Night-time Snacks

Plain popcorn (with non-fat, cholesterol-freemargarine if you must).

Indulgences

You can have one bar of sugar-free milk or

dark chocolate. (With raisins, is ok, but avoid

nuts.)

http://www.vitacost.com/

http://www.vitacost.com/



31

Intake on Game Days

Avoid any heavy or large meals before a

game. Eat a light sensible meal. (Consider the

above breakfast menu or the Lunch and

Dinner menu in ½ proportions.)

NO SUGAR!!!

Game Time

Five minutes before game time, imbibe one 5-

hour ENERGY® drink (regular). This is a 3

ounce liquid shot, that is zero sugar, zero

herbal stimulants, 4 calories B-vitamins and

amino acids and as much caffeine as a cup of

the leading premium coffee, so it doesn’t break any of the laws of intake before a

tournament chess game (Still, imbibe it

outside the tournament hall to avoid any

possible hassles.) The key ingredients in 5-

hour ENERGY® are also available in every

day foods – like broccoli, avocados, bananas

and apples – or already in you. This drink can

be obtained at almost all grocery stores or

pharmacies.

Who should not take 5-Hour Energy?

Women who are pregnant or nursing.

Children under 12 years of age.

People diagnosed with phenylketonuria

(PKU).

Check with your doctor before taking 5-

Hour Energy if…

You are currently taking any

prescription medicines.

You have been advised by your

physician to avoid stimulants or

caffeine.

You have a medical condition that

makes you concerned about taking it.

You are concerned about taking it for

any reason.

For further information:

http://www.5hourenergy.com/

If you have any reservations, about 5 hour

Energy, then instead, eat a bar of sugar-free

dark chocolate before the game, and take an

extra to nibble on during the game.

Always take a bottle of water to your games.

It is important to remain well-hydrated during

play.





32

The Mind Connection

Now we come to the more tricky subject of

your mental processes and game psychology.

The major complaint of most chess-players is

an inability to concentrate and to calculate

and/or remember variations.

Memory and Calculation

Memory and calculation can be handled

simply. Study and solve puzzles from the

Study Supplement you received with this

book, or from the sources mentioned in the

Supplemental Training section. A minimumof two hours a week is suggested, and more, if

you have the time. Never let more than six

days go by without a study session. (By the

way, by employing the Algorithm of Play, and

calculating every possible move in the

Primary Chains, you will notice that you can

solve any chess puzzle usually in under 2

minutes, and any combination from actual

games in under 1 minute.)

Concentration

To concentrate fully during a game, it is first

necessary to train the ability. Practice the

following as often as you can:

BE HERE NOW

This deceptively simple strategy is probably

the most effective. When you notice your

thoughts wandering astray, say to yourself

"Be here now"

and gently bring your attention back to where

you want it.

FOR EXAMPLE:

You're performing a mental activity (studying

a chess position), and your mind begins to

wander. Say mentally to yourself,

"Be here now"

you focus back on the position and maintain

your attention there as long as possible.

When it wanders again, repeat

"Be here now"

You might do this hundreds of times a week,if you're normal. But, you'll find that the

period of time between your straying thoughts

gets a little longer every few days. So be

patient and keep at it. You'll see improvement!

SPECIFIC TIME

Humans tend to do what they tell themselves

to do. Therefore, it’s easier to concentrate if

you set a specific length of time to study and

consciously tell yourself that “I willconcentrate” for that length of time.

THE DOT TRICK

On a piece of paper, draw a small, yet visible,

dot, and start staring and concentrating on the

dot for 60 seconds. Start taking deep breaths

while staring and for a short time after you

have finished staring at the dot.. You should

now find an increase in your concentration

power.



33

THE COUNT METHOD

Count backwards from 100 in various types of

segments(2, 4, 6...etc). At the end, reverse the

process and count from 1 up to 100 in various

segments.

CUPPING

You can actually cup your hands around your

own eyes. This may serve as a trigger to tell

your mind to focus on a particular

responsibility. For example, you are in a room

and you need to study but there are many

things preventing you from concentrating.

Cupping your hands around your eyes may

help your brain switch to focus mode and keepit on its track.

KNEE TO ELBOW

You can stimulate your left and right cerebral

hemispheres by touching your right elbow to

your left-knee and then doing the same for the

left-elbow/right-knee. Do this three times.

FOCUS

Before you begin studying (or beginning play

in a game of chess), take a few minutes to

summarize a few objectives (opening and plan

of play), gather what you will need, and think

of a general strategy of accomplishment

FIGURE EIGHTS

On a large piece of paper taped to the wall,

draw large sideways figure 8s (the infinity

symbol) over and over with the right hand, the

left hand, and both hands. If you don't have

paper, do the drawing motion in the air (Don’t

do this at the chessboard. People will think

you are nuts. Draw the 8's on your knee under

the table.) Start drawing really large sideways

figure 8s and continue making the figure

smaller and smaller until you are drawing

really tiny Figures. You are then ready to

begin mental activity, or any task that requires

concentration.

Anytime you feel you are losingconcentration, stop the work and do figure 8

exercise again. This exercise can also be done

with closed eyes by imagining drawing figure

8's.

This exercise helps to activate both the right

and left visual fields and hence makes the

brain more focused.

FIRST AND LAST TIME

Do something as if for first or last time:

We take a lot of everyday things for granted

and do not observe as intently as we should. In

order to develop focus and observation, try to

look at tasks which you do everyday as if you

are doing or seeing them for the first or the

last time. This will encourage you to observe

details which you may have missed before,

thus improving your observation,

concentration and also in gaining newinsights.

UNNECESSARY MOVEMENT

Avoid unnecessary movements:

Stop all useless gestures and movements of

the body. These mean that you have not

proper control over your body. After you have

acquired this control, notice how "ill-at-ease"

people are that have not gained this control.

Watch people and see how many of them

make unnecessary movements and lack poise.

Get rid of any habit you have of twitching or

jerking any part of your body. You will find

you make many involuntary movement. You



34

can quickly stop any of these by merely

centering your attention on the thought, "I will

not."

The purpose of the above exercises is to gain

control over the involuntary muscular movement, making your actions entirely

voluntary.

