TIGER AND

DRAGON

A COMPLETE CHESS SYSTEM

WALTER THOMAS DOWNS

Copyright©2011 by Walter Thomas Downs

The author gives the reader of this book permission todistribute the book freely, provided that none of thecontents of this book is changed.

TABLE OF CONTENTS

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

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

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

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

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

CHAPTER 4: Opening Repertoire and Game Analysis: 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 in Analysis of the Tiger and Dragon Chess System..............39

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

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

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

4

FOREWORD

In late 2010, I was surfing the Web, searchingfor some chess-related information, and Ihappened to come upon Gary Danelishin’ssite: The Final Theory of Chess

Gary’s project was an attempt to beginquantifying and codifying chess variationsusing computers, with the twin goals ofproducing interesting opening repertoires forchess players, and attempting to answer someage-old questions about the game, such aswho should win a game of chess given“perfect” play? Should White or Black win, oris it a draw?

Gary published a book with the same name ashis web-site, and has also produced a wiki-sitethat gives much of his analysis of chessopenings and variations he feels are relevantto his project.

After examining his web-site and wiki, andpurchasing and studying his book, my interestin this project was piqued.

I contacted Gary, because I was interested inmaking some contributions to the wiki, andbecame even more enthralled with the projectafter several e-mails had been exchanged.

I found Gary to be extremely knowledgeableabout chess, especially where computers wereinvolved, and an intelligent, and truly humbleperson.

In my research and analysis that followed, Ibegan to formulate some questions aboutchess of my own, and a plan of attack began toform in my mind about how to approach theproject.

Gary’s approach was a “brute-force”computational method, where he usedcomputers to crunch through all of therelevant openings and variations, in an effortto build a body of chess knowledge based oncomputer analyses which could be continuallyadded to ad-infinitum.

Still, I realized that this method wouldprobably take several hundred human life-spans before we would have any resolution tothe questions the project was designed toanswer.

There is an old Chinese saying:

“When the student is truly ready, the teacherwill appear.”

In the beginning Gary was my teacher duringmy assimilation of information found in theproject, but now it was my turn to introduceconcepts that had not previously beenconsidered, and which I believed would yieldthe prospect of answering the questions theproject asked, in our life-time.

I strongly recommend that all readers of thisbook visit Gary Danelishin’s web-site at:

http://finaltheoryofchess.com/

I also suggest that you buy Gary’s book, TheFinal Theory of Chess.

Anyone who loves chess will find the bookand web-site very interesting and informative.

5

INTRODUCTION

What constitutes a perfect game of chess?

To my mind, chess perfection would come ina 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 thatcontrols the structure of the game frombeginning to end. To accomplish this, themoves must consist of maneuvers that buildtowards an attack on my opponent’s position,and also provide prophylaxis, or preventivemeasures that preclude the opponent fromdoing the same to me.

Therefore, my opening must be comprised notonly of straight-forward attack, but of theability to accept any attack my opponentgenerated, and turn it back against him.

The next question that comes to mind is:

What would constitute an optimal chesssystem?

The answer to this would be, a system thatcould be played either as White or Black, thatcould be playable against all possible plans theopponent might generate, and which met thestructure and move characteristics assumedwhen we answered the question of whatperfect chess must be.

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

How will we be able to judge that thesystem we devise is indeed an optimalapproach?

First, we will observe Modern Chess Strategy,and Eastern Martial Theory to make sure weare in accordance with what they consider tobe Optimal Strategy.

Then, Using my background in advancedmathematics, and using a top-flight chessengine, we can follow the structure of thegame in very concrete mathematical terms,and this will allow us to draw very objectiveconclusions about the structures that arecreated, and what they mean.

Melding these approaches in to a cohesivewhole, we will then derive an Algorithm ofPlay, that will allow us to play optimal movesthroughout the entire course of a game.

We will use these methods to generate a seriesof games that should provide us with deepinsight and a complete conceptual analysisfrom the opening move of a game, to the pointat which the game is determined as won, lostor drawn.

But we won’t stop there. We will also addressthe mind and body relationship a player mustattain and maintain to play the best chess hepossibly can. After all, he is part of the systemtoo!

So, read on....

Walter T. DownsJanuary, 2011

6

CHAPTER 1:The Theory of Chess

By this time, the theory of chess is welladvanced, yet it seems that no one has reallytaken the time to codify all of the theory inexistence in to an over-all approach that iscohesive.

Let us start at the dawn of modern theory, andreview all of the relevant axioms so that whenI apply them later on, you will understandwhere I am coming from.

First, we consider the thoughts of WilhelmSteintitz, Emanuel Lasker and SiegbertTarrasch in what I term to be the “classical”era of chess. Note that I do not include AronNimzowitsch in this group. This is becauseNimzowitsch’s concepts were so far advancedfor his time, that I really had to include themin the axioms of modern chess theory.

We will cover none of Tarrasch’s work, as theauthor shares the opinion of Lasker in hisbelief that Tarrasch was too dogmatic in hisapproach to the game.

We will deal with the axioms of theory inchronological order of the years in which theyfirst appeared.

The Axioms of Steinitz

1. A plan must have a reason.

This concept was a novelty in the time ofSteinitz. In his era, the plan in any game ofchess was simple: Attack, attack and attacksome more. Participants were honor bound toaccept gambits, and such theories asprevention of the opponent’s plans were in thefuture. Steinitz opined that one should only

attack if one was justified by the position, orin other words, if one had a concrete andviable reason to believe an attack wouldsucceed.

2. The basis of a successful plan is always avaluation of advantages and disadvantages.

Plans of attack should logically only succeedif one held some type of advantage in theposition on the board.

3. Valuations of advantage or disadvantageshould stem from the body of chessknowledge.

Factors such as advantages or disadvantagesin material, time and space are all relevant.

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

Building on the previous axioms, it is simplelogic that one must build carefully from theopening moves in to a position where areasonable advantage has been achieved, andone now has the right to attack.

5. The way to a strong advantage isthrough efficiently placed (optimal) pieces,and the accumulation of many small,seemingly insignificant, advantages.

Steinitz felt that small advantages such asmore actively placed pieces and/or a betterpawn structure, would tell in the end. Fromsuch positions of advantage, combinationswould grow like flowers on the vine.

7

6. Economy of Defense is important.

One should play all moves necessary to thedefense of one’s position, but never more. Theminimal number of moves to establishadequate defense is all that is required. Nomore, no less.

7. The natural end of all balanced positionsare more balanced positions, from which itis not possible for either side to win.Therefore, seek imbalances in the positionon the board, and seek balance in theposition in the form of compensation instructure or material

Imbalances in structure of the opposing sides,or material imbalances such as rook + piece +pawn versus queen, or rook + pawns versus apair of minor pieces, as a few examples, aredesirable, and should be actively sought whentheir creation is of advantage to the player.

8. Don’t be afraid to make strange orprovocative moves.

As long as a move meets the dictates of ouraxioms, in that it brings a piece to an efficient(optimal) square, performs a necessaryfunction of defense, or serves to provoke theopponent in to a rash and/or precipitous act, itis permissible.

9. Think of your and your opponent’sposition as a chain of interlocking andcomplex links.

Steinitz felt that one could then discern whatmoves to play based on the strength orweaknesses of the various links (squares orpieces). (Author’s Note: Lasker felt thisdevice too simplistic, but I disagree. - WTD)

The Axioms of Lasker

1. Pieces must co-operate.

“The result of co-operation, in attackingpositions is to strengthen each element of thegroup; in positions of defense, to protect eachother; in positions of balance, to complementeach other” – Emanuel Lasker

2. The less distance between pieces, thestronger and more cohesive is the whole ofthe position.

“A defect in co-operation is often indicated bygreat distance between the points [that]pieces occupy.....considering the simplegeometry of the chess-board and the laws ofmotion of the pieces, distance is afirst...measure of the degree [to which piecesco-operate.]”

– Emanuel Lasker

3. One must combine both the exploitationand defense of weaknesses.

Whereas Steinitz and Tarrasch concentratedmainly on the exploitation of weaknesses,Lasker espoused the defense of weaknesses asan integral part of the game.

4. Memorization of vast numbers ofopening variations is folly.

“[Lasker] did not believe in memorizing...fashionable variations [that] would soon beout of fashion...In opening theory, the onlycertainty is change, flux and capricious taste.Most players prefer to have their choice ofopenings derived from dogmatic authority.”

– Fred Reinfeld

8

5. Every game of chess is unique.

“[Lasker feels that each position] ...has somehidden aspect [that] the sceptic; the man ofresource, will unearth.”

– Fred Reinfeld

6. Avoid Dogma

“Of my fifty-seven years, I have applied atleast thirty to forgetting most of what I hadlearned or read, and since I have succeeded inthis I have acquired a certain ease and cheerwhich I should never again like to bewithout.”

– Emanuel Lasker

7. The value of a victory often lies in itsaesthetics.

“When mind overcomes matter, we arecharmed.

In chess, the brutal force is composed of thenumber, strength and mobility of the pieces,and the difficulty of the task set. If this brutalforce is bested by the few in number, the slightin strength, in moves which [seem weak],...bythe power of the spirit, by an idea which,seemingly absurd, is truth itself, we aredelighted.”

– Emanuel Lasker

8. At its core, chess is a matter ofmathematics.

In contrasting Tarrasch, who was admittedlypoor at mathematics, to Lasker, Fred Reinfeldwrites:

“A chess master who lacks a gift formathematics may very well be deficient in

specific chess qualities as well. Mathematicsrequires imagination and exactitude.Tarrasch was able to conceive great plans,but he was inclined to be [poor] inexecution....To overcome the relatively weakresistance of lesser players was not aninsoluble task for Tarrasch, [but] to beatdown the resistance of Lasker was...too muchfor him.”

Now, we will move on to modern chesstheory. We will draw on the guiding lights ofIsaac Lipnitsky, John Watson, Mihai Suba,R.N. Coles and Hans Berliner. Theories, alaNimzowitsch, are mirrored in the commentsof Watson and Lipnitsky.

Axioms of Modern Chess Theory

1. Flanking pawn moves are acceptable inthe opening, nor is the number of pawnsmoved in the opening relegated to one ortwo.

Concerning our pawn moves in the opening,in the books, Questions of Modern ChessTheory, and Secrets of Modern ChessStrategy, Isaac Lipnitsky and John Watsonwrite:

“There is no doubt that flank attacks as ameans of fighting for the center have a greatfuture.”

“Whether in closed, semi-open or openpositions, flank pawn moves are regularlyemployed for a variety of reasons, e.g., theestablishment of space, [or the]discouragement of castling by the opponent....the number of pawn moves in the openingcan range from one to eight or more,depending on the requirements of theposition.”

9

2. Static strategical aims should be basedsolely on the position currently on theboard.

Concerning our static strategical aims, basedon a purely pragmatic point of view, Lipnitskywrites:

“The basis for a game of chess is a purposefulplan which, beginning in the opening, isconsistently developed in the middlegame. Ahighly characteristic feature of modernopening play is that from the very start of thegame, the players will try to predetermine thechannels in which the middlegame fight willbe conducted. “

“In the opening, you have to contend not somuch with your opponent’s individual movesas with his ideas and plans....The masking ofyour own plans, which demands flexibility inyour play, is also a very significant factor.”

These statements are the essence of modernchess prophylaxis, which Watson says,consists of

“...prevention of the opponent’s plans ingeneral, and protection of key points in ourposition.”

3. Dynamic strategical aims are based noton aesthetic placement of pieces, but on thetotal latent or potential activity of all piecesand pawns.

Concerning our dynamic strategical aims, inhis book, Dynamic Chess Strategy, MihaiSuba writes:

“As a chess player my feelings were thatdynamism was something else, not just atemporary superiority, either numerical orqualitative. Strange combinations sometimescome right out of the blue. Dynamism should

should show itself not as a momentary‘firework display’, but also as the latent orpotential 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 whereobjectives were small but clear-cut from theoutset... preferred to build up a position full ofdynamic energy - ‘malignant’ energy,Tartakower called it - which could be releasedat will at a suitable target and at a suitablemoment. In the early part of the game, duringwhich this energy was created andaccumulated, Breyer often made moves thatwere in direct conflict with the tenets of theclassical style but which were found later tofit perfectly in to his scheme of play, when thepent up energy was finally released. His veryodd opening moves are none-the-less inkeeping with his dynamic play, for thoughcontrary to Tarrasch’s teaching, he gives upboth time and space, his game therebyacquires a certain extra hidden energy.”

Turning to a more purely quantitative view ofour strategy, I refer to Hans Berliner’s book,The System, in which he puts forth severalalgorithmic formulae for determining validityof a dynamic chess strategy.

