Tigre and Dragon_Chess
Transcript of Tigre and Dragon_Chess
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TIGER AND
DRAGON
A COMPLETE CHESS SYSTEM
WALTER THOMAS DOWNS
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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.
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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
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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.
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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
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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.
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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
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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.”
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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.
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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.
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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
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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.
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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.
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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?
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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.
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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.
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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
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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
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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
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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
$sGQIBdRConsidering the Primary Chains of Black, we
see that he is going to apply pressure to the
a1-h8 and h1-a8 diagonals. Therefore, the
move that has the greatest offensive and
defensive value is clearly g3, as we will soon
develop our bishop to contest the diagonal,
and may then castle. We build the Chain
g3/f2/Ke1.
7. g3 Bb7 8. e4 Bg7 9. Bg2 O-O 10. O-O c5
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rds1s4kd0bdnhpgps0s0pdpd
ds0sdsdssdsdPdsd)sdPds)Ps)PHN)Bd$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$sGQdRIs
Black is re-deploying his pieces, and intends
Nd4. It is best for us to also re-deploy and
defend against this possibility, with Ne2.
13. Ne2 d5
The move, e5 has the best offensive/defensive
value, blocking out the diagonals of Black's
dark-squared bishop, and building the Chain
g3/f4/e5.
14. e5 Qd7
It is logical to continue king-side expansionhere, with g4, building the Chains h3/g4 and
g4/Ne2/Qd1.
15. g4 a5
The move Nf3 fills the geometric center of our
Primary Chain, creating the solid Chain
Qd1/Ne2/Nf3/g4 and the Chains Rf1/Nf3/f4
and Bg2/Nf3.
16. Nf3 d4
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Ng3 develops a knight to the third rank and
further compresses the geometric square of
h1-h4-f4-f1. Note that we have 8 pieces on 12
squares here, forming a "nuclear"
configuration. Our original defensive square
in this area of the board has now morphed into a quite ominous attacking configuration. It
is clear that our attack is going to come first,
before Black can establish any kind of
counter-play. Notice the typical Tiger attribute
that Black is suffering from zug-zwang. He
has no really good moves, but must play
something. With Ng3, we also build the Chain
Ng3/f4/e5.
17. Ng3 Nd5
rdsds4kddbdqdpgps0ndpdpd0s0n)sdssds0s)Pd)sdPdNHP
s)PdsdBd$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$RIs
White has achieved a total domination of board. Black will now try some exchanges,
but it doesn't help.
30. h4 Nd8 31. Bxb7 Nxb7 32. Qg2 Nd8
33. f5
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sdshr4kddsgqdsdpsdsdpdpd
0s0sdPdsP0N0sdP)dPdPdsdssdPGsdQddsds$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)$sdQdRIs
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White plays a threatening move, yet here we
follow Algorithm of Play Golden Rule #2 and
play Nb6, expanding on the queen-side. It is
the promise of the Tiger, that we will always
have adequate tactical resources. Now,
11.fxg5 hxg5 would accelerate our king-sideattacking chances, and is clearly bad. The
aggressive 11.f5?! is no problem, as evidenced
by the following line:
11. f5?! exf5 12. exf5 Nh4 13. Bg4 O-O 14.
g3 Qe7 15. Qc1 Re8 16. f6 Qxe3+ 17. Qxe3
Rxe3 18. Bxc8 Rxc8 19. gxh4 Bf8 20. hxg5
hxg5 21. Rf5 Bh6 When Black has a better
pawn structure and more active pieces, and is
therefore better in this end-game.
10...Nb6 11. Kh1 Nc4 12. Bg1 O-O 13. Qc1
Here, Black continues to expand on the
queen-side with b5. However there are always
plenty of viable options with the Tiger.
Another plan might be 13...f5 14.exf5 exf5
15.b3 Nb6 16.Bh5 Kh7 18.Bf2 g4 19.h3
gxh3....etc.
13...b5 14. a4 Bb7 15. b3
rds1s4kddb0sdpgspds0pdn0dpdsds0sPdn)P)sddPHNdsds
sdPdBdP)$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)$sdsdRdK
Always be sure to calculate all moves possible
in relation to the Primary Chains, especially
where they intersect with the enemy. Wequickly find the very interesting g4!?
21...g4!? 22. Bxg4 Ba6! 23. Rxa6 (23.Nc3
Nxd4 when Black is better.)
23...Rxa6 24. Qd2 Qe7 25. Re1 Rfa8
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rdsdsdkdds0s1pgsrdn0pdnd
dNdsdsdssds)sdBddPdNdsdssdP!sGP)dsds$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.
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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
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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
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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.
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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.
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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.)
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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.
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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.
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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
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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.
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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.
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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/
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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.)
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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.
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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
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.
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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.
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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.
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Graphical Examples of Fibonacci/Lucas
Systems Propagating Through Time and
Space.
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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:
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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.
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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.
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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.
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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.
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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:
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