POISE

Watch yourself during the day and see that

your muscles do not become tense or strained.

See how easy and relaxed you can keep

yourself. See how poised you can be at all

times. Cultivate a self-poised manner, instead

of a nervous, strained appearance. This mentalfeeling will improve your carriage and

demeanor.

HOLD A THOUGHT

Select some thought (chess position) and see

how long you can hold your mind on it. It is

nice to have a clock at first and keep track of

the time.

Make it a daily habit of concentrating on thisthought for, maybe ten minutes. Practice

doing this until you can hold it to the

exclusion of everything else. You might have

to do this exercise regularly for 10 days or

more in order to sharpen your concentration

skills. The time you can hold concentration

will begin to lengthen.

EXPRESS A MOTIF

No one can think without first concentrating

his thoughts on the subject on hand. Every

man and woman should train himself to think

clearly. An excellent exercise is to read an

article in a newspaper, (or look at a chess

position) and see in how few words you can

express it. Reading an article (studying a

position) to get only the essentials requires the

closest concentration. If you are unable to

write out (or express succinctly) what you

read, you will know you are weak in

concentration. Instead of writing it out you can

express it orally if you wish. You will findexercises like this of the greatest value in

developing concentration and learning to

think.

Study parts of this book (any section) for

twenty minutes and then write down, in your

own words, what you have read. The chances

are that at first you will not remember very

many details, but with a little practice you will

be able to write a very good account of what

you have read. The closer the concentrationthe more accurate the account will be.

If time is limited to read only one axiom in the

classical and modern chess theory, or

Knowledge Base section. Write it down word

for word. When you are able to do this, read

two axioms/precepts and treat similarly. The

practice will produce very good results if you

keep it up until the habit is fixed.

BEAT THE CLOCK

Sit in a chair and place a clock with a second

hand on the table. Follow the second hand

with your eyes as it goes around. Keep this up

for five minutes, thinking of nothing else but

the second hand, This is a very good exercise

when you only have a few minutes to spare, if

you are able to keep every other thought in

the stream of consciousness subordinate to it.

As there is little that is particularly interesting

about the second hand, it is hard to do this,

but in the extra effort of will power required

to make it successful lies its value. Always try

to keep as still as possible during these

exercises.



35

TAKE IT TO THE MAX

Do a thing wholeheartedly. If you approach

something half-heartedly, it can show in the

quality of your thought processes. In order to

do things better, do them with interest.Whatever you are doing, try to find some

aspect of it that interests you. If you can find

something interesting in each thing you do,

you can enjoy even the most mundane and

boring tasks. (This is why I mention some

alternatives of play if you ever get bored of

just playing the straight Tiger or Dragon (See

Games Analysis Section)).

GAME DAY

45 minutes before the game, on an MP3 player

listen to EXTREME FOCUS. This is a 25

minute segment of music. This session

stimulates SAR in the right brain hemisphere

and Beta in the left. It is ideal to help focus the

mind before a mentally strenuous task. It is

based on the ADD research from psychologist

Michael Joyce and David Sever.

It can be obtained at:

http://www.musicmefree.com/page_single_d

ownloads.php

EXTREME FOCUS $5.00 25 Minutes MP3

During the game, on your MP3 player, play

the following music to create and maintain

concentration.

Coming Into Focus 5:25 192 kbps $0.09

03 Powers Of Concentration 4:51 $0.09

04 In The Zone 5:41 192 kbps $0.09

05 Think 5:04 192 kbps $0.09

06 Total Lucidity 5:23 192 kbps $0.09

07 Balance 5:25 192 kbps $0.09

08 The Settled Mind

These can be obtained for the price listed, at:

http://www.legalsounds.com/download-mp3

/david-bradstreet-%26-john-herberman/musi

c-to-enhance-concentration/album_87139

Legalsounds asks for a $25.00 deposit against

future purchases.

OR

if you don’t think you will ever purchase any

additional music, and don’t want to spend

$25.00, go to:

http://www.amazon.com/Music-To-Enhance

-Concentration/dp/B002HH5W9S/ref=sr_1_ 3?ie=UTF8&qid=1295245203&sr=8-3

You can buy the whole “Concentration”

album which includes two or three additional

tracks to the ones mentioned, for $9.00

Game Notation

It is recommended that you obtain either a

MonRoi electronic notation device, or a PDA

with the E-Notate electronic notation

software, that can be obtained from the North

American Chess Association.

http://www.monroi.com/

or

http://www.nachess.org/





36

WHEN YOU SIT DOWN TO PLAY A

GAME OF CHESS, DON’T FORGET TO

BRING YOUR GAME!!

Any time you sit down to play a game of

chess, you should have in mind the following psychology:

1. Play with confidence. If you have practiced

everything I preach in this book, you are by

now an awesome chess powerhouse.

2. Play to win. Worry about draws when your

opponent offers you one.

3. Have the attitude of, “I will do what I want,

no matter what you do.”

4. Be the Puppet-Master, not the puppet!

5. Meet every move by your opponent with

scepticism (or scorn if you want). Challenge

all his ideas. Responding to a fake threat is

like stopping an opponent from losing the

game.

6. If an obvious plan conforms to the position,

follow it.

7. Concentrate fully on the game. On your

move, build Chains and calculate tactics in the

Primary Chains. On his time, study the over-

all aspects of the position, and consider

various strategies.

8. Always expect your opponent to make the

strongest move possible to him, and play

accordingly.

9. Before playing a move, ask, “What

wonderful thing does this move do for my

position?”. If you can’t answer this question,

you are playing the wrong move.

10. In all cases of logic versus fear, you must

follow logic.

11. Material gain or loss is just another type of

imbalance. The total play of the position is

what matters.

12. Material inequalities cause psychological

paralysis. You will probably see quite a few

with the Tiger and Dragon. Embrace them. Let

your opponent cower in fear.

13. Fear no aspect of the game. (With this

book, you will never have to.)

14. If your opponent is in time pressure, do

not speed up your moves. Take your time andfind the best move. The best move is always

the move that sets the most problems for your

opponent to solve.

15. If you are lost, put yourself in your

opponent’s shoes, and play the move that you

would least like to see if you were him. Fight

to the bitter death, and never give up! (I

personally believe that practitioners of the

complete Tiger and Dragon Chess System

need never lose a game.)