The most important consideration is to controlthe entire chessboard. Towards this end,Berliner gives the following elements:

1. Pieces placed on optimal squares and in thefewest number of moves.

2. Play moves that leave open the greatestnumber of attractive options available to otherpieces. The piece to be moved ought to haveno more than one attractive option at itsdisposal given the current position.

10

Berliner states that the strategy can beconsidered successful if we are better in:

1.Optimal Pieces.2. Piece Co-operation3. More fixed targets4. Good defensive qualities5. Control of more squares.

11

CHAPTER 2:Eastern Martial Theory

Although it has never been applied to chessbefore, the author believes that an overview ofEastern martial arts is also of benefit to thechess player.

According to Shaolin Martial Arts, the Tigervs. the Dragon is the symbol of the lineovercoming the circle and vice versa. Thetiger fights in a straightforward attackbulldozing it's opponent. The dragon fightsusing circular flexible attacks. They arecertainly worthy opponents.

Both the tiger and dragon are old Buddhistsymbols. They have come to be known asopposite symbols - one reflecting a 'hard' style(attacking and unrelenting) form of martialarts, this is symbolized by the Tiger.Conversely, the 'soft' style is represented bythe Dragon and is a form that embodies adefensive and more fluid 'circular-attack'.Thus, these symbols have come to beinterpreted to represent (in the same wayYin/Yang represent) duality and balanceattained through the balance of opposingforces, etc., and are often used as symbols ofthis philosophy which is found in manyEastern cultures and practices. Many systemsof study recognize a need for both 'hard' and'soft' styles, therefore, many systems requiretraining in both 'styles' in order to offer thestudent a balanced base of training andexperience. The Tiger and the Dragonrepresent 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 ofthe player. Given the thousands of years ofexperience gleaned in the Eastern martial arts,it would seem to be beneficial to create stronganalogies in our play over the chessboard.

Therefore, the optimal or most efficient modeof play is a style which is both “hard” and“soft”; offensive and defensive. A soliddefense that is also capable of swift attack.

No doubt, you have heard of the great Chinesemilitary strategist, Sun Tzu. Here is what hehas to say:

“A General may defeat an adversary byattacking when the adversary does not havean adequate defense prepared, or byencouraging his adversary to launch animproperly prepared attack against hisprepared defenses.” (Paraphrased)

“In battle, there are...two methods of attack -The direct and the indirect; yet these two incombination, give rise to an endless series ofmaneuvers...That General is skillful in attackwhose opponent does not know what todefend; and he is skillful in defense whoseopponent does not know what to attack.”

- Sun Tzu The Art of War

12

CHAPTER 3:Algorithm of Play

Now I will propose an algorithm of play thatis based on the axioms of classical/modernchess theory and Eastern martial theory.

The algorithm of play gives you an entire planand framework on which to base your movesin a game of chess, from the opening, to theend of the game.

Golden Rule #1

Moves that perform both an offensive anddefensive function are highly desirable.

Golden Rule #2

Control over the entire board, andtherefore of the entire position, is highlydesirable.

Silver Rule #1

Pieces must be developed and arranged inthe form of Chains and Geometric Control.

A Chain is defined either as a series ofconnected squares on which pawns or piecesreside, or a rank, file or horizontal group ofsquares on which a group of pieces line-up.

Geometric Control is defined as a group ofsquares controlled by the Chains. Theseconstellations 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 currentlyinter-acting or connected with the Chains ofyour adversary are termed Primary Chains.

Pieces or squares in your own or youradversary’s position that are either not welldefended, or in many cases, are devoid of anydefense at all, are termed Broken Links.

rdb1kgs4dpdnhp0spds0pds0ds0sdsdssds)PdsddsHsGNdsP)Pds)P)$sdQIBdR

In this position, Black has the inter-connectedsquare/piece Chains, Ra8/a6, Bc8/b7/a6,Bc8/Nd7/e6, Qd8/Nd7/d6, Bf8/Ne7/d6/c5,Bf8/g7/h6 and Rh8/h6. Of Geometricimportance, is the compact geometricalformation 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 andsafe formation. The Primary Chain would bethe Bf8/Ne7/d6/c5 Chain, since the terminusof the Chain at c5 interacts with the Whitepawn on d4. The pawn on d6 could be termeda Broken Link, since the pawn and the squareis momentarily not defended by anything.

Before Black had played c5, here, and with thepawn still on c7, Black could have consideredany logical move that interacted with theWhite position, such as f5, e5, d5 or c5.

13

Silver Rule #2

Moves are made by simply calculatingevery move possible to you in the PrimaryChains and specifically in relation toBroken Links. If there are no critical movesin the Primary Chains (Moves thatengender Golden Rules 1 or 2, or winmaterial out-right.), other moves may beconsidered. Selection of the best move inthe position is governed by the KnowledgeBase (APPENDIX C).

Notes on Calculation:

Remember that you will calculate everypossible move that interacts with youropponent’s pieces. Calculate possiblecaptures and any moves that give checkfirst, followed by any move that challengesor attacks an enemy piece next.

In general, you should have to calculate nosingle move deeper than 5 moves in thefuture, and often you will be able todispense with many of the possible moveswith just 1 or 2 moves of calculation.

If none of these moves seems particularlystrong, you may consider moves that can bemade on strictly strategical principles asoutlined in the Knowledge Base and theAlgorithm of Play’s Golden and Silverrules.

With practice, you should be able tocomplete this process in well under 2minutes, which is the average time permove given you in most tournament games.

Learn the Knowledge Base cold, and followthe Golden and Silver Rules, and you willnever be without a plan or a good move!

This approach is a powerful method of playbecause it assures that you will always beafforded optimal tactical and positionalcapabilities. I.e. you will always have moretactical opportunities and resources than youropponent, and you should never be worsepositionally.

Detailed examples and use of the Algorithmof Play will be presented in the next chapter.

14

CHAPTER 4:Opening Repertoire and Game Analysis: Tiger and Dragon

Now, it is time to draw together ModernChess Theory, Eastern Martial Theory, theAlgorithm of Play and the Knowledge Base into a cohesive whole in order to form aneffective repertoire for both White and Black.

We will observe the operation of our theoriesand structures through the eyes of DeepRybka 4 us ing a mathemat icalFibonacci/Lucas/Fractal paradigm to confirmthe structures and make highly accurateestimates of future results based on theconcrete math.

Bringing together all of the above, I havedetermined that we should aim for two mainpossible structures.

0sdp0sdps0phn0pd4sgqibdr

DOWNS TIGER

dpdp0sdspgphn0p04sdqibdr

UJTELKY DRAGON

The first structure I call the Downs Tiger. Thesecond, I call the Ujtelky Dragon, in honor ofMaximilian Ujtelky an innovative Russianplayer who experimented with a similarset-up.

We see that these two structures have adoptedopening moves that are primary to bothoffensive and defensive tasks. We also seedevelopment using the Chain method, inwhich pieces are initially grouped tightlytogether. In reviewing our chess axioms andAlgorithm of Play, we see that the structuresmeet the requirements of both classical andmodern schools of thought and seek attributesof both the Tiger and Dragon schools ofmartial systems.

There are, however some questions that I amsure spring to mind, and that need to beaddressed:

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 h6weaken our pawn structure?

Are there any statistics in chess databases onthese positions?

What does Deep Rybka 4 think of thesepositions?

15

ANSWERS:

We have adjusted our development to gaintotal control of Black’s fourth rank, ratherthan attempting to play a pawn to the fifthrank, as is the common practice. We see thatwe can quickly strike all along our front in theTiger with b5,c5,d5,e5,f5 or g5. We see thatthe knights will be able to shift quickly toeither the king-side or queen-side with Nc6and Nb6 or Ng6 and Nf6. In the Dragon, wecan strike with d5 or f5.We have alreadyattained a highly flexible and dangerous set-upcapable of exploding on any front. There isnothing passive about these positions. We seefurther, that by dominating the third rank, wedefend all major points of ingress in to ourposition.

Regarding the bishops in the Tiger, it iscommonly known in theory that in positionslike this, the bishops are actually well placedon their home squares. They can bedeveloped, later on, to classical squares suchas c5, b4, f5, g4, e7, d7, e6, d6 or can bedeveloped earlier to b7 and/or g7.

In the Tiger the moves a6 and h6 serve to takethe aggressive squares of b5 and g5 away fromthe opponent, we threaten g5 and b5ourselves, along with possible majorexpansions in the form of pawn "phalanxes"on g5 and f5 or b5 and c5. Further, the movesare provocative in nature. I.e. if the opponentrashly tries to attack with a pawn thrust of g4or b4, we would be able to see the attemptfrom a mile away, and would have plenty oftime to react and counter, in which case ouropponent would find that he hasover-extended his position. It is also ofinterest to note that these positions are socentrally solid that Black may never have tocastle, which often gains several tempi atsome point.

Of the Tiger, there is little in the databases.Only a correspondence player, Dieter Luebke,experimented with a similar idea. He scored86% with it. There are a few games in theover-the-board bases, and Black apparentlydid poorly. However on closer examination,Black lost in games where he playedpassively. When Black played actively, hewon almost every game. Of the Dragon, theinitial position scored 50% in games withplayers over 2200, and 61% in games withplayers over 2300, mainly against English andd4 systems, where White had played c4(Ujtelky scored 60% with it.)

Of Deep Rybka 4, allow me to presage theanalysis games with the mathematicalstatistics produced by them, and what thosestatistics mean(For general information on thelogic, math and terms used, see APPENDIXB). In the games, using various set-ups, Whitegained a maximum evaluation of + 55centi-pawns (+ 0.55). No doubt thisevaluation was due to Rybka's over-estimationof having more space. Yet, at no time duringthe games, could the evaluation expand pastthe key 62 centi-pawn level, which wouldindicate a possible real advantage. In point offact, in every case (except for our gameswhere White played the Tiger himself) Theevaluation eroded quickly, and Black had soonaccumulated advantages surpassing the 62centi-pawn level, indicating that victorywas at hand.

16

Throughout the games analyzed, Deep Rybka4's evaluations moved smoothly from oneFibonacci/Lucas number to the next.Fibonacci/Lucas numbers were generatedbetter than 95% of the time during the games.Contrast this to "normal" openings such as theSicilian or Ruy Lopez, where analysis yieldedFibonacci/Lucas numbers no more than 70%of the time. Further, moves of importance inthe games generated conformed to the movesequence 1, 2, 3, 4, 5, 7, 8, 13, 18, 21, 24, 29,34....etc.

What does this mean? It means that instandard openings (those openings given inFundamental Chess Openings, by Paul vander Sterren), there can exist great variance inthe structures produced, thus it would beimpossible for any human to adequatelyprepare against all of the structures possible.And of course, possible predictions of futureresults would hold no water. In our structures,the numbers generated indicated that therewere only about four possible structures thatcould be adopted in the positions generated.The mathematical analysis indicated thatattempts by your opponent to deviate from thethese basic structures, leaves him in a statewhich can only hasten his demise. I.e. Theelements of the position which were negativesfor your opponent were accelerated. Also,using the Algorithm of Play, and Playing theTiger and Dragon assures you that, to a highdegree of mathematical certainty, you willconsistently enjoy greater tacticalopportunities and more positional trumps.Analysis indicates this factor to be a minimumof 3 to 1 in your favor at all times. I.e. Youwill be able to generate three tactics for everyone tactic your opponent can generate, andyou will have at least three positive positionalelements or factors for every one youropponent has. The end result is that we canprepare deeply for our games, often from theopening to well in to the end-game, and in our

games, we will always enjoy the inherentadvantages mentioned. Further, the fact thatthe Tiger and Dragon won these gamesimplies that when faced with standardresponses 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 isbecause Fractal mathematics tells us that theseself-similar structures will repeat unto infinity,and will consistently produce the same results

. In addition to the Rybka/Fibonacci/Lucasanalysis, we can also consider themathematical analysis provided by theShashin method (APPENDIX B). In analysisof the initial positions in the games, we findthat, combining over-all defensive andoffensive attributes, we find that the Tiger andDragon have the scores, 1.237 versus 1.125for White, indicating that, mathematically wehold an over-all advantage in these positions.

And of course, since the structures can beplayed as either White or Black, we have acomplete chess repertoire.

Don't be worried by the fact that most of thesegames ended in fairly long end-games. This isbecause Rybka was able to offer the stiffesttactical resistance possible. Statistically, up to70% of your games will end long before theend-game. Simply play for Chains andGeometric square control, and be sure tocalculate all moves in the Primary Chains, andseven times out of ten, by never missing atactic, you will have tactical shots that win thegame on the spot.

Note also, that at times the computer playedsuperfluous or seemingly redundant moves.These moves were included in order toexamine all the possible options in thestructures.