37

CHAPTER 6:Your ELO Rating

So, just how strong can you expect to be,

playing the Tiger and Dragon Chess System?

Given the mathematics, and projected

performance based on the results of all the

analysis, if you do everything this book says to

do, you should have an estimated playing

strength of :

ELO 3511

This is provided that you do everything this book suggests you do.



38

APPENDIX A:SUPPLEMENTAL STUDY

Study the 700 puzzles in the Study

Supplement regularly. This will buildcalculating and memorization capabilities, and

improve concentration. This supplement was

selected especially because it has a large

number of self-mates. This type of puzzle

teaches you to think and calculate a

combination both forwards and backwards.

Make sure to utilize the method of calculating

every possible move that interacts with the

opposing forces (For the best methods of

calculation, refer back to “Notes on

Calculation” in the Algorithm of Play section

of the book.). Time how long it takes you to

complete each problem. The goal is to solve

all problems in well under 2 minutes.

Study every aspect of this book until you have

it down “cold”, and can site it “chapter and

verse”.

If you need additional puzzles once you have

gone through and are completely familiar withthose supplied, I recommend:

Chess: 5334 Problems, Combinations and

Games , by Laszlo Polgar

The Complete Chess Workout: Train Your

Brain with 1200 Puzzles, by Richard Palliser

All who play the Tiger and Dragon are

encouraged to submit their games to me at

[email protected]

Players are also encouraged to submit their

performance ratings from tournaments.Tournaments that qualify are those that have

sections, plus a top section that is an “Open”.

You must have played in the Open section,

against all the strongest players, to submit a

performance rating. I will also accept Tiger

and Dragon performance ratings attained in

matches against computers.

To calculate your performance rating, go to:

http://main.uschess.org/content/view/7875/4

00/

It is recommended that you study your own

games with the Tiger and Dragon intensely,

especially any games that you lose. A strong

computer chess engine will be able to help

you work through the game. Work out where

the win for you was. It should be there in one

of the possible variations given by your

computer. Above all, work out exactly whyand how you lost. Learn from any mistakes

you make.

Be sure to follow the Mind and Body section.

mailto:[email protected]




39

APPENDIX B:Logic and Math Used in

Analysis of the Tiger and

Dragon Chess System

For those that are interested, I have given here,

an entire breakdown of the logic and math that

functioned in analysis of the Tiger and Dragon

structure and games.

Term 1: SYSTEM

A system is any process that follows a

progressive path through time and/or space.

Some systems are perpetual and go on for

ever, and some systems terminate or end at a

point of completion, and then start over again.

All systems have structure.

Term 2: STRUCTURE

A structure is an over-all framework within

which a system works. The structure will

define which systems will thrive. All systems

and structures are born from an initial state.

Term 3: INITIAL STATE

The concept of the initial state comes from

the mathematics of Chaos Theory. All

attributes of the systems and structures that

follow are intensely dependent upon this

beginning state. A popular example of

dependence of systems on the initial state, is

the flapping of a butter-fly’s wings producing

an initial air current which eventually grows into a hurricane half-way across the world. From

the initial state, all systems and structures

progress through time and/or space through an

iterative and/or branching process.

TERM 4: ITERATIVE PROCESS

An iterative process is where a system

combines two or more previous attributes to

create a new attribute. The new attribute then

combines with previous attributes to form

another new attribute, and this process

continues ad infinitum, or until the system

terminates.

Term 5: BRANCHING PROCESS

In a branching process, a system propagates

by splitting from its initial state in to two or

more separate processes. These processes then

branch in to two or more new processes, and

so on ad infinitum, or until the system

terminates.

The iteration and/or branching process of any

system will always follow a pattern of growthwhich is roughly equivalent to the Golden

Ratio.

Term 6: GOLDEN RATIO

The Golden ratio stipulates that the iterative

and/or branching processes of a system will

progress through time and/or space at a

growth rate of roughly 1.618034.... . This

process can be expressed in a series of

numerical values in which each value is addedto the proceeding value, where it can be

shown that the values will converge on the

Golden Ratio, as the series progresses through

time. Popular representations of these

numerical values are Fibonacci Numbers and

Lucas Numbers. System processes can also

be expressed as a series of Fibonacci Ratios.



40

Term 7: FIBONACCI NUMBERS

Fibonacci numbers are derived by starting a

series of numerical values at 0,1,1, and then

adding successive values to previous values.

These values converge to the Golden Ratio asthey move through time. For our purposes, the

numbers we will use are:

0,1,1,2,3,5,8,13,21,34 and 55.

Term 8: LUCAS NUMBERS

Lucas numbers are derived by starting a

series of numerical values at 2,1,3 and then

adding successive values to previous values.

These values converge to the Golden Ratio asthey move through time. For our purposes, the

numbers we will use are:

2,1,3,4,7,11,18,29 and 47.

Term 9: FIBONACCI RATIOS

Fibonacci Ratios are derivatives of the

Golden Ratio, and all systems will adhere in

their growth cycles roughly to them. For our

purposes, the important ratios are:

.24 , .38, .50 and .62

Placed together, Fibonacci numbers and ratios

and Lucas numbers form the set:

{0,1,2,3,4,5,7,8,11,13,18,21,24,29,34,38,47,

50,55 and 62}

As systems progress through time and/or

space, the interaction of the Golden Ratio,

expressed as Fibonacci and Lucas numbers

and/or ratios will form specific

Action/Reaction States, and specific, self-

repeating, structures as dictated by the

mathematics of Fractal Mathematics.

Term 10: ACTION/REACTION STATES

An action/reaction state is a simple binary

process where a specific action is countered

by a specific reaction, which then becomes an

action, which is countered by a reaction, andso on ad infinitum, or until the system

terminates.

Term 11: FRACTAL MATHEMATICS

All systems have structure, and, according to

the mathematics of Fractal Geometry that

structure will continue to repeat, no matter

how large or complex the system becomes,

or for how long the system exists.

Essentially, the structure will remaininviolate unto infinity.



41

Graphical Examples of Fibonacci/Lucas

Systems Propagating Through Time and

Space.



42

Use of the Mathematics and Logic WithComputer-Aided Analysis.

First, a computer chess engine of optimal

strength, running on sufficient hardware is

required.

I used Deep Rybka 4, running on a 2.93

Gigahertz machine with a hash-table of 7,359

Megabytes, and an 8 CPU Intel i7 processor.

Next, we will examine the application of the

math. It has often been noted by computer

experts and chess-players of considerable

strength, that computer evaluations of positions have no bearing on the reality of the

position on the board, and are often erroneous.

This is true if you are looking at the numbers

generated in the evaluations as representations

of who is “better” or who is “winning or

losing”. However, one can glean very

important information from the numbers, on

the structure of the game as it unfolds. The

structure has to do with how the pieces array

themselves on the board, and, more

importantly, how those pieces will interactwith each other throughout the entirety of the

game.

By analyzing the numbers that various

structures produce, we can predict with great

certainty, the number of additional structures

that can be created, and therefore the variance

or complexity of the position on the board,

and whether or not we can control it.

Structures that produce numbers that areFibonacci/Lucas numbers indicate a very

specific (and often small) set of structures

possible. Though still complex, these

structures are subject to very little variance,

and therefore, can be accounted and planned

for by the player, to a depth reaching from the

opening to well in to the end-game.

Adoption and analysis of standard openings

(as defined in Fundamental Chess Openings

by Paul van der Sterren) produced

Fibonacci/Lucas numbers only about 70% of

the time. This leaves 30% of the possible

structures unaccounted for, and therefore

indicates great possible variance, and, of

course, an inability of any human to

adequately prepare for them.

Adoption of structures such as those found in

the Tiger and Dragon, producedFibonacci/Lucas relationships in excess of

95% of the time. Further, critical moves in the

game also displayed Fibonacci/Lucas

relationships. I.e. Critical moves occurred on

moves 1, 2, 3, 4, 5, 7, 8, 11, 13, 18, 21, 24, 29,

34, 38, 47, 50, 55 and 62.

Of note in computer evaluations, was the key

“Tipping point” of exactly 62 (+/- 0.62) centi-

pawns when the evaluation of the computer

represented a “real” estimation of who waswinning or losing the game. Numbers below

62 centi-pawns were irrelevant in estimation

of advantage. However, A series of

evaluations that exceeded 62 centi-pawns

indicated a continued series of expansion up

to and exceeding 100 (+/- 1.00) centi-pawns,

the level of evaluation in a game commonly

believed to represent a decisive advantage in

a game of chess between two evenly matched

players.



43

Error correction in the analysis was given the

following parameters:

All moves in the games, analyzed to a depth

of 21 ply. Fibonacci/Lucas math allows us to

calculate the possibility of an inferior move being played at 1 in 1000.

In order to be considered with

Fibonacci/Lucas numbers, the evaluation

given by Deep Rybka 4 had to be within +/-

one number to be considered valid.

In closing, generation of structures yielding

high Fibonacci/Lucas values indicated that the

position on the board was being played at a

peak efficiency, and conversely, that DeepRybka 4 was finding the strongest moves in

the position in both a positional and tactical

sense.

Observation of the characteristics of these

phenomena, allowed for the development of a

general Algorithm of Play, that humans could

adopt. We should not be surprised that this

algorithm jibed with the most valuable tenets

of classical and modern chess theory and

Eastern martial theory.

Additional Mathematical Methods andProofs

Once we devised the Tiger and Dragon

structures, it was possible to estimate their

inherent strength mathematically, using a

method devised by Alexander A. Shashin, a

strong russian chess player with wins over

Korchnoi and Epishin to his credit. Shashin, anuclear physicist by profession, developed the

following mathematical method for estimation

of the strengths of a chess position:

The Shashin Method

There are four factors in evaluating a chess

position:

1) Material (m). A very simple andw e l l - k n o w n c a l c u l a t i o n

9(queen)-5(rook)-3(minor piece)-1(pawn).

Divide your sum by the opponent’s sum.

Usually m=1.

2) Mobility (p). The number of legal moves in

a given position. P1 is the mobility of our

pieces, P2 is the mobility of the opponent’s

pieces. P1/ P2 = p.

3) Expansion factor. This is defined bycalculating the center of gravity of a given

position. Take the starting position. White has

8 pieces on the 1st rank, and 8 on the 2nd

rank: 8*1+8*2=24, divided by the number of

pieces, 24/16=1.5, so the center of gravity lies

between the first and second ranks.

.

4) Packing density. There are several different

types of packing density: by all pieces and

pawns; by king and pawns; by king, pawns

and knights (short-range pieces); by pawns

only; and local density at certain sections of

the board. The most informative densities are

those by short-range pieces. The denser a

position is, the safer it is.

If p(mobility) > 1.25 :

1) first we look for an open attack, 2) optimal

piece deployment, 3) sacrifice, 4) material

gains. In an open attack; we attack materialtargets according to the hierarchy: king,

queen, rook, bishop, knight, pawn, or an

empty square.



44

If p(mobility) < 0.80:

Your position is “bad” and you must defend

by retreating your forces in to a more compact

position.

If p is between 0.80 and 1.25:

No advantage in mobility exists. Therefore,

concentrate on:

1) optimal piece deployment, 2) pawn

advances, 3)exchanges

In addition to Shashin’s analysis, I believe it is

possible to estimate who is “better” in the

position, by multiplying the expansion factor by the packing density, thus giving a number

that estimates the total ability to attack and

defend from a given position.

First, let’s consider the Dragon against the

Broad Front:

rdb1kds40p0nhpgpsds0pdpddsdsdsdssdP)P)sddsHsdNdsP)sdsdP)$sGQIBdR

Material is even so this value is 1.Mobility is 31 / 33 = .939

Expansion = 4*4+2*3+4*2+1*6 = 36 versus

8*2+3*3+1*5 = 30. 16 / 36 = 2.25 and 16 / 30

= 1.875. So we wind up with 2.25 for White

and 1.875 for Black.

Density = 16 / 32 = .50 for White, and 16 / 24

= .66 for Black.

From these values we can ascertain that White

does not have sufficient mobility to claim an

advantage and attack.