17

We begin our analysis of games with thestructure playing itself first, and then playingagainst another popular set-up, theHippopotamus. We consider only the Tiger, asthis is our main weapon, with the UjtelkyDragon used only on those occasions whenour opponent plays an early f4. This will giveus basic and valuable information as to whatmoves constitute good attacking and defensivemoves when we face the more standardresponses in later games. Use a real chess-set,and play through the games move by move, asyou read the commentary. You should alsohave a pen and paper handy, as well as aprintout of the Algorithm of Play andKnowledge Base, to refer to.

Tiger vs. Tiger

1. e3 e6 2. Ne2 Ne7 3. d3 d6 4. Nd2 Nd7 5. a3a6 6. h3 h6

Now White makes the first thrust. He choosesb4, building the Chain b4/a3, and planning themove Bb2, which builds the Chain Bb2/Ra1and controls the chain of squares on the a1-h8diagonal.

7. b4 b6

rdb1kgs4ds0nhp0sp0s0pds0dsdsdsdss)sdsdsd)sdP)sdPsdPHN)Pd$sGQIBdR

Black responds by building the Chainb6/c7/Qd8

8. Bb2 c5

rdb1kgs4dsdnhp0sp0s0pds0ds0sdsdss)sdsdsd)sdP)sdPsGPHN)Pd$sdQIBdR

Black responds to Bb2 by striking at the headof the White Primary Chain on b4,establishing the Chains c5/b6 andc5/d6/Ne7/Bf8. He also controls a geometrictriangle on the squares f8-c5-a7.

9.Ng3 Bb7

rds1kgs4dbdnhp0sp0s0pds0ds0sdsdss)sdsdsd)sdP)sHPsGPHs)Pd$sdQIBdR

18

b4 is adequately defended, so following theprecepts of the Algorithm of Play(GoldenRule #1), White plays the move that has thegreatest offensive and defensive qualities,Ng3, adding a defender/aggressor to theking-side, freeing the bishop on f1 andestablishing the Chains Ke1/f2/Ng3 andNg3/g2. Black responds with Bb7, whichseeks to control the h1-a8 chain of squares,builds the Chain Bb7/Ra8 and Ne7/Nd7/Bb7and allows a future Rc8. Also, developing aknight to the third rank is in accordance withKnowledge Base C10A.

10. c4 Ng8

rds1kgn4dbdndp0sp0s0pds0ds0sdsdss)Pdsdsd)sdP)sHPsGsHs)Pd$sdQIBdR

White now expands the control of his PrimaryChain with the move c4, which builds theChain c4/e3/Bf1, establishes a geometrictriangle on the points f1-c4-b4-a3, and a pawnphalanx on c4 and b4. Black employs theoptimal offensive/defensive move by planningto re-deploy a knight to f6, blocking the strongb2 bishop, developing the knight to a moreaggressive square (3rd rank knight, seeKnowledge Base C10A.) and preparing Be7and 0-0. His move builds the ChainsRh8/Ng8/Bf8/Ke8/Qd8 and Ng8/f7/e6. Notethat both sides are attempting to build solid

areas of dominance encompassing the breadthof the entire board. (See Knowledge Base C3and 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 hisPrimary Chain, and sees that Qb3 "x-rays" theBroken Link in Black's position: The bishopon b7 (undefended piece) and eliminates hisBroken Link, the lone Bb2. He also creates theChain Bb2/Qb3/b4 and further solidifies theconnective links of the squares, pieces andpawns on the white 3rd rank. Black sees noimmediate threat, and so continues with hisoriginal plan, creating the Chains Nf6/Qd8and Nf6/g7/Rh8, and building a very solidgeometric square on the points f8-f6-d6-d8.Note that in this square, there are 8 pieces on9 squares, a type of position which I describeas "nuclear" in that it is capable of unleashingtremendous force in to the position when itunwinds.

12. e4! Be7

19

rds1kds4dbdngp0sp0s0phs0ds0sdsdss)PdPdsd)QdPdsHPsGsHs)Pd$sdsIBdR

White looks at the relationship of his PrimaryChains to Black's Primary, and quicklycalculates that e4 offers the best in aggressionand defense, as it expands his Primary Chainand also anticipates a possible d5 by Black.He builds the Chains d3/e4 and e4/c4/b4.Black answers by solidifying the center of thegeometric square mentioned previously,building the solid Chains Nf6/Be7/Qd8,e6/Be7/Ke8 and g7/f7/Be7/Nd7 and creatinga new, solid, piece rectangle on the pointse8-e6-d6-d8 (6 pieces on six squares).

13. Be2 O-O 14. O-O Qc7

rdsds4kddb1ngp0sp0s0phs0ds0sdsdss)PdPdsd)QdPdsHPsGsHB)Pd$sdsdRIs

Note that the last few moves, both sidescomplete the defense of their respectivepositions and prepare future attackingpossibilities by castling (Which alsoeliminates momentary Broken Links on g2and g7). White has created the Chains c4/ d3/Be2/Rf1, Rf1/g2/h3 and Kg1/g2/Ng3. He hasalso created a strong geometric defensivesquare at the points f1-f3-h3-h1 (6 pieces onnine squares). Black plays Qc7, creating thesolid Chain g7/f7/Be7/Nd7/Qc7/Bb7 andeliminating his Broken Link of the Bb7.

We have now reached a position where it ispossible to look far in to the future and foreseehow the game will play out. This is one of theattributes 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 creatingcounter-play. Work out the logic of the Chainscreated in the rest of the game, and be sure topractice calculating ALL moves in thePrimary Chain. Refer often to the KnowledgeBase, and record the applicable precepts. Keepa sharp eye out for Broken Links.

15. Bc3 Rfc8 16. Rac1 Nh7 17. Rfe1 a5 18. b5Re8 19. Qb2 Bf6

White clamps down on the queen-side,denying Black counter-play there. Blackresponds by forcing exchanges that reducesWhite's pull.

20. Bxf6 Nhxf6 21. f4 Nf8 22. Ngf1 Red8 23.g3 Re8 24. Ne3 Ng6 25. a4 Rab8 26. Bf3Rbd8 27. Qb3 Ne7 28. Qd1 Kh7 29. Qe2 g630. Rf1 Rf8 31. Rf2 d5 32. e5 Ne8 33. Nb3 d434. Ng2 Bc8 35. Re1 Kg8 36. Nd2 Kg7 37.Ba8 Ba6 38. Be4 Bc8 39. Nf3 Nf5 40. Kh2Kh8 41. g4 Ne7 42. Ngh4 Ng7 43. Kg1 Rg844. Nd2 Rgf8 45. Nhf3 Rg8 46. Rg2 Ne8 47.Qf2 Rg7 48. Qg3 Kg8 49. Kh1 Kf8 50. Reg1

20

Kg8 51. Qf2 Kh8 52. Qh4 Rh7 53. Qg3 Kg854. h4 h5 55. Ng5 Rh6 56. gxh5 Ng7 57. Nxf7Kxf7 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 along-term static advantage, he denied Blackall counter-play, and built his position slowlyNote also the attribute of the Tiger found inthe Knowledge Base that states that positionswhere your opponent is in a near state ofzug-zwang, will exist. For his part, Black isfollowing the precept of Knowledge BaseC16D. I.e. Relying on his "fortress" to holdthe position, and counting on the Tigerattributes that state that he will always havegood squares for his pieces, and that whatevertactics arise will never disfavor him. Note thatthe combination White initiated with 57.Nxf7lasted 5 moves, another Tiger/Dragonattribute.

62. Ne4 Bxe4+ 63. dxe4 Rxg6 64. Qxg6 Qe765. 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. Thepromise to Black that resulting pawnstructures would never disfavor him, theability to create a fortress that White could notpenetrate, and therefore the promise fulfilledthat tactics would always be in his favor. ForWhite's part, tactics were good to him too, ashe was able to win a pawn, although it wasn'tenough to win the game.

Tiger vs. Hippopotamus

1. e3 e6 2. d3 Ne7 3. Ne2 d6 4. Nd2 Nd7 5. h3g6 6. a3 b6

rdb1kgs40s0nhpdps0s0pdpddsdsdsdssdsdsdsd)sdP)sdPs)PHN)Pd$sGQIBdR

Considering the Primary Chains of Black, wesee that he is going to apply pressure to thea1-h8 and h1-a8 diagonals. Therefore, themove that has the greatest offensive anddefensive value is clearly g3, as we will soondevelop our bishop to contest the diagonal,and may then castle. We build the Chaing3/f2/Ke1.

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

21

rds1s4kd0bdnhpgps0s0pdpdds0sdsdssdsdPdsd)sdPds)Ps)PHN)Bd$sGQdRIs

We have built a rock-solid Chain of c2/d3/e4and Bg2/e4, and have built a very strongdefensive geometric square at the pointsh1-h3-f3-f1 in which our king resides. Alsonote the powerful geometric triangle ofsquares we control at the points h1-e4-b1.Now, Nc3 offers the best offensive/defensivequalities, possible defending the queen-sideand opening up squares for the queen on theking-side. Nc3 builds the Chains Nd2/Nc3,Nc3/b2, Bc1/c2/Nc3, and also builds a solidgeometric rectangle at the points c1-c3-d3-d1(6 squares filled by 6 pieces). We also developa knight to the third rank ala Knowledge BaseC10A.

11. Nc3 Ne5

Now, the move f4 is logical, in order toexpand our Primary Chain on the king-sideand create the pawn phalanx f4 and e4.

12. f4 N5c6

rds1s4kd0bdshpgps0n0pdpdds0sdsdssdsdP)sd)sHPds)Ps)PHsdBd$sGQdRIs

Black is re-deploying his pieces, and intendsNd4. It is best for us to also re-deploy anddefend against this possibility, with Ne2.

13. Ne2 d5

The move, e5 has the best offensive/defensivevalue, blocking out the diagonals of Black'sdark-squared bishop, and building the Chaing3/f4/e5.

14. e5 Qd7

It is logical to continue king-side expansionhere, with g4, building the Chains h3/g4 andg4/Ne2/Qd1.

15. g4 a5

The move Nf3 fills the geometric center of ourPrimary Chain, creating the solid ChainQd1/Ne2/Nf3/g4 and the Chains Rf1/Nf3/f4and Bg2/Nf3.

16. Nf3 d4

22

Ng3 develops a knight to the third rank andfurther compresses the geometric square ofh1-h4-f4-f1. Note that we have 8 pieces on 12squares here, forming a "nuclear"configuration. Our original defensive squarein this area of the board has now morphed into a quite ominous attacking configuration. Itis clear that our attack is going to come first,before Black can establish any kind ofcounter-play. Notice the typical Tiger attributethat Black is suffering from zug-zwang. Hehas no really good moves, but must playsomething. With Ng3, we also build the ChainNg3/f4/e5.

17. Ng3 Nd5

rdsds4kddbdqdpgps0ndpdpd0s0n)sdssds0s)Pd)sdPdNHPs)PdsdBd$sGQdRIs

Now, Ne4 develops a knight to the fourth rank(Knowledge Base C10B.) and creates a solidgeometric triangle at the points g2-e4-c2. Italso builds and joins the Chains Bg2/Nf3/Ne4and Ne4/d3/c2.

18. Ne4 f6

Black seeks to alleviate some of the pressure.White now plays a few exchanges, and thengoes after the Broken Link on b6. Beforecontinuing with any other plan, he generatesplay on the queen-side for a while inaccordance with Algorithm of Play GoldenRule #2.

19. exf6 Nxf6 20. Nxf6+ Bxf6 21. Nd2 Rae822. Nc4 Bd8 23. Qe2 b5 24. Nd2 Qc7 25. a4b4 26. Nc4 Re7 27. Bd2 Qd7 28. Rae1 Ree829. b3 Bc7

sdsdr4kddbgqdsdpsdndpdpd0s0sdsdsP0N0s)PddPdPdsdPsdPGQdBddsds$RIs

White has achieved a total domination ofboard. Black will now try some exchanges,but it doesn't help.

30. h4 Nd8 31. Bxb7 Nxb7 32. Qg2 Nd8 33. f5

23

sdshr4kddsgqdsdpsdsdpdpd0s0sdPdsP0N0sdP)dPdPdsdssdPGsdQddsds$RIs

At this point, Rybka's evaluation of theposition exceeded the 62 centi-pawn mark,and we can probably conclude that White hasa strategically won game. In the rest of thegame, it is clear that the white pieces clearlydominate the black pieces. White tucks hisking away safely, and then goes to work onthe incredibly weak black king-side. Carefullyplay through the rest of this game, noting theease with which White converts hisadvantage.