Taking my formula for the estimation of total

strength of a position, we multiply theexpansion by the density, and we get:

White: 2.25 * .50 = 1.125

Black: 1.875 * .66 = 1.2375

Therefore, Black is better over-all.

Now, let’s consider the Standard Set-up

versus the Tiger:

rdb1kgs4dp0nhp0spds0pds0dsdsdsdssds)PdsddsHBGNdsP)Pds)P)

$sdQIsdR

Material is even and = 1.

Mobility = 26 / 36 = .72

Expansion = 4*2+4*3+2*6+4*1 = 36 versus

4*3+6*2+1*6 = 30. Dividing by the number

of pieces, we once again get 2.25 for White,

and 1.875 for Black.

Density = 16 / 32 for White and 16 / 24 for

Black once again.

Here we see that according to Shashin’s

formula, White has the right to attack. But the

question is, “Attack what ?” Black has no

weak points. Applying my formula for over-

all strength of position we once again get

1.125 for White and 1.2375 for Black.



45

To close, let’s compare these findings to the

Pirc defense, which is a solid and respected

defense. From the initial Pirc set-up with a

pawn on d6, knight on f6, pawn on g6 and

bishop on g7, the Pirc scores a rating of only

1.114. So, in the Pirc we see that White hasthe right to attack, and also has weaknesses to

target, such as a break in the center, or moves

like Bg5, or the formation of the Qd2/Be3

battery to play Bh6 and eliminate the strong

g7 bishop.

We see that the Tiger is stronger

mathematically and logically, since its

mathematical evaluation is higher, and White

has no points of attack.

So, if the Pirc is considered sound and

playable, the Tiger and Dragon must be as

well.



46

APPENDIX C:Knowledge Base

By playing in the form of Chains andGeometric Controls, you are assured to a high

degree of mathematical certainty, the

following:

! The tactics will always favor you.

! You will never miss a tactic.

! Length of tactical combinations will

seldom exceed 5 moves.

! Pawn structures will always be

favorable to you. I.e. If you have an

isolated pawn, you will always gain

good attacking chances, and your

isolani will always be strong. If you

have doubled pawns, you will always

have good attacking chances, and the

doubled pawns will be of the variety

that are mobile, easily dissolved, or

defend key squares in your position.Conversely, if your opponent has

isolated or doubled pawns they will

always be of a variety that present a

liability to your opponent’s position.

! Your pieces will always control the

most important squares in the game.

! The aggregate of all these pluses is

due to the fact that you are always

playing from a position that is positionally sound.

! Many times your opponent will find

himself in zug-zwang positions were

he has no really good move or options.

So the first axiom of the Knowledge Base is

to always be confident. You have reason to

be!

The Knowledge Base is organized with the

most important factors being first, and the

least important factors last.

A. If one of your calculations in the

Primary Chains wins material, and offers

the opponent no compensation either in

position or attack, 9 times out of 10, this

will be the move to play.

B. In the type of play we espouse,

imbalances of material will occur often.

Memorize the following:

Valuation of Imbalances1

Bishop vs. Knight

an unpaired bishop and knight are of equal

value Positional considerations will decide

which piece is better. Knights are better with

12 or more pawns on the board. Bishops are

better with 8 pawns or less on the board. The

bishop is a bit better than the knight when

fighting against a rook or against multiple

pawns in an end-game.

The Bishop Pair

The bishop pair has an average value of an

additional half a pawn (more when the

opponent has no minor pieces to exchange for

one of the bishops).

As analyzed by GM Larry Kaufman1



47

It is worth losing a tempo to save the bishop

pair, but it is reasonable to give up the bishop

pair if you can gain two tempi by doing so.

If you have the bishop pair, and your

opponent's single bishop is hemmed in by hisown pawns, you already have full

compensation for a pawn. In other words, if

most of your opponent's pawns are fixed on

one color and you both still have both bishops,

it is worth losing a pawn to trade a knight for

his "good" bishop.

Bishop or Knight Versus 3 Pawns

As long as there are other pieces on the board

(so minimum mating material is not a major issue), the minor piece is worth about 3¼

pawns.

Winning the Exchange

Now let's move on to discussing the Exchange

(rook for knight or unpaired bishop). My

research puts its average value squarely at 1¾

pawns

When the side down the Exchange has the bishop pair, the exchange is worth 1.15

pawns.

The value of the Exchange is influenced by

two factors. First of all, the presence of more

major pieces on the board favors the minor

piece. In general, with no major pieces traded,

the Exchange value drops to 1½ pawns, and if

the minor side has the bishop pair just one

pawn makes things even. But with queens and

a pair of rooks gone, the Exchange is worth

slightly more than its nominal value of two

pawns, or about 1½ when opposed by the

bishop pair. Also important is the number of

pawns on the board, especially when the

minor piece is the knight. With most of the

pawns on the board the Exchange is worth

less; each pawn trade helps the rook. Rooks

need open files!

If you have a rook for a knight and two pawns,

even though you are nominally a quarter pawn

behind in material, you should try very hard toexchange major pieces.

Two Minor Pieces Versus Rook and Pawns

All of the above applies with even more force

to the case of two minor pieces vs. rook and

pawns; the side with the rook should trade

major pieces, even if he is a bit behind in

material.

Rook + 2 pawns vs. a bishop pair is equal.Rook + 1 pawn vs. other minor piece pairs is

+ 1 ½ pawns.

The Queen

When not opposed by the bishop pair, the

queen is worth rook, minor piece, and 1½

pawns.

the side without the queen wants to keep the

extra rooks if possible.

Queen Versus Two Rooks

with two or more minors each, the queen

needs no pawns to equal two rooks.

Queen Versus 3 Minor Pieces

3 minor pieces versus a queen are worth a

half-pawn more than the queen, unless the 3

minors does not include the bishop pair, in

which case, things are even.



48

Piece Relationships to Pawns

Rooks gain in value with every pawn

exchange because rooks need open files to be

effective. Knights lose relative value with

each pawn exchange, as their value diminishesin open positions.

Average Scoring:

Pawn = 1

Bishop pair = + ½ pawn

Rook = 5

Bishop = 3 ¼

Knight = 3 ¼

Queen = 9 ¾

C. General Principles

C1. A spatial advantage in the opening phase

of the game is not an advantage if the

opponent has a flexible and dynamic position.