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. Qf1Kg8 43. Kb2 Kg7 44. Qf2 Kg8 45. Qe2 Bd846. Qg4 Kg7 47. Bf4 Nxf4 48. Qxf4 Kh7 49.Ka2 Qe6 50. Qf3 Kg7 51. h5 Qf6 52. Qd5Qg5 53. h6+ Kh7 54. Qxg5 Bxg5 55. Nxa5Bf4 56. Nc6 g5 57. a5 g4 58. a6 g3 59. a7 g260. A8=Q g1=Q 61. Qa7+ Kxh6 62. Qxc5Bd2 63. Nxd4 Kh7 64. Qc7+ Kh8 65. Nf3Qc1 66. Nxd2 Qxd2 67. Qc5 Kg7 68. d4 Kf669. d5 Kg5 70. Kb2 Kg6 71. d6 Kf6 72. Ka2Kg6 73. Qc7 Qf4 74. Qc6 Qf6 75. Qd5 Qd876. 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 thebasic plan of the Tiger, which is attackingwith the pawn thrusts (as White or Black)g4/g5, f4/f5, b4/b5 and c4/c5. We also see thatit is important to maneuver with the knights,probing at whatever structure our opponentsets up. The central pawn thrusts such as e4/e5or d4/d5 are possible, but usually held inreserve until later, although they do play a keyrole in the Ujtelky Dragon, which we willanalyze 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 isstill very flexible, one approach is to embarkon a plan of king-side expansion. g5 createsthe Chain h6/g5 and intends to develop theking's bishop to g7, collecting the squareChain a1-h8.

7...g5 8. Ne1

Ng6 is the logical continuation of our plan. Itcreates the Chains h6/Ng6, g5/Ng6 andNg6/f7/Ke8. I also develops a knight to thethird rank. (Knowledge Base C10A.)

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

rdb1kds4dp0ndpgspds0pdn0dsdsds0ssds)P)sddsHNGsdsP)PdBdP)$sdQdRIs

24

White plays a threatening move, yet here wefollow Algorithm of Play Golden Rule #2 andplay Nb6, expanding on the queen-side. It isthe promise of the Tiger, that we will alwayshave adequate tactical resources. Now,11.fxg5 hxg5 would accelerate our king-sideattacking chances, and is clearly bad. Theaggressive 11.f5?! is no problem, as evidencedby the following line:

11. f5?! exf5 12. exf5 Nh4 13. Bg4 O-O 14.g3 Qe7 15. Qc1 Re8 16. f6 Qxe3+ 17. Qxe3Rxe3 18. Bxc8 Rxc8 19. gxh4 Bf8 20. hxg5hxg5 21. Rf5 Bh6 When Black has a betterpawn structure and more active pieces, and istherefore better in this end-game.

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

Here, Black continues to expand on thequeen-side with b5. However there are alwaysplenty of viable options with the Tiger.Another plan might be 13...f5 14.exf5 exf515.b3 Nb6 16.Bh5 Kh7 18.Bf2 g4 19.h3gxh3....etc.

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

rds1s4kddb0sdpgspds0pdn0dpdsds0sPdn)P)sddPHNdsdssdPdBdP)$s!sdRGK

Here we simply retreat the knight with Na5,but to show the tremendous tactical ability ofthe Tiger, also possible was 15...c5!? 16.bxc4cxd4 17.fxg5 hxg5 18.axb5 dxc3 19.Qe3 axb520.cxb5 Ra5....etc.

15...Na5 16. fxg5 hxg5 17. axb5 axb5 18.Nxb5 Bxe4 19. Qe3 Bb7 20. Bf3 Nc6 21. Bf2

rds1s4kddb0sd0gssdn0pdnddNdsds0ssds)sdsddPdN!BdssdPdsGP)$sdsdRdK

Always be sure to calculate all moves possiblein relation to the Primary Chains, especiallywhere they intersect with the enemy. Wequickly find the very interesting g4!?

21...g4!? 22. Bxg4 Ba6! 23. Rxa6 (23.Nc3Nxd4 when Black is better.)

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

25

rdsdsdkdds0s1pgsrdn0pdnddNdsdsdssds)sdBddPdNdsdssdP!sGP)dsds$sdK

Per Knowledge Base B., "Winning theExchange", we know that since White still hasthe bishop pair, we gain about 1.15 for theexchange which makes the material balanceonly slightly in our favor. Yet here, we mustconsider that Black's pieces are much moreactive, and therefore, we hold a clearadvantage at this point.

26. Bf3 Qd7 27. h4 Ra1 28. h5 Rxe1+ 29.Nxe1 Nge7 30. g4 Ra1 31. Kg1 d5 32. Kh2Nd8 33. h6 Bf8 34. c4 c6

sdshsgkddsdqhpdssdpdpds)dNdpdsdssdP)sdPddPdsdBdssds!sGsI4sdsHsds

Black has a strategically won game here. Thisis because of his incredibly dangerous centralpawn mass which will be unstoppable. Studythe 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 Ra842. 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 Qxe552. Nf3 Ne3+ 53. Bxe3 Qxe3 54. Qxe3 fxe355. Bb3 Bxb4 56. Bxd5+ Kg7 57. Bc4 Ba558. Be2 Rh8 59. Nd4 Kf6 60. Bd3 Bb6 61.Ne2 Kg5 62. Bf5 Bc7 63. Kf3 Rh3+ 64. Ke4Bb6 65. Kd3 Rh2 66. Be6 Rh7 67. Ke4 Rh668. Bf5 Rh2 69. Kd3 Rf2 70. Be6 Rf8 71. Ke4Re8 72. Ke5 Ba7 73. Kd5 Kf6 74. g5+ Kxg575. 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 fromqueening, and is totally lost.

0-1

For the sake of completeness, allow me toshow two other possible game continuationswhere Black drew with ease.

7... c5 8. a3 Qc7 9. Qd2 Ng6 10. d5 e5 11. h3Be7 12. a4 b6 13. Rfe1 O-O 14. Rab1 Re8 15.b3 Qd8 16. Rb2 Nh4 17. Nxh4 Bxh4 18. Ra1Rb8 19. Rab1 Qc7 20. Bc4 Be7 21. Qe2 Qb722. Bd3 Qa7 23. Na2 f5!

A typical example of the explosive tactics theTiger offers, out of seemingly quiet and stablepositions.

24. exf5 e4 25. Bxe4 Bf6 26. Qf3 Bxb2 27.Rxb2 Ne5 28. Qg3 Qf7 29. Bxh6 Kf8 30. Bc1Bxf5 31. Bxf5 Qxf5 32. Qf4 Qxf4 33. Bxf4b5 34. axb5 Rxb5 35. Rb1 c4 36. Nc3 ½ - ½White must shuffle the knight from a2 to c3acquiescing to a draw by perpetual if Blackmoves the rook back and forth.

26

9... e5 10. dxe5 11. Qd2 Nf6 12. f3 Bd6 13.Rfd1 Rg8 14. Kh1 Nf4 15. Na4 Bd7 16. Nac5Bc6 17. c4 Qe7 18. Nb3 Qe6 19. Bxf4 gxf420. 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. Kg2Rxe4 33. Nc5 Re2+ 34. Kf3 Rxa2 35. Rg1Kb8 36. Rg8+ Ka7 37. Rh8 Kb6 38. Nxe6 A539. 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. Ra8Rc5+ 49. Kg4 Rc4+ 50. Kg3 Rc1 51. Nf3 Kb452. h5 Rh1 53. Nh2 Rg1+ 54. Kh4 Rh1 55.Kh3 Re1 56. h6 Re7 57. Kg4 Kb3 58. Nf3 a259. Ng5 Kb2 60. h7 Rxh7 61. Nxh7 a1=Q 62.Rxa1 Kxa1 ½ - ½

Next, we will examine two possible plans ofplay when your opponent assumes anAuerbach structure with pawns on e4, d4 andc4. You will see that there is nothing to fearhere at all. Remember that having some spacein the opening does not mean you have anadvantage (Knowledge Base C1.).

Tiger vs. Auerbach # 1

In this game, Black adopts the early g5 planand blows White away. I offer the game withvery little comment. Remember to Study theChains and Geometric that are developed, andto calculate all moves in the Primary Chains.Don't forget to look for Broken Links. Studythe whole game and the techniques used,carefully. Black is a pawn up in the end-game,but of key importance is the superior activityof his pieces.

1. d4 e6 2. c4 Ne7 3. Nc3 d6 4. Nf3 Nd7 5. e4a6 6. Be2 h6 7. Be3 b6 8. O-O g5 9. d5 e5 10.h4 g4 11. Ne1 h5 12. Nd3 Ng6 13. Bg5 Be714. Bxe7 Qxe7 15. g3 Nxh4! 16. gxh4 Qxh417. 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

sdkdsdrddb0ndRdsp0s0sdsddsdP0sdpsdPdPdrddsHsdsdqP)s!RdNddsdBdsIs

It is move 24, and Black already has astrategically won game! The rest is nothingbut torture for White. Study carefully howBlack uses his superior pieces, and how he iscareful to squash any type of whitecounter-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. b4axb4 35. axb4 Na6 36. Nb5 Rh3+ 37. Kf2 h438. Bf3 Rg3 39. Rh7 Nxb4 40. Rxh4 Rg7 41.Ke3 Na6 42. Rh2 Nc5 43. Rg2 Rh7 44. Rg1Bd7 45. Rh1 Rg7 46. Nc3 Nb3 47. Kf2 Nd248. Be2 Bg4 49. Bd3 Rf7+ 50. Ke3 Nb3 51.Rf1 Rh7 52. Rf8+ Kb7 53. Bf1 Rh1 54. Rf7Nc5 55. Rg7 Rxf1 56. Rxg4 Rh1 57. Nb5Rh3+ 58. Kd2 Rh2+ 59. Ke3 Rh7 60. Rg3Ka6 61. Rg8 Ka5 62. Rc8 Kb4 63. Nxc7 Rh464. Ne8 Rxe4+ 65. Kf3 Rf4+ 66. Ke2 Kxc467. Nxd6+ Kxd5 68. Nb5 Re4+ 69. Kd2 Rh470. 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. Rc8e4 83. Ng3 e3 84. Ke1 Kc3 85. Kf1 Kd4 86.Ne2+ Ke5 87. Rg8 Ne6 88. Rg3 Rb1+ 89.Kg2 Nf4+ 90. Kf3 Nxe2 91. Kxe2 Rb2+ 92.Ke1 Kf4 93. Rg7 b5 94. Re7 b4 95. Re8 Rc2

27

96. Rf8+ Ke4 97. Re8+ Kd4 98. Kf1 b3 99.Rd8+ Kc3 100. Ke1 Kb2 101. Rb8 Ka2 102.Kf1 b2 103. Ra8+ Kb1 104. Ra3 Kc1 105.Rxe3 b1=Q

0-1

Tiger vs. Auerbach # 2

In this game Black adopts a plan with the c5advance. Note the board-wide and swift attackon all fronts. The Tiger is NOT a passiveopening.

1. d4 e6 2. c4 d6 3. Nc3 Nd7 4. Nf3 Ne7 5. e4h6 6. Be3 a6 7. Bd3 c5 8. d5 exd5 9. exd5 g510. Qc2 Bg7 11. h3 b5 12. cxb5 axb5 13.Bxb5 Bb7 14. h4 g4 15. Nh2 f5 16. Rd1 O-O17. O-O f4

rds1s4kddbdnhsgssds0sds0dB0Pdsdssdsds0p)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. a4Bf5 25. Qe2 Bg6 26. Bf4 Nf5 27. Bc6 Ra7 28.Nb5 Re7 29. Qd2 Qd8

sds1sdsidsds4sgssdB0sdb0dN0PhndsPdsdsGp)dsdsds)ss)s!sdsHdsdRdsIs

Black has a strategically won game here.White will not be able to stop the Black pieceinvasion. 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 ofImbalances/Bishop Pair") and ALL of Black'spieces are aggressive and mobile. We arewinning...

30. b3 h5 31. A5 Qc8 32. Bxe5 Bxe5 33. Nf1Kh7 34. Re1 Rf7 35.Rxe5

Total desperation.

35...dxe5 36. Qe1 Nd4 37. Nxd4 exd4 38. Bb5Qf8 39. Bc4 d3 40. d6 Rd7 41. Qe5 Qxd6 42.Qxd6 Rxd6 43. Nd2 Rd7 44. Bb5 Re7 45. Kf1Kg7 46. a6 Kf6 47. Bc6 Ra7 48. Bb7 Ke5 49.Kf2 Kd4 50. Nc4 Kc3 51. Ke3 Kxb3 52. Ne5Kc3 53. Nxg6 d2 54. Ke2 Kc2

0-1

28

In our final game, we examine the UjtelkyDragon. In addition to the Tiger, the Dragoncan be played against systems where Whiteplays c4 English set-ups, Auerbach set-ups orqueen-pawn set-ups of d4 and c4. The mainuse of the Dragon is in structures where Whiteplays an early f4. In these cases, the Dragon isoften best.