C2. Closed positions nullify an initial lead in

development.

C3. The main Precept of the Tiger and Dragon

is to Dominate every phase of the game andall areas of the board.

C4. We will dominate by creating dynamic

imbalances in the position.

C5. With the center closed, attack with pawns.

C6. In closed positions, pawns often

“point” in the direction you should attack.

C6A. Pawns on d6 and e5 for Black means

king-side attack.

C6B. Pawns on e6 and d5 means queen-side

attack.

C6C. Pawns that have been advanced should

have additional pawns advance beside them.

I.e. d5 and c5, or e5 and f5 for Black.

C6D. Flank pawn moves “compress” the

opponent in to a narrow central area of limited

activity. I.e. the moves a6 and/or h6 for Black.

C7. With the center open, attack with pieces.

C8. If cramped, one or two exchanges are

acceptable. (Analyze any exchange in relation

to the Valuation of Imbalances (B.).

C9. Attack Broken Links in the opponent’s

position, and eliminate any Broken Links in

your position (weak squares or pieces of

material or strategic importance).

C10. Squares for Knights

C10A. N on 3 rank is good for defense, andrd

can activate quickly.

C10B. N on 4 rank is equal to a bishop.th

C10C. N on 5 rank is a powerful attacker.th

Better than a bishop.

C10D. N on 6 rank is in heaven. Often better th

than a rook.

C11. Knights need outposts that they can not

be easily driven from.

C12. A knight gains value if the important

points of the position are close together.

C13. Considerations of the Bishop Pair

C13A. The bishop pair dominates both white

and black square complexes.

C13B. The bishop pair has the ability to easily

exchange a bishop to gain a favorable bishop

vs. knight or bishop vs. bishop situation.



49

C13C. The bishop pair can coordinate in an

attack on the enemy king.

C13D. The bishop pair has good chances to

draw when down the exchange.

C13E. Always seek to open the position and

exchange pawns down to 8 or less with the

bishop pair.

C13F. Bishops are strong in the support of

passed pawns.

C14. To battle against a bishop pair, build a

series of “blockades” on same-color square

complexes. This hinders the mobility of the

bishops and prevents the position from beingopened up.

C15. With bishops of opposite color, the side

that is attacking has the advantage.

C16. Defending a Position

C16A. Eliminate or adequately defend all

Broken Links in your position.

C16B. 9 times out of 10 it is better to defend by counter-attacking (actively) than by a

passive defense.

C16C. Do not open a file your opponent can

claim. (It is ok to allow an opponent to claim

a file if there is no way in to your position

from it.)

C16D. Build a “fortress”: A position in which

your opponent has no way to break through. If

the player has only a small area to defend, it

may take a very great material superiority for

your opponent to win.

C16E. Drawing Mechanisms

C16EA. Tie the opponent to the defense of a

pawn. I.e. Establish threats against a pawn that

inhibit the opponent from moving freely and

improving his position.

C16EB. Tie down the opponent with piece

threats. I.e. establish a series of recurring

threats which inhibits the opponent from

moving freely or making progress.

C16EC. Create a passed pawn. I.e. Generate a

passed pawn that the opponent must either

guard against advance or blockade, inhibiting

the opponent’s progress in the position.

C16ED. Establish an “eternal” pin. I.e. A pin

that can not be broken or escaped from, and

which impedes further progress by the

opponent.

C17. General Strategy in the End-game

According to statistics, expect to reach an end-

game in 30% of your games.

C17A. While Tiger and Dragon end-games areoften good to those who simply want to

calculate all the variations, it is also possible,

and often advisable, to think “schematically”

in the end-game. I.e. Picture in your mind a

target position you would like to reach, that

you feel would give you an advantage, then

work out a plan of moves to get you there.

C17B. Prophylactic thought is important in

end-games. Ask yourself often, “What is my

opponent’s plan here?”

C17C. Unlike the opening, owning more

space on the board is an advantage in the end-

game.





51

pawn a free road to a queening square. In

general, it is best to advance first, the pawn in

the majority that is unopposed by an

opponent’s pawn on its file.

C17S. Passed pawns can also be created bysacrificing a pawn to “break through” an

opposing wall of pawns, or by sacrificing a

minor piece for some pawns.

C17T. “Outside” passed pawns (pawns

disconnected from the main group of forces,

and far distant from the opponent’s pawns and

pieces.) Are especially dangerous.

C17U. “Protected” (Guarded by another

pawn) passed pawns are also valuable,especially in king and pawn end-games, where

they are often decisive.

C17V. “Connected” (Two pawns on adjacent

files that are un-opposed and can move

forward supporting each other) are also good.

C17W. Blockading passed pawns is often

important. The best piece for blockading is a

knight, which can reside on the square in front

of the pawn, and still attack nearby squares.

Technical End-Games

Our processes up to this point, have taken us

through the opening and middle-game, and

now we arrive at the ending.

The end-game is really a zebra of a different

stripe. As such, we must develop separatealgorithms that will help us cope.

Piece Characteristics

Pawns

Doubled, backward or isolated pawns are

almost always an inferior aspect in end-games.

Bishops and Knights

Fixed or immobile pawns are bad for a bishop,

and good for a knight.

Pawns on only one wing favors knights.

Pawns on both wings favors bishops.

Four pawns or less favors bishops. Six pawns

or more favors knights.

A bishop pair is even stronger if no rooks are

on the board.

Rooks

If pawns are on one wing only, this favors

knights and diminishes the power of rooks.

If there are pawns on both wings this favors

rooks and bishops.

If you have rooks + pieces versus Queen +

rook, keep your rooks and exchange the

pieces.

Rook + bishop is better than rook + knight.

Queen

A queen versus a rook and piece requires a

“target rich” environment for the queen to be

better. Lots of targets like weak pawns...etc.



52

King

In the end-game, the King is often an

attacking piece, generally considered worth 4

pawns.

Hierarchy of Mobilization

In general, mobilize forces in the following

order: queens, rooks, kings, bishops and

knights, pawns

Hierarchy of Piece Combinations

Rook + bishop > rook + knight

Queen + knight > queen + bishop.

Less than five pawns: Two bishops > twoknights or bishop and knight.

More than five pawns: two knights > two

bishops.

End-Game Praxis

What follows is a compilation of end-game

praxis that is considered to be sufficient to

play an entire game of chess. Get to know it

by heart. Knowledge of the praxis given,

should give you the end-game knowledgeequivalent of a strong International Master.

King and Pawn End-Games

Basic Opposition

sdsdsdsddsdsdsdsssdsdkdsds

dsdsdsdssdsdsdsddsdsIsdssdsdsdsddsdsdsds

In this position, the side to move gains the

opposition by either 1.Ke4, or 1...Ke5. You

can see that the other side cannot move

forward, and must give ground, allowing hisopponent to advance.

sdsdsdsddsdsdsdssdsdsdsddsdsisdssdsdPdsd

dsdsIsdssdsdsdsddsdsdsds

Can White win?

1...Ke6 2.Kf4 Kf6 3.e5+ Ke6 4.Ke4 Ke7

5.Kf5 Kf7 6.e6+ Ke7 7.Ke5 Ke8 8.Kd6 Kd8

9.e7+ Ke8 10.Ke6....stalemate.

Black was able to draw because he had the

opposition. I.e., Black was able to place his

king on squares that prevented White from

making progress.

Distant Opposition

If kings are on the same file, rank or diagonal,

the player on the move can gain distant

opposition by moving towards the opposing

king so that there are an odd number of

squares between them.

For kings that are on different files, ranks or

diagonals, the player with the move gains

distant opposition by moving towards the

opposing king and on to the square color that



53

is the same as the color square on which the

opposing king resides.

Sdsdsdsd

dsdsdsdssdsdsdsddsdsisdssdsdsdsddsdsIsdssdsdPdsddsdsdsds

In games of this sort, the salient factors are if

the player with the pawn can get his king in

front of his pawn, and who has the opposition.

With White to move, 1.Kf3 Kf5 2.Ke3 Ke5

3.Kd3 Kd5 draw...With Black to move,

1...Kf5 2.Kd4 Ke6 3.Ke4 Kf6 4.Kd5 Ke7

5.Ke5 Kd7 6.Kf6 Ke8 7.Ke6 Kf8 8.e4 Ke8

9.e5 Kf8 10.Kd7 Kf7 11.e6+ and White wins

If the side with the pawn can ever get his king

two squares in front of the pawn, it is always

a win.

SdsdkdsddsdsdsdssdsdKdsd

dsdsdsdssdsdPdsd

White will gain the opposition and win

Fox in the Chicken Coup

sdsdsdsddsdsdsds

sdkdsdpddsdsds)psIPdsds)dsdsdsdssdsdsdsddsdsdsds

In the diagram from the previous page, Black

must eventually take White’s c pawn, leaving

the White king free to scoop up the other

Black pawns: 1.c5 Kc7 2.Kb5 Kb7 3.c6+ Kc7

4.Kc5 Kc8 5.Kd6 Kd8 6.Ke6 Kc7 7.Kf6 Kxc6

8.Kxg6 Kd7 9.Kxh5 and wins...

Pawn Freeze

sdsdsdsddsdsdsdssisds0sd0sdsdsdsKdsdsdsddsdsdP)ssdsdsdsd

dsdsdsdsThe correct move here is 1.g4 with a draw.

However, 1.f4?? f5!! freezes White’s pawns,

and 2.Ka3 Kc5 3.Ka4 Kd4 4.Kxa5 Ke4!!

5.Kd4 Kf3 6.Kc3 Kxg3 7.Kd3 Kxf4 wins for

Black.



54

Trebuchet

dpIk)s

Whoever has the move, must leave the

defense of his pawn, and the pawn is lost.

SdsdsdsddsdsdsdssdsdsdpddsdpdsIssds)sdsdiPdsdsdssdsdsdsddsdsdsds

1.Kxg6 Kxb3 2.Kf5 Kc3 3.Ke5 Kc4, and

Black wins

Triangulation

sdsdsdsddsdsdsdssdsdkdpddsdpds)psds)s0s)

ds)sdsdssdsdsIsddsdsdsds

Triangulation is a maneuver designed to give

your opponent the move, and as a result, you

the opposition. 1.Kg2 f3+ 2.Kf2 Kf5 3.Kxf3

and wins.

Outflanking Maneuver

Outflanking is a maneuver where the stronger

side’s king moves to the side, placing a file

between the kings. This allows the outflanking

king to march forward towards the target,

without allowing the opponent’s king to step

in front and take direct opposition. From the

position, White reaches a8, b8 or c8 by force:

Sdsdsdsidsdsdsdssdsdsdsddsdsdsdssdsdsdsddsdsdsdssdsdsdsd

dsdsdsdK1.Kh2 Kg8 2.Kg2 Kf8 3.Kf2 Ke8 4.Ke2 Kd8

5.Kd2 Kc8 6.Kc2 Kb8 7.Kb2 Ka8 8.Kc3 Kb7

9.Kb3 Kc7 10.Ka4 Kb6 11.Kb4 Ka6 12.Kc5

Kb7 13.Kb5 Kc7 14.Ka6 Kb8 15.Kb6 Kc8

16.Ka7 and a8 next move. This exercise

teaches triangulation, opposition and

outflanking.



55

Minor Piece End-Games

Bishop + Rook Pawn vs. Lone King

If the bishop is on the same color as the

queening square of the rook pawn, the game is

a win. If the bishop in on the opposite color of

the rook pawn queening square, the game is

drawn, as the opponent’s king can not be

driven from the queening square.

Knight + Rook Pawn vs. Lone King

This end game is usually a win, with the

following exception:

sdsisdnddsdsdsdssdsdsdK0dsdsdsds

This position is drawn, as Black can not force

the White king from h1 or g2.

Two Bishops vs. Lone King

Place the bishops on adjacent diagonals. This

traps the opponent’s king in one sector of the

board. Continually shrink the diagonal box.

Chase the defending king in to a corner, and

then deliver mate.