Dragon vs. Broad Front

1. e4 e6 2. d4 Ne7 3. f4 d6 4. Nf3 Nd7 5. c4g6 6. Nc3 Bg7 7. Be2 O-O 8. O-O

rdb1s4kd0p0nhpgpsds0pdpddsdsdsdssdP)P)sddsHsdNdsP)sdBdP)$sGQdRIs

White’s position looks impressive. However,according to the Shashin method ofmathematical position estimation, Black isbetter! Observe how Black swiftly dismantlesthe white position.

8...d5 9. cxd5 exd5 10. e5 a6 11. a3 b5 12.Be3 c6 13. b3 a5 14. Qd2 Rb8 15. Bf2 Nb616. 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. Qe3Bf8 26. Bd1 Rb2 27. Rc2 Qb4 28. Ne1 Rb329. Nd3 Bf5 30. Be2 Qe7 31. Rd2 Qd7 32.Bf3 Rc3 33. Qe2 Rbb3 34. Rad1 h5

sdsdsgkddsdqdpdssdsdsdpd0sdp)bdpPds)s)sd

dr4NdB)sssds$Qds)dsdRdsIs

It is move 34, and White is strategically lost.The rook pawn is going to fall, and then ouroutside 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. Bh3Bxh3 42. Nxh3 h4 43. Qg4 hxg3 44. hxg3Raa3 45. Rg2 Rc1 46. Rxc1 Qxc1+ 47. Kh2Ra1 48. Nf2 A4 49. Qd7 Qe1 50. Qe8 Qe2 51.Nh3 Qf1 52. Nf2 Re1 53. f5 gxf5 54. Qd7Qa6 55. Qxf5 Qg6 56. Qxg6+ fxg6 57. Ng4Be7 58. Rb2 A3 59. Rb8+ Kg7 60. Ra8 Re461. Ra7 Kf8 62. Ra8+ Kf7 63. Nh6+ Kg7 64.Ra7 Kxh6 65. Rxe7 Re2+ 66. Kh3 a2 67. Ra7Kg5 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. Rd7Ke2 78. Rd6 Rd3+ 79. Kg2 Ke3 80. Ra6 d481. 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 powerfulimpression. White never really seemed to havea chance at all.

29

Study these games over and over, until youunderstand the techniques thoroughly.According to concrete mathematical analysisyou will face similar themes in every gameyou play.

Now, if you study the Algorithm of Play andthe Knowledge Base, until you have themdown cold, and can site them "chapter andverse", I see no reason why you should everlose a game of chess again.

If you get bored, or you want to change thingsup a bit, the system is very flexible. Possibleare: e6 and Ne7 followed by an early d5 or f5,d6 and Nd7 followed by an early c5 or e5, orif you want to play a super-positional game,e6, Ne7, g6 and d5. If White plays e5, seedingyou the f5 square for your knight then h5 andNf5. If White doesn't advance the e pawn,then dxe4, and after he captures back with apiece, then h5 and Nf5. This is the super-solidGurgenidze set-up, and it is a tough nut tocrack.

Another pleasant attribute of the Algorithm ofPlay, is that you will be able to find movesquite rapidly, so you should always be aheadon the clock. You should be able to play outyour games to completion in quite a bit lessthan 2 hours (The standard time control inmost tournaments.)

Finally, the Tiger and Dragon can also beplayed as White, so you now have a completeand very dangerous chess repertoire!

A Note on early Advances and MoveOrders

early advances by the opponent such as anearly e5 or d5 do not impress. You have thechoice of either capturing, if advantageous toyou, or stepping past the pawn, which oftencloses the center for a long time to come, andgives good play and squares to your knights.

In general, the first six moves of the game canbe played on auto-pilot, and you can chooseany move order you like that reaches theTiger or Dragon. It is usually advisable to playout the two center pawns first, followed by theknights or bishop, and then the a6/h6advances.

30

CHAPTER 5:MIND AND BODY

Of course, our games are not played bycomputers, but by us. We as humans can tendto be a bit fragile physically and/orpsychologically, and thus, our game maysuffer.

The Body Connection

First, we will consider the physical body, asbasic physical well-being is required to playchess optimally.

Daily Exercise Quota

Always get at least 8 hours of sleep per night.

A 20 minute brisk walk, or if your notcapable, a 40 minute, more leisurely walk, isrecommended.

Daily Diet

1 cup of Ginko/Green Tea decaffeinated teataken any time during the day, or with mealsif stomach sensitive. (I recommend the TripleLeaf brand, which can be gotten athttp://www.vitacost.com/ A 6 month supplywill 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 cupgranola or other sugar-free, high fiber cereal,with fat-free milk or apple-juice.

Lunch and Dinner

3 ounces of broiled skinless chicken, fish orlean beef.

Lots of brightly colored steamed vegetables,especially any green vegetable.

½ a baked potato (with non-fat, cholesterolfree-margarine and imitation fat-free baconbits if you must).

OR

Brown non-processed rice.

If you feel this is too stringent, once everyweek, take one day and eat what-ever youwant.

Night-time Snacks

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

Indulgences

You can have one bar of sugar-free milk ordark chocolate. (With raisins, is ok, but avoidnuts.)

31

Intake on Game Days

Avoid any heavy or large meals before agame. Eat a light sensible meal. (Consider theabove breakfast menu or the Lunch andDinner menu in ½ proportions.)

NO SUGAR!!!

Game Time

Five minutes before game time, imbibe one 5-hour ENERGY® drink (regular). This is a 3ounce liquid shot, that is zero sugar, zeroherbal stimulants, 4 calories B-vitamins andamino acids and as much caffeine as a cup ofthe leading premium coffee, so it doesn’tbreak any of the laws of intake before atournament chess game (Still, imbibe itoutside the tournament hall to avoid anypossible hassles.) The key ingredients in 5-hour ENERGY® are also available in everyday foods – like broccoli, avocados, bananasand apples – or already in you. This drink canbe obtained at almost all grocery stores orpharmacies.

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 anyprescription medicines.

You have been advised by yourphysician to avoid stimulants orcaffeine.

You have a medical condition thatmakes 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 hourEnergy, then instead, eat a bar of sugar-freedark chocolate before the game, and take anextra to nibble on during the game.

Always take a bottle of water to your games.It is important to remain well-hydrated duringplay.

32

The Mind Connection

Now we come to the more tricky subject ofyour mental processes and game psychology.

The major complaint of most chess-players isan inability to concentrate and to calculateand/or remember variations.

Memory and Calculation

Memory and calculation can be handledsimply. Study and solve puzzles from theStudy Supplement you received with thisbook, or from the sources mentioned in theSupplemental Training section. A minimumof two hours a week is suggested, and more, ifyou have the time. Never let more than sixdays go by without a study session. (By theway, by employing the Algorithm of Play, andcalculating every possible move in thePrimary Chains, you will notice that you cansolve any chess puzzle usually in under 2minutes, and any combination from actualgames in under 1 minute.)

Concentration

To concentrate fully during a game, it is firstnecessary to train the ability. Practice thefollowing as often as you can:

BE HERE NOW

This deceptively simple strategy is probablythe most effective. When you notice your thoughts wandering astray, say to yourself

"Be here now"

and gently bring your attention back to whereyou want it.

FOR EXAMPLE:

You're performing a mental activity (studyinga chess position), and your mind begins towander. Say mentally to yourself,

"Be here now"

you focus back on the position and maintainyour 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 theperiod of time between your straying thoughtsgets a little longer every few days. So bepatient and keep at it. You'll see improvement!

SPECIFIC TIME

Humans tend to do what they tell themselvesto do. Therefore, it’s easier to concentrate ifyou set a specific length of time to study andconsciously 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 thedot for 60 seconds. Start taking deep breathswhile staring and for a short time after youhave finished staring at the dot.. You shouldnow find an increase in your concentrationpower.

33

THE COUNT METHOD

Count backwards from 100 in various types ofsegments(2, 4, 6...etc). At the end, reverse theprocess and count from 1 up to 100 in varioussegments.

CUPPING

You can actually cup your hands around yourown eyes. This may serve as a trigger to tellyour mind to focus on a particularresponsibility. For example, you are in a roomand you need to study but there are manythings preventing you from concentrating.Cupping your hands around your eyes mayhelp your brain switch to focus mode and keepit on its track.

KNEE TO ELBOW

You can stimulate your left and right cerebralhemispheres by touching your right elbow toyour left-knee and then doing the same for theleft-elbow/right-knee. Do this three times.

FOCUS

Before you begin studying (or beginning playin a game of chess), take a few minutes tosummarize a few objectives (opening and planof play), gather what you will need, and thinkof a general strategy of accomplishment

FIGURE EIGHTS

On a large piece of paper taped to the wall,draw large sideways figure 8s (the infinitysymbol) over and over with the right hand, theleft hand, and both hands. If you don't havepaper, do the drawing motion in the air (Don’tdo this at the chessboard. People will thinkyou are nuts. Draw the 8's on your knee underthe table.) Start drawing really large sidewaysfigure 8s and continue making the figure

smaller and smaller until you are drawingreally tiny Figures. You are then ready tobegin mental activity, or any task that requiresconcentration.

Anytime you feel you are losingconcentration, stop the work and do figure 8exercise again. This exercise can also be donewith closed eyes by imagining drawing figure8's.

This exercise helps to activate both the rightand 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 grantedand do not observe as intently as we should. Inorder to develop focus and observation, try to look at tasks which you do everyday as if youare doing or seeing them for the first or thelast time. This will encourage you to observedetails 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 ofthe body. These mean that you have notproper control over your body. After you haveacquired this control, notice how "ill-at-ease"people are that have not gained this control.

Watch people and see how many of themmake unnecessary movements and lack poise.Get rid of any habit you have of twitching orjerking any part of your body. You will find you make many involuntary movement. You

34

can quickly stop any of these by merelycentering your attention on the thought, "I willnot."

The purpose of the above exercises is to gaincontrol over the involuntary muscularmovement, making your actions entirelyvoluntary.

POISE

Watch yourself during the day and see thatyour muscles do not become tense or strained.See how easy and relaxed you can keepyourself. See how poised you can be at alltimes. Cultivate a self-poised manner, insteadof a nervous, strained appearance. This mentalfeeling will improve your carriage anddemeanor.

HOLD A THOUGHT

Select some thought (chess position) and seehow long you can hold your mind on it. It isnice to have a clock at first and keep track ofthe time.

Make it a daily habit of concentrating on thisthought for, maybe ten minutes. Practicedoing this until you can hold it to theexclusion of everything else. You might haveto do this exercise regularly for 10 days ormore in order to sharpen your concentrationskills. The time you can hold concentrationwill begin to lengthen.

EXPRESS A MOTIF

No one can think without first concentratinghis thoughts on the subject on hand. Everyman and woman should train himself to thinkclearly. An excellent exercise is to read anarticle in a newspaper, (or look at a chessposition) and see in how few words you canexpress it. Reading an article (studying a

position) to get only the essentials requires theclosest concentration. If you are unable towrite out (or express succinctly) what youread, you will know you are weak inconcentration. Instead of writing it out you canexpress it orally if you wish. You will findexercises like this of the greatest value indeveloping concentration and learning tothink.

Study parts of this book (any section) fortwenty minutes and then write down, in yourown words, what you have read. The chancesare that at first you will not remember verymany details, but with a little practice you willbe able to write a very good account of whatyou have read. The closer the concentrationthe more accurate the account will be.

If time is limited to read only one axiom in theclassical and modern chess theory, orKnowledge Base section. Write it down wordfor word. When you are able to do this, readtwo axioms/precepts and treat similarly. Thepractice will produce very good results if youkeep it up until the habit is fixed.

BEAT THE CLOCK

Sit in a chair and place a clock with a secondhand on the table. Follow the second handwith your eyes as it goes around. Keep this upfor five minutes, thinking of nothing else butthe second hand, This is a very good exercisewhen you only have a few minutes to spare, ifyou are able to keep every other thought inthe stream of consciousness subordinate to it.As there is little that is particularly interestingabout the second hand, it is hard to do this,but in the extra effort of will power requiredto make it successful lies its value. Always tryto keep as still as possible during theseexercises.

35

TAKE IT TO THE MAX

Do a thing wholeheartedly. If you approachsomething half-heartedly, it can show in thequality of your thought processes. In order todo things better, do them with interest.Whatever you are doing, try to find someaspect of it that interests you. If you can findsomething interesting in each thing you do,you can enjoy even the most mundane andboring tasks. (This is why I mention somealternatives of play if you ever get bored ofjust playing the straight Tiger or Dragon (SeeGames Analysis Section)).

GAME DAY

45 minutes before the game, on an MP3 playerlisten to EXTREME FOCUS. This is a 25minute segment of music. This sessionstimulates SAR in the right brain hemisphereand Beta in the left. It is ideal to help focus themind before a mentally strenuous task. It isbased on the ADD research from psychologistMichael Joyce and David Sever.

It can be obtained at:

http://www.musicmefree.com/page_single_downloads.php

EXTREME FOCUS $5.00 25 Minutes MP3

During the game, on your MP3 player, playthe following music to create and maintainconcentration.

Coming Into Focus 5:25 192 kbps $0.09 03 Powers Of Concentration 4:51 $0.09 04 In The Zone 5:41 192 kbps $0.09 05 Think 5:04 192 kbps $0.09 06 Total Lucidity 5:23 192 kbps $0.09 07 Balance 5:25 192 kbps $0.09 08 The Settled Mind

These can be obtained for the price listed, at:

http://www.legalsounds.com/download-mp3/david-bradstreet-%26-john-herberman/music-to-enhance-concentration/album_87139

Legalsounds asks for a $25.00 deposit againstfuture purchases.

OR

if you don’t think you will ever purchase anyadditional music, and don’t want to spend$25.00, go to:

http://www.amazon.com/Music-To-Enhance-Concentration/dp/B002HH5W9S/ref=sr_1_3?ie=UTF8&qid=1295245203&sr=8-3

You can buy the whole “Concentration”album which includes two or three additionaltracks to the ones mentioned, for $9.00

Game Notation

It is recommended that you obtain either aMonRoi electronic notation device, or a PDAwith the E-Notate electronic notationsoftware, that can be obtained from the NorthAmerican Chess Association.

http://www.monroi.com/

or

http://www.nachess.org/

36

WHEN YOU SIT DOWN TO PLAY AGAME OF CHESS, DON’T FORGET TOBRING YOUR GAME!!

Any time you sit down to play a game ofchess, you should have in mind the followingpsychology:

1. Play with confidence. If you have practicedeverything I preach in this book, you are bynow an awesome chess powerhouse.

2. Play to win. Worry about draws when youropponent 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 withscepticism (or scorn if you want). Challengeall his ideas. Responding to a fake threat islike stopping an opponent from losing thegame.

6. If an obvious plan conforms to the position,follow it.

7. Concentrate fully on the game. On yourmove, build Chains and calculate tactics in thePrimary Chains. On his time, study the over-all aspects of the position, and considervarious strategies.

8. Always expect your opponent to make thestrongest move possible to him, and playaccordingly.

9. Before playing a move, ask, “Whatwonderful thing does this move do for myposition?”. If you can’t answer this question,you are playing the wrong move.

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

11. Material gain or loss is just another type ofimbalance. The total play of the position iswhat matters.

12. Material inequalities cause psychologicalparalysis. You will probably see quite a fewwith the Tiger and Dragon. Embrace them. Letyour opponent cower in fear.

13. Fear no aspect of the game. (With thisbook, you will never have to.)

14. If your opponent is in time pressure, donot speed up your moves. Take your time andfind the best move. The best move is alwaysthe move that sets the most problems for youropponent to solve.

15. If you are lost, put yourself in youropponent’s shoes, and play the move that youwould least like to see if you were him. Fightto the bitter death, and never give up! (Ipersonally believe that practitioners of thecomplete Tiger and Dragon Chess Systemneed never lose a game.)

37

CHAPTER 6:Your ELO Rating

So, just how strong can you expect to be,playing the Tiger and Dragon Chess System?

Given the mathematics, and projectedperformance based on the results of all theanalysis, if you do everything this book says todo, you should have an estimated playingstrength of :

ELO 3511

This is provided that you do everything thisbook suggests you do.

38

APPENDIX A:SUPPLEMENTAL STUDY

Study the 700 puzzles in the StudySupplement regularly. This will buildcalculating and memorization capabilities, andimprove concentration. This supplement wasselected especially because it has a largenumber of self-mates. This type of puzzleteaches you to think and calculate acombination both forwards and backwards.Make sure to utilize the method of calculatingevery possible move that interacts with theopposing forces (For the best methods ofcalculation, refer back to “Notes onCalculation” in the Algorithm of Play sectionof the book.). Time how long it takes you tocomplete each problem. The goal is to solveall problems in well under 2 minutes.

Study every aspect of this book until you haveit down “cold”, and can site it “chapter andverse”.

If you need additional puzzles once you havegone through and are completely familiar withthose supplied, I recommend:

Chess: 5334 Problems, Combinations andGames , by Laszlo Polgar

The Complete Chess Workout: Train YourBrain with 1200 Puzzles, by Richard Palliser

All who play the Tiger and Dragon areencouraged to submit their games to me atwalt123@verizon.net

Players are also encouraged to submit theirperformance ratings from tournaments.Tournaments that qualify are those that havesections, plus a top section that is an “Open”.You must have played in the Open section,against all the strongest players, to submit aperformance rating. I will also accept Tigerand Dragon performance ratings attained inmatches against computers.

To calculate your performance rating, go to:

http://main.uschess.org/content/view/7875/400/

It is recommended that you study your owngames with the Tiger and Dragon intensely,especially any games that you lose. A strongcomputer chess engine will be able to helpyou work through the game. Work out wherethe win for you was. It should be there in oneof the possible variations given by yourcomputer. Above all, work out exactly whyand how you lost. Learn from any mistakesyou make.

Be sure to follow the Mind and Body section.

39

APPENDIX B:Logic and Math Used in Analysis of the Tiger and Dragon Chess System

For those that are interested, I have given here,an entire breakdown of the logic and math thatfunctioned in analysis of the Tiger and Dragonstructure and games.

Term 1: SYSTEM

A system is any process that follows aprogressive path through time and/or space.Some systems are perpetual and go on forever, and some systems terminate or end at apoint of completion, and then start over again.All systems have structure.

Term 2: STRUCTURE

A structure is an over-all framework withinwhich a system works. The structure willdefine which systems will thrive. All systemsand structures are born from an initial state.

Term 3: INITIAL STATE

The concept of the initial state comes fromthe mathematics of Chaos Theory. Allattributes of the systems and structures thatfollow are intensely dependent upon thisbeginning state. A popular example ofdependence of systems on the initial state, isthe flapping of a butter-fly’s wings producingan initial air current which eventually grows into a hurricane half-way across the world. Fromthe initial state, all systems and structuresprogress through time and/or space through aniterative and/or branching process.

TERM 4: ITERATIVE PROCESSAn iterative process is where a systemcombines two or more previous attributes tocreate a new attribute. The new attribute thencombines with previous attributes to formanother new attribute, and this processcontinues ad infinitum, or until the systemterminates.

Term 5: BRANCHING PROCESS

In a branching process, a system propagatesby splitting from its initial state in to two ormore separate processes. These processes thenbranch in to two or more new processes, andso on ad infinitum, or until the systemterminates.

The iteration and/or branching process of anysystem will always follow a pattern of growthwhich is roughly equivalent to the GoldenRatio.

Term 6: GOLDEN RATIO

The Golden ratio stipulates that the iterativeand/or branching processes of a system willprogress through time and/or space at agrowth rate of roughly 1.618034.... . Thisprocess can be expressed in a series ofnumerical values in which each value is addedto the proceeding value, where it can beshown that the values will converge on theGolden Ratio, as the series progresses throughtime. Popular representations of thesenumerical values are Fibonacci Numbers andLucas Numbers. System processes can alsobe expressed as a series of Fibonacci Ratios.

40

Term 7: FIBONACCI NUMBERS

Fibonacci numbers are derived by starting aseries of numerical values at 0,1,1, and thenadding successive values to previous values.These values converge to the Golden Ratio asthey move through time. For our purposes, thenumbers 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 aseries of numerical values at 2,1,3 and thenadding successive values to previous values.These values converge to the Golden Ratio asthey move through time. For our purposes, thenumbers we will use are:

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

Term 9: FIBONACCI RATIOS

Fibonacci Ratios are derivatives of theGolden Ratio, and all systems will adhere intheir growth cycles roughly to them. For ourpurposes, the important ratios are:

.24 , .38, .50 and .62

Placed together, Fibonacci numbers and ratiosand 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/orspace, the interaction of the Golden Ratio,expressed as Fibonacci and Lucas numbersand/or rat ios will form specificAction/Reaction States, and specific, self-repeating, structures as dictated by themathematics of Fractal Mathematics.

Term 10: ACTION/REACTION STATES

An action/reaction state is a simple binaryprocess where a specific action is counteredby a specific reaction, which then becomes anaction, which is countered by a reaction, andso on ad infinitum, or until the systemterminates.

Term 11: FRACTAL MATHEMATICS

All systems have structure, and, according tothe mathematics of Fractal Geometry thatstructure will continue to repeat, no matterhow large or complex the system becomes,or for how long the system exists.Essentially, the structure will remaininviolate unto infinity.

41

Graphical Examples of Fibonacci/LucasSystems Propagating Through Time andSpace.

42

Use of the Mathematics and Logic With Computer-Aided Analysis.

First, a computer chess engine of optimalstrength, running on sufficient hardware isrequired.

I used Deep Rybka 4, running on a 2.93Gigahertz machine with a hash-table of 7,359Megabytes, and an 8 CPU Intel i7 processor.

Next, we will examine the application of themath. It has often been noted by computerexperts and chess-players of considerablestrength, that computer evaluations ofpositions have no bearing on the reality of theposition on the board, and are often erroneous.This is true if you are looking at the numbersgenerated in the evaluations as representationsof who is “better” or who is “winning orlosing”. However, one can glean veryimportant information from the numbers, onthe structure of the game as it unfolds. Thestructure has to do with how the pieces arraythemselves on the board, and, moreimportantly, how those pieces will interactwith each other throughout the entirety of thegame.

By analyzing the numbers that variousstructures produce, we can predict with greatcertainty, the number of additional structuresthat can be created, and therefore the varianceor 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 veryspecific (and often small) set of structurespossible. Though still complex, thesestructures are subject to very little variance,and therefore, can be accounted and plannedfor by the player, to a depth reaching from theopening to well in to the end-game.

Adoption and analysis of standard openings(as defined in Fundamental Chess Openingsby Paul van der Sterren) producedFibonacci/Lucas numbers only about 70% ofthe time. This leaves 30% of the possiblestructures unaccounted for, and thereforeindicates great possible variance, and, ofcourse, an inability of any human toadequately prepare for them.

Adoption of structures such as those found inthe Tiger and Dragon, producedFibonacci/Lucas relationships in excess of95% of the time. Further, critical moves in thegame also displayed Fibonacci/Lucasrelationships. I.e. Critical moves occurred onmoves 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 computerrepresented a “real” estimation of who waswinning or losing the game. Numbers below62 centi-pawns were irrelevant in estimationof advantage. However, A series ofevaluations that exceeded 62 centi-pawnsindicated a continued series of expansion upto and exceeding 100 (+/- 1.00) centi-pawns,the level of evaluation in a game commonlybelieved to represent a decisive advantage ina game of chess between two evenly matchedplayers.

43

Error correction in the analysis was given thefollowing parameters:

All moves in the games, analyzed to a depthof 21 ply. Fibonacci/Lucas math allows us tocalculate the possibility of an inferior movebeing played at 1 in 1000.

In order to be considered withFibonacci/Lucas numbers, the evaluationgiven by Deep Rybka 4 had to be within +/-one number to be considered valid.

In closing, generation of structures yieldinghigh Fibonacci/Lucas values indicated that theposition on the board was being played at apeak efficiency, and conversely, that DeepRybka 4 was finding the strongest moves inthe position in both a positional and tacticalsense.

Observation of the characteristics of thesephenomena, allowed for the development of ageneral Algorithm of Play, that humans couldadopt. We should not be surprised that thisalgorithm jibed with the most valuable tenetsof classical and modern chess theory andEastern martial theory.

Additional Mathematical Methods andProofs

Once we devised the Tiger and Dragonstructures, it was possible to estimate theirinherent strength mathematically, using amethod devised by Alexander A. Shashin, astrong russian chess player with wins overKorchnoi and Epishin to his credit. Shashin, anuclear physicist by profession, developed thefollowing mathematical method for estimationof the strengths of a chess position:

The Shashin Method

There are four factors in evaluating a chessposition:

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 n9(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 ina given position. P1 is the mobility of ourpieces, P2 is the mobility of the opponent’spieces. P1/ P2 = p.