Bishop of Opposite Color vs. Bishop + 2

Pawns

If the pawns are one file apart, the game is

drawn:

sdsdsdsddsdsisdssdsdPdsddsdsdsIssdBdsdPddsgsdsdssdsdsdsddsdsdsds

1.Kh6 Bb2 2.g5 Bc3 3.g6 Kf8 4.Kg5 Bb2

5.Kf5 Bc3 6.Ke4 Bb2 7.Kd5 Ke7, White

makes no headway: Draw.

In general, if the pawns are more than one file

apart, it is a win. However, the defending side

can still draw if his bishop can freeze both

pawns:



56

sdsdsdsddsdsdsdssds)sdkd

dsdsdsdssdsGKdsddsdsds)bsdsdsdsddsdsdsds

Both pawns are advancing to white squares, so

the White bishop can not help in their

advance. The Black bishop covers bothsquares the pawns can advance to,

simultaneously, and Black’s king simply

follows the White king back and forth,

stopping and progress.

It can also be a drawn game, if one of the

pawns is a rook pawn and has a queening

square of the same color as the defending

bishop.

SdsdsdsddsdkdsdssdsdsdPd)sdbdsdssdsdsdKddsGsdsdssdsdsdsddsdsdsds

1.Kg5 Kd6 2.Kh6 Kc6 3.Kh7 Kb7 4.g7 Ka8

5.g8 = Q Bxg8 6.Kxg8....draw.

If the pawns are connected, the defending side

can draw by attacking the pawns and driving

them forward, and always tying the attacking

king to the defense of a pawn.

sdsdsdsddsdsds0ssdsds0sddsdsdsdksGbdsdsddsdsdsIs

sdsdsdsddsdsdsds

1...Kg5 2.Bf8 g6 3.Be7 Kf5 4.Bd8 Ke6 5.Kf4,

and Black must advance his pawns, which

leads to positions like the diagram on the next

page.

sdsdsdsddsdsdsdssdsdsdsddsdkdsdssds0pdbddsdsdsdssdsIsGsddsdsdsds

This position is dead drawn. Any time Black

tries something fancy with his king, White just

attacks a pawn, forcing the king back.



57

Bishop of the Same Color vs. Bishop +

Pawn

A bishop, rook, or knight pawn is a win. A

queen or king pawn is a draw, if the defending

king is nearby. In the diagram, Black draws because his king and bishop cover the d7

square. White’s king must defend the pawn

and Black will never run out of tempi, since

he can shuffle his bishop back and forth.

SdsIsdsddsds)sds

sdsisdsddBdsdsdbsdsdsdsddsdsdsdssdsdsdsddsdsdsds

Rook End-Games

The Lucena Position

sdsdKdsddsds)sissdsdsdsddsdsdsds

sdsdsdsddsdsdsdssdsds$sddsdrdsds

1.Rg2+ Kh7 2.Rg4!(This is referred to as

“building the bridge”.) Rd2 3.Kf7 Rf2+ 4.Ke6

Re2+ 5.Kf6 Rf2+ 6.Ke5 Re2+ 7.Re4 and

wins.

The Lucena works for center, knight and bishop pawns. For rook pawns, the defending

king must be at least four files away.

The Philidor Position

sdsds$sddsdkds4ssdsdsdsd

dsIPdsdssdsdsdsddsdsdsdssdsdsdsddsdsdsds

1...Rg6! 2.Rf7+ Kd8 3.Ra7 Rf6 4.d6 Rf1!

Draws. White can not avoid the checks. Thekey with the Philidor is to not let the king

advance, force the pawn to advance, and there

is no shelter for the attacking king from

perpetual check.



58

Another Rook End-Game to Remember

sisdsds4dsdsdsds

s)sdsdsddKdsdsdssdsdsdRddsdsdsdssdsdsdsddsdsdsds

This Black position against a rook or knight

pawn is always drawn. Black just shuffles his

king or rook back and forth, and there is no

way White can break through.

Rook vs. Rook + Two Connected Pawns

1. Advance your pawns together. They

will defend each other and can also

provide shelter for the king.

2. Keep your king and pawns in close

contact.

3. Make sure your pawns can shield the

king from checks.

4. Push the enemy king back, making

sure the first 3 considerations are met.

5. With the defending king on the back

rank, move your rook (Which should be on the 7 rank.) A couple of files toth

the side of your pawns.

6. Place both pawns on the 6 rank.th

7. Move your king to the 7 rank.th

8. Give check with your rook, on the 8th

rank, which forces an exchange of

rooks, and now your pawns will win.

The Golden Rules of Rook End-Games:

1.Keep your rooks active!!

2. Rooks belong behind passed pawns,

whether your own, or your adversary’s.

Queen End-Games

Queen vs. Pawn on the 7 Rank th

A queen against the c,f,a or h pawns is a draw,

due to the stalemate possibilities, unless theattacker’s king just happens to be very

advantageously placed.

Sdsdsdsddsdsdsdssdsdsdsddsdsdsds

sdsdsdsddsdsds!ssdsds0sddsdsdsis

1...Kh1!! Draws, as Qxf2 is stalemate.



59

sdsdsdsdIQdsdsdssdsdsdsd

dsdsdsdssdsdsdsddsdsdsdspdsdsdsdisdsdsds

A possible exception to the rule. White wins

with 1.Kb6 Kb2 2.Kc5+ Kc2 3.Qg2+ Kb1

4.Kb4 a1 = Q 5.Kc3, and White wins due to

Qf2 mate, or loss of the queen.

A queen against the b, g,d or e pawns on the 7th

rank, is a win for the side with the queen. The

opponent’s king is forced in front of the pawn,

and the attacker can now move his king over

and win the pawn.

Fortresses

When you hold a weaker position in game, or

are down material, always be aware of the

possibility of building a fortress. A fortress is a

position that your opponent can not penetrate:

sdsdsdsddsdbisdssdsdsdsd

dsdsdrdss)s!s)sddsdsIsdssdsdsdsddsdsdsds

In this position, Black has created an

impregnable fortress. The rook and bishop

prevent the pawns from advancing, and the

attacking king can not penetrate. It is a draw.



60

About the Author

Walter T. Downs holds advanced degrees in mathematics and complex systems. He is an independent

systems analyst who has worked primarily in the aerospace industry and financial markets. He is a also a

member of the International High I.Q. Society.

He can be contacted at:

[email protected]





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