3) Expansion factor. This is defined bycalculating the center of gravity of a givenposition. Take the starting position. White has8 pieces on the 1st rank, and 8 on the 2ndrank: 8*1+8*2=24, divided by the number ofpieces, 24/16=1.5, so the center of gravity liesbetween the first and second ranks..4) Packing density. There are several differenttypes of packing density: by all pieces andpawns; by king and pawns; by king, pawnsand knights (short-range pieces); by pawnsonly; and local density at certain sections ofthe board. The most informative densities arethose by short-range pieces. The denser aposition is, the safer it is.

If p(mobility) > 1.25 :

1) first we look for an open attack, 2) optimalpiece deployment, 3) sacrifice, 4) materialgains. In an open attack; we attack materialtargets according to the hierarchy: king,queen, rook, bishop, knight, pawn, or anempty square.

44

If p(mobility) < 0.80: Your position is “bad” and you must defendby retreating your forces in to a more compactposition.

If p is between 0.80 and 1.25:

No advantage in mobility exists. Therefore,concentrate on:

1) optimal piece deployment, 2) pawnadvances, 3)exchanges

In addition to Shashin’s analysis, I believe it ispossible to estimate who is “better” in theposition, by multiplying the expansion factorby the packing density, thus giving a numberthat estimates the total ability to attack anddefend from a given position.

First, let’s consider the Dragon against theBroad Front:

rdb1kds40p0nhpgpsds0pdpddsdsdsdssdP)P)sddsHsdNdsP)sdsdP)$sGQIBdR

Material is even so this value is 1.Mobility is 31 / 33 = .939Expansion = 4*4+2*3+4*2+1*6 = 36 versus8*2+3*3+1*5 = 30. 16 / 36 = 2.25 and 16 / 30= 1.875. So we wind up with 2.25 for Whiteand 1.875 for Black.Density = 16 / 32 = .50 for White, and 16 / 24= .66 for Black.

From these values we can ascertain that Whitedoes not have sufficient mobility to claim anadvantage and attack.

Taking my formula for the estimation of totalstrength of a position, we multiply theexpansion by the density, and we get:

White: 2.25 * .50 = 1.125Black: 1.875 * .66 = 1.2375

Therefore, Black is better over-all.

Now, let’s consider the Standard Set-upversus the Tiger:

rdb1kgs4dp0nhp0spds0pds0dsdsdsdssds)PdsddsHBGNdsP)Pds)P)$sdQIsdR

Material is even and = 1.Mobility = 26 / 36 = .72Expansion = 4*2+4*3+2*6+4*1 = 36 versus4*3+6*2+1*6 = 30. Dividing by the numberof pieces, we once again get 2.25 for White,and 1.875 for Black.Density = 16 / 32 for White and 16 / 24 forBlack once again.

Here we see that according to Shashin’sformula, White has the right to attack. But thequestion is, “Attack what?” Black has noweak points. Applying my formula for over-all strength of position we once again get1.125 for White and 1.2375 for Black.

45

To close, let’s compare these findings to thePirc defense, which is a solid and respecteddefense. From the initial Pirc set-up with apawn on d6, knight on f6, pawn on g6 andbishop on g7, the Pirc scores a rating of only1.114. So, in the Pirc we see that White hasthe right to attack, and also has weaknesses totarget, such as a break in the center, or moveslike Bg5, or the formation of the Qd2/Be3battery to play Bh6 and eliminate the strongg7 bishop.

We see that the Tiger is strongermathematically and logically, since itsmathematical evaluation is higher, and Whitehas no points of attack.

So, if the Pirc is considered sound andplayable, the Tiger and Dragon must be aswell.

46

APPENDIX C:Knowledge Base

By playing in the form of Chains andGeometric Controls, you are assured to a highdegree of mathematical certainty, thefollowing:

! The tactics will always favor you.

! You will never miss a tactic.

! Length of tactical combinations willseldom exceed 5 moves.

! Pawn structures will always befavorable to you. I.e. If you have anisolated pawn, you will always gaingood attacking chances, and yourisolani will always be strong. If youhave doubled pawns, you will alwayshave good attacking chances, and thedoubled pawns will be of the varietythat are mobile, easily dissolved, ordefend key squares in your position.Conversely, if your opponent hasisolated or doubled pawns they willalways be of a variety that present aliability to your opponent’s position.

! Your pieces will always control themost important squares in the game.

! The aggregate of all these pluses isdue to the fact that you are alwaysplaying from a position that ispositionally sound.

! Many times your opponent will findhimself in zug-zwang positions werehe has no really good move or options.

So the first axiom of the Knowledge Base isto always be confident. You have reason tobe!

The Knowledge Base is organized with themost important factors being first, and theleast important factors last.

A. If one of your calculations in thePrimary Chains wins material, and offersthe opponent no compensation either inposition or attack, 9 times out of 10, thiswill 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 equalvalue Positional considerations will decidewhich piece is better. Knights are better with12 or more pawns on the board. Bishops arebetter with 8 pawns or less on the board. Thebishop is a bit better than the knight whenfighting against a rook or against multiplepawns in an end-game.

The Bishop Pair

The bishop pair has an average value of anadditional half a pawn (more when theopponent has no minor pieces to exchange forone of the bishops).

As analyzed by GM Larry Kaufman1

47

It is worth losing a tempo to save the bishoppair, but it is reasonable to give up the bishoppair if you can gain two tempi by doing so.

If you have the bishop pair, and youropponent's single bishop is hemmed in by hisown pawns, you already have fullcompensation for a pawn. In other words, ifmost of your opponent's pawns are fixed onone color and you both still have both bishops,it is worth losing a pawn to trade a knight forhis "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 majorissue), the minor piece is worth about 3¼pawns.

Winning the Exchange

Now let's move on to discussing the Exchange(rook for knight or unpaired bishop). Myresearch puts its average value squarely at 1¾pawns

When the side down the Exchange has thebishop pair, the exchange is worth 1.15pawns.

The value of the Exchange is influenced bytwo factors. First of all, the presence of moremajor pieces on the board favors the minorpiece. In general, with no major pieces traded,the Exchange value drops to 1½ pawns, and ifthe minor side has the bishop pair just onepawn makes things even. But with queens anda pair of rooks gone, the Exchange is worthslightly more than its nominal value of twopawns, or about 1½ when opposed by thebishop pair. Also important is the number ofpawns on the board, especially when theminor piece is the knight. With most of thepawns on the board the Exchange is worth

less; each pawn trade helps the rook. Rooksneed open files!

If you have a rook for a knight and two pawns,even though you are nominally a quarter pawnbehind 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 forceto the case of two minor pieces vs. rook andpawns; the side with the rook should trademajor pieces, even if he is a bit behind inmaterial.

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, thequeen is worth rook, minor piece, and 1½pawns.

the side without the queen wants to keep theextra rooks if possible.

Queen Versus Two Rooks

with two or more minors each, the queenneeds no pawns to equal two rooks.

Queen Versus 3 Minor Pieces

3 minor pieces versus a queen are worth ahalf-pawn more than the queen, unless the 3minors does not include the bishop pair, inwhich case, things are even.

48

Piece Relationships to Pawns

Rooks gain in value with every pawnexchange because rooks need open files to beeffective. Knights lose relative value witheach pawn exchange, as their value diminishesin open positions.

Average Scoring:

Pawn = 1 Bishop pair = + ½ pawnRook = 5 Bishop = 3 ¼ Knight = 3 ¼ Queen = 9 ¾

C. General Principles

C1. A spatial advantage in the opening phaseof the game is not an advantage if theopponent has a flexible and dynamic position.

C2. Closed positions nullify an initial lead indevelopment.

C3. The main Precept of the Tiger and Dragonis to Dominate every phase of the game andall areas of the board.

C4. We will dominate by creating dynamicimbalances 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 meansking-side attack.

C6B. Pawns on e6 and d5 means queen-sideattack.

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” theopponent in to a narrow central area of limitedactivity. 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 areacceptable. (Analyze any exchange in relationto the Valuation of Imbalances (B.).

C9. Attack Broken Links in the opponent’sposition, and eliminate any Broken Links inyour position (weak squares or pieces ofmaterial 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 betterth

than a rook.

C11. Knights need outposts that they can notbe easily driven from.

C12. A knight gains value if the importantpoints of the position are close together.

C13. Considerations of the Bishop Pair

C13A. The bishop pair dominates both whiteand black square complexes.

C13B. The bishop pair has the ability to easilyexchange a bishop to gain a favorable bishopvs. knight or bishop vs. bishop situation.

49

C13C. The bishop pair can coordinate in anattack on the enemy king.

C13D. The bishop pair has good chances todraw when down the exchange.

C13E. Always seek to open the position andexchange pawns down to 8 or less with thebishop pair.

C13F. Bishops are strong in the support ofpassed pawns.

C14. To battle against a bishop pair, build aseries of “blockades” on same-color squarecomplexes. This hinders the mobility of thebishops and prevents the position from beingopened up.

C15. With bishops of opposite color, the sidethat is attacking has the advantage.

C16. Defending a Position

C16A. Eliminate or adequately defend allBroken Links in your position.

C16B. 9 times out of 10 it is better to defendby counter-attacking (actively) than by apassive defense.

C16C. Do not open a file your opponent canclaim. (It is ok to allow an opponent to claima file if there is no way in to your positionfrom it.)

C16D. Build a “fortress”: A position in whichyour opponent has no way to break through. Ifthe player has only a small area to defend, itmay take a very great material superiority foryour opponent to win.

C16E. Drawing Mechanisms

C16EA. Tie the opponent to the defense of apawn. I.e. Establish threats against a pawn thatinhibit the opponent from moving freely andimproving his position.

C16EB. Tie down the opponent with piecethreats. I.e. establish a series of recurringthreats which inhibits the opponent frommoving freely or making progress.

C16EC. Create a passed pawn. I.e. Generate apassed pawn that the opponent must eitherguard against advance or blockade, inhibitingthe opponent’s progress in the position.

C16ED. Establish an “eternal” pin. I.e. A pinthat can not be broken or escaped from, andwhich impedes further progress by theopponent.

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 tocalculate all the variations, it is also possible,and often advisable, to think “schematically”in the end-game. I.e. Picture in your mind atarget position you would like to reach, thatyou feel would give you an advantage, thenwork out a plan of moves to get you there.

C17B. Prophylactic thought is important inend-games. Ask yourself often, “What is myopponent’s plan here?”

C17C. Unlike the opening, owning morespace on the board is an advantage in the end-game.

50

C17D. Having the initiative is important inend-games. It is important with bishops ofopposite color, in rook + knight end-games(and with knights in general) and in rook end-games, where it is even often acceptable tosacrifice some material to give a rook activityand the initiative.

C17E. In positions where you have a long-term or static advantage, and your opponenthas no means of counter-play, it is best toimprove your position in every possible waybefore closing in for the kill. I.e. bring all ofyour pieces in to play, and position them ontheir ideal or strongest squares...etc.

C17F. In the end-game, zug-zwang is acommon tool of the attacker. (And may proveto be an oft seen and prevalent concept inmany Tiger and Dragon games.)

C17G. It is important in end-games, to stayactive. In general, activate your pieces in thefollowing order: queen, rook, king, minorpiece and then pawns.

C17H. It is important in end-games, to restrictthe mobility of your opponent’s pieces andpawns if you can.

C17I. Of greatest practical importance are theking and rook. These pieces often play asignificant role in end-games, and it is oftenworth sacrificing a pawn to fully activatethem, in most end-games.

C17J. Rooks are not made to passively protectour own pawns, or to try and blockade enemypawns. Rooks should always be on the attackand should almost always reside behindpassed pawns, either our own or ouropponent’s

C17K. In double rook end-games, if you are

attacking, and want to diminish youropponent’s counter-play, exchange off onerook. Conversely, if you are defending an end-game, work to exchange off one rook to reacha rook and pawn end-game, or both rooks toreach a bishops of opposite color end-game.Both these end-game types almost alwaysoffer excellent drawing chances.

C17L. Calculate carefully before entering arook and pawn end-game if you are winning,as these end-games tend to be drawish.

C17M. The position of the king is often asignificant factor in the assessment of an end-game position. The fewer the pieces on theboard, the more important is the position ofthe king in evaluation of the position. Ingeneral, the more advanced and the moreactive your king is, the better.

C17N. Often a superior maneuver to executein an end-game is to play a move that activatesyour king, and at the same time, denies theopponent’s king access to key squares forattack or defense.

C17O. The king often has more than one routeto a destination square. Any move thataccomplishes multiple tasks, such asremaining in range of attack or defense ofpassed pawns, or limiting the moves of anopposing piece are the best routes to take.

C17P. Only trade down to a king and pawnend-game if you have calculated it to the endas either a win or draw for you.

C17Q. Passed pawns are important in end-games, playing either a diversionary or centralrole.

C17R. Passed pawns are created by advancinga greater number of pawns against a lessernumber of pawns, often leaving at least one

51

pawn a free road to a queening square. Ingeneral, it is best to advance first, the pawn inthe majority that is unopposed by anopponent’s pawn on its file.

C17S. Passed pawns can also be created bysacrificing a pawn to “break through” anopposing wall of pawns, or by sacrificing aminor piece for some pawns.

C17T. “Outside” passed pawns (pawnsdisconnected from the main group of forces,and far distant from the opponent’s pawns andpieces.) Are especially dangerous.

C17U. “Protected” (Guarded by anotherpawn) passed pawns are also valuable,especially in king and pawn end-games, wherethey are often decisive.

C17V. “Connected” (Two pawns on adjacentfiles that are un-opposed and can moveforward supporting each other) are also good.

C17W. Blockading passed pawns is oftenimportant. The best piece for blockading is aknight, which can reside on the square in frontof the pawn, and still attack nearby squares.

Technical End-Games

Our processes up to this point, have taken usthrough the opening and middle-game, andnow we arrive at the ending.

The end-game is really a zebra of a differentstripe. As such, we must develop separatealgorithms that will help us cope.

Piece Characteristics

Pawns

Doubled, backward or isolated pawns arealmost 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 pawnsor more favors knights.

A bishop pair is even stronger if no rooks areon the board.

Rooks

If pawns are on one wing only, this favorsknights and diminishes the power of rooks.

If there are pawns on both wings this favorsrooks and bishops.

If you have rooks + pieces versus Queen +rook, keep your rooks and exchange thepieces.

Rook + bishop is better than rook + knight.

Queen

A queen versus a rook and piece requires a“target rich” environment for the queen to bebetter. Lots of targets like weak pawns...etc.

52

King

In the end-game, the King is often anattacking piece, generally considered worth 4pawns.

Hierarchy of Mobilization

In general, mobilize forces in the followingorder: queens, rooks, kings, bishops andknights, pawns

Hierarchy of Piece Combinations

Rook + bishop > rook + knightQueen + knight > queen + bishop.Less than five pawns: Two bishops > twoknights or bishop and knight.More than five pawns: two knights > twobishops.

End-Game Praxis

What follows is a compilation of end-gamepraxis that is considered to be sufficient toplay an entire game of chess. Get to know itby 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

sdsdsdsddsdsdsds

ssdsdkdsdsdsdsdsdssdsdsdsddsdsIsdssdsdsdsddsdsdsds

In this position, the side to move gains theopposition by either 1.Ke4, or 1...Ke5. Youcan see that the other side cannot moveforward, and must give ground, allowing hisopponent to advance.

sdsdsdsddsdsdsdssdsdsdsddsdsisdssdsdPdsddsdsIsdssdsdsdsddsdsdsds

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 Kd89.e7+ Ke8 10.Ke6....stalemate.

Black was able to draw because he had theopposition. I.e., Black was able to place hisking on squares that prevented White frommaking progress.

Distant Opposition

If kings are on the same file, rank or diagonal,the player on the move can gain distantopposition by moving towards the opposingking so that there are an odd number ofsquares between them.

For kings that are on different files, ranks ordiagonals, the player with the move gainsdistant opposition by moving towards theopposing king and on to the square color that

53

is the same as the color square on which theopposing king resides.

SdsdsdsddsdsdsdssdsdsdsddsdsisdssdsdsdsddsdsIsdssdsdPdsddsdsdsds

In games of this sort, the salient factors are ifthe player with the pawn can get his king infront of his pawn, and who has the opposition.

With White to move, 1.Kf3 Kf5 2.Ke3 Ke53.Kd3 Kd5 draw...With Black to move,1...Kf5 2.Kd4 Ke6 3.Ke4 Kf6 4.Kd5 Ke75.Ke5 Kd7 6.Kf6 Ke8 7.Ke6 Kf8 8.e4 Ke89.e5 Kf8 10.Kd7 Kf7 11.e6+ and White wins

If the side with the pawn can ever get his kingtwo squares in front of the pawn, it is alwaysa win.

SdsdkdsddsdsdsdssdsdKdsddsdsdsdssdsdPdsd

White will gain the opposition and win

Fox in the Chicken Coup

sdsdsdsddsdsdsdssdkdsdpddsdsds)psIPdsds)dsdsdsdssdsdsdsddsdsdsds

In the diagram from the previous page, Blackmust eventually take White’s c pawn, leavingthe White king free to scoop up the otherBlack pawns: 1.c5 Kc7 2.Kb5 Kb7 3.c6+ Kc74.Kc5 Kc8 5.Kd6 Kd8 6.Ke6 Kc7 7.Kf6 Kxc68.Kxg6 Kd7 9.Kxh5 and wins...

Pawn Freeze

sdsdsdsddsdsdsdssisds0sd0sdsdsdsKdsdsdsddsdsdP)ssdsdsdsddsdsdsds

The 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 forBlack.

54

Trebuchet

dpIk)s

Whoever has the move, must leave thedefense of his pawn, and the pawn is lost.

SdsdsdsddsdsdsdssdsdsdpddsdpdsIssds)sdsdiPdsdsdssdsdsdsddsdsdsds

1.Kxg6 Kxb3 2.Kf5 Kc3 3.Ke5 Kc4, andBlack wins

Triangulation

sdsdsdsddsdsdsdssdsdkdpddsdpds)psds)s0s)ds)sdsdssdsdsIsddsdsdsds

Triangulation is a maneuver designed to giveyour opponent the move, and as a result, youthe opposition. 1.Kg2 f3+ 2.Kf2 Kf5 3.Kxf3and wins.

Outflanking Maneuver

Outflanking is a maneuver where the strongerside’s king moves to the side, placing a filebetween the kings. This allows the outflankingking to march forward towards the target,without allowing the opponent’s king to stepin front and take direct opposition. From theposition, White reaches a8, b8 or c8 by force:

SdsdsdsidsdsdsdssdsdsdsddsdsdsdssdsdsdsddsdsdsdssdsdsdsddsdsdsdK

1.Kh2 Kg8 2.Kg2 Kf8 3.Kf2 Ke8 4.Ke2 Kd85.Kd2 Kc8 6.Kc2 Kb8 7.Kb2 Ka8 8.Kc3 Kb79.Kb3 Kc7 10.Ka4 Kb6 11.Kb4 Ka6 12.Kc5Kb7 13.Kb5 Kc7 14.Ka6 Kb8 15.Kb6 Kc816.Ka7 and a8 next move. This exerciseteaches triangulation, opposition andoutflanking.

55

Minor Piece End-Games

Bishop + Rook Pawn vs. Lone King

If the bishop is on the same color as thequeening square of the rook pawn, the game isa win. If the bishop in on the opposite color ofthe rook pawn queening square, the game isdrawn, as the opponent’s king can not bedriven from the queening square.

Knight + Rook Pawn vs. Lone King

This end game is usually a win, with thefollowing exception:

sdsisdnddsdsdsdssdsdsdK0dsdsdsds

This position is drawn, as Black can not forcethe White king from h1 or g2.

Two Bishops vs. Lone King

Place the bishops on adjacent diagonals. Thistraps the opponent’s king in one sector of theboard. Continually shrink the diagonal box.Chase the defending king in to a corner, andthen deliver mate.

Bishop of Opposite Color vs. Bishop + 2Pawns

If the pawns are one file apart, the game isdrawn:

sdsdsdsddsdsisdssdsdPdsddsdsdsIssdBdsdPddsgsdsdssdsdsdsddsdsdsds

1.Kh6 Bb2 2.g5 Bc3 3.g6 Kf8 4.Kg5 Bb25.Kf5 Bc3 6.Ke4 Bb2 7.Kd5 Ke7, Whitemakes no headway: Draw.

In general, if the pawns are more than one fileapart, it is a win. However, the defending sidecan still draw if his bishop can freeze bothpawns:

56

sdsdsdsddsdsdsdssds)sdkddsdsdsdssdsGKdsddsdsds)bsdsdsdsddsdsdsds

Both pawns are advancing to white squares, sothe White bishop can not help in theiradvance. The Black bishop covers bothsquares the pawns can advance to,simultaneously, and Black’s king simplyfollows the White king back and forth,stopping and progress.

It can also be a drawn game, if one of thepawns is a rook pawn and has a queeningsquare of the same color as the defendingbishop.

SdsdsdsddsdkdsdssdsdsdPd)sdbdsdssdsdsdKddsGsdsdssdsdsdsddsdsdsds

1.Kg5 Kd6 2.Kh6 Kc6 3.Kh7 Kb7 4.g7 Ka85.g8 = Q Bxg8 6.Kxg8....draw.

If the pawns are connected, the defending sidecan draw by attacking the pawns and drivingthem forward, and always tying the attackingking to the defense of a pawn.

sdsdsdsddsdsds0ssdsds0sddsdsdsdksGbdsdsddsdsdsIssdsdsdsddsdsdsds

1...Kg5 2.Bf8 g6 3.Be7 Kf5 4.Bd8 Ke6 5.Kf4,and Black must advance his pawns, whichleads to positions like the diagram on the nextpage.

sdsdsdsddsdsdsdssdsdsdsddsdkdsdssds0pdbddsdsdsdssdsIsGsddsdsdsds

This position is dead drawn. Any time Blacktries something fancy with his king, White justattacks a pawn, forcing the king back.

57

Bishop of the Same Color vs. Bishop +Pawn

A bishop, rook, or knight pawn is a win. Aqueen or king pawn is a draw, if the defendingking is nearby. In the diagram, Black drawsbecause his king and bishop cover the d7square. White’s king must defend the pawnand Black will never run out of tempi, sincehe can shuffle his bishop back and forth.

SdsIsdsddsds)sdssdsisdsddBdsdsdbsdsdsdsddsdsdsdssdsdsdsddsdsdsds

Rook End-Games

The Lucena Position

sdsdKdsddsds)sissdsdsdsddsdsdsdssdsdsdsddsdsdsdssdsds$sddsdrdsds

1.Rg2+ Kh7 2.Rg4!(This is referred to as“building the bridge”.) Rd2 3.Kf7 Rf2+ 4.Ke6Re2+ 5.Kf6 Rf2+ 6.Ke5 Re2+ 7.Re4 andwins.

The Lucena works for center, knight andbishop pawns. For rook pawns, the defendingking must be at least four files away.

The Philidor Position

sdsds$sddsdkds4ssdsdsdsddsIPdsdssdsdsdsddsdsdsdssdsdsdsddsdsdsds

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 kingadvance, force the pawn to advance, and thereis no shelter for the attacking king fromperpetual check.

58

Another Rook End-Game to Remember

sisdsds4dsdsdsdss)sdsdsddKdsdsdssdsdsdRddsdsdsdssdsdsdsddsdsdsds

This Black position against a rook or knightpawn is always drawn. Black just shuffles hisking or rook back and forth, and there is noway White can break through.

Rook vs. Rook + Two Connected Pawns

1. Advance your pawns together. Theywill defend each other and can alsoprovide shelter for the king.

2. Keep your king and pawns in closecontact.

3. Make sure your pawns can shield theking from checks.

4. Push the enemy king back, makingsure the first 3 considerations are met.

5. With the defending king on the backrank, move your rook (Which shouldbe 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 ofrooks, 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 Rankth

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 veryadvantageously placed.

Sdsdsdsddsdsdsdssdsdsdsddsdsdsdssdsdsdsddsdsds!ssdsds0sddsdsdsis

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

59

sdsdsdsdIQdsdsdssdsdsdsddsdsdsdssdsdsdsddsdsdsdspdsdsdsdisdsdsds

A possible exception to the rule. White winswith 1.Kb6 Kb2 2.Kc5+ Kc2 3.Qg2+ Kb14.Kb4 a1 = Q 5.Kc3, and White wins due toQf2 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. Theopponent’s king is forced in front of the pawn,and the attacker can now move his king overand win the pawn.

Fortresses

When you hold a weaker position in game, orare down material, always be aware of thepossibility of building a fortress. A fortress is aposition that your opponent can not penetrate:

sdsdsdsddsdbisdssdsdsdsddsdsdrdss)s!s)sddsdsIsdssdsdsdsddsdsdsds

In this position, Black has created animpregnable fortress. The rook and bishopprevent the pawns from advancing, and theattacking king can not penetrate. It is a draw.

60

About the Author

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

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

member of the International High I.Q. Society.

He can be contacted at:

walt123@verizon.net

61

Donations Gladly Accepted

If you liked this book, please consider making a donation. I know it will take a fewminutes of your time, but even a dollar or two would be very helpful.

Your money will be used to fund future projects like this one.

You can make a donation to my PayPal account (e-mail) at:

walt123@verizon.net

Specify the donation as the “transfer of money to friend....”

Thank-you for your support.