# Understanding Minor Piece Endgames

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• A Combinatorial Game Theoretic Analysis of Chess Endgames
A COMBINATORIAL GAME THEORETIC ANALYSIS OF CHESS ENDGAMES QINGYUN WU, FRANK YU,¨ MICHAEL LANDRY 1. Abstract In this paper, we attempt to analyze Chess endgames using combinatorial game theory. This is a challenge, because much of combinatorial game theory applies only to games under normal play, in which players move according to a set of rules that deﬁne the game, and the last player to move wins. A game of Chess ends either in a draw (as in the game above) or when one of the players achieves checkmate. As such, the game of chess does not immediately lend itself to this type of analysis. However, we found that when we redeﬁned certain aspects of chess, there were useful applications of the theory. (Note: We assume the reader has a knowledge of the rules of Chess prior to reading. Also, we will associate Left with white and Right with black). We ﬁrst look at positions of chess involving only pawns and no kings. We treat these as combinatorial games under normal play, but with the modiﬁcation that creating a passed pawn is also a win; the assumption is that promoting a pawn will ultimately lead to checkmate. Just using pawns, we have found chess positions that are equal to the games 0, 1, 2, ?, ", #, and Tiny 1. Next, we bring kings onto the chessboard and construct positions that act as game sums of the numbers and inﬁnitesimals we found. The point is that these carefully constructed positions are games of chess played according to the rules of chess that act like sums of combinatorial games under normal play.
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• ZUGZWANGS in CHESS STUDIES G.Mcc. Haworth,1 H.M.J.F. Van Der
See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/290629887 Zugzwangs in Chess Studies Article in ICGA journal · June 2011 DOI: 10.3233/ICG-2011-34205 CITATION READS 1 2,142 3 authors: Guy McCrossan Haworth Harold M.J.F. Van der Heijden University of Reading Gezondheidsdienst voor Dieren 119 PUBLICATIONS 354 CITATIONS 49 PUBLICATIONS 1,232 CITATIONS SEE PROFILE SEE PROFILE Eiko Bleicher 7 PUBLICATIONS 12 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Chess Endgame Analysis View project The Skilloscopy project View project All content following this page was uploaded by Guy McCrossan Haworth on 23 January 2017. The user has requested enhancement of the downloaded file. 82 ICGA Journal June 2011 NOTES ZUGZWANGS IN CHESS STUDIES G.McC. Haworth,1 H.M.J.F. van der Heijden and E. Bleicher Reading, U.K., Deventer, the Netherlands and Berlin, Germany ABSTRACT Van der Heijden’s ENDGAME STUDY DATABASE IV, HHDBIV, is the definitive collection of 76,132 chess studies. The zugzwang position or zug, one in which the side to move would prefer not to, is a frequent theme in the literature of chess studies. In this third data-mining of HHDBIV, we report on the occurrence of sub-7-man zugs there as discovered by the use of CQL and Nalimov endgame tables (EGTs). We also mine those Zugzwang Studies in which a zug more significantly appears in both its White-to-move (wtm) and Black-to-move (btm) forms. We provide some illustrative and extreme examples of zugzwangs in studies.
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• 1. Development
By Natalie & Leon Taylor 1. DEVELOPMENT ID Shelf Title Author Brief Description No. No. 1 1.1 Chess Made Easy C.J.S. Purdy & G. Aimed for beginners, Koshnitsky 1942, 64 pages. 2 1.2 The Game of Chess H.Golombek Advance from beginner, 1945, 255pages 3 1.3 A Guide to Chess Ed.Gerard & C. Advance from beginner Verviers 1969, 156 pages. 4 1.4 My System Aron Nimzovich Theory of chess to improve yourself 1973, 372 pages 5 1.5 Pawn Power in Chess Hans Kmoch Chess strategy using pawns. 1969, 300 pages 6 1.6 The Most Instructive Games Irving Chernev 62 annotated masterpieces of modern chess strat- of Chess Ever Played egy. 1972, 277 pages 7 1.7 The Development of Chess Dr. M. Euwe Annotated games explaining positional play, Style combination & analysis. 1968, 152pgs 8 1.8 Three Steps to Chess MasteryA.S. Suetin Examples of modern Grandmaster play to im- prove your playing strength. 1982, 188pgs 9 1.9 Grandmasters of Chess Harold C. Schonberg A history of modern chess through the lives of these great players. 1973, 302 pages 10 1.10 Grandmaster Preparation L. Polugayevsky How to prepare technically and psychologically for decisive encounters where everything is at stake. 1981, 232 pages 11 1.11 Grandmaster Performance L. Polugayevsky 64 games selected to give a clear impression of how victory is gained. 1984, 174 pages 12 1.12 Learn from the Grandmasters Raymond D. Keene A wide spectrum of games by a no. of players an- notated from different angles. 1975, 120 pgs 13 1.13 The Modern Chess Sacrifice Leonid Shamkovich ‘A thousand paths lead to delusion, but only one to the truth.’ 1980, 214 pages 14 1.14 Blunders & Brilliancies Ian Mullen and Moe Over 250 excellent exercises to asses your apti- Moss tude for brilliancy and blunder.
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• Weltenfern a Commented Selection of Some of My Works Containing 149 Originals
Weltenfern A commented selection of some of my works containing 149 originals by Siegfried Hornecker Dedicated to the memory of Dan Meinking and Milan Velimirovi ć who both encouraged me to write a book! Weltenfern : German for other-worldly , literally distant from the world , describing a person’s attitude In the opinion of the author the perfect state of mind to compose chess problems. - 1 - Index 1 – Weltenfern 2 – Index 3 – Legal Information 4 – Preface 6 – 20 ideas and themes 6 – Chapter One: A first walk in the park 8 – Chapter Two: Schachstrategie 9 – Chapter Three: An anticipated study 11 – Chapter Four: Sleepless nights, or how pain was turned into beauty 13 – Chapter Five: Knightmares 15 – Chapter Six: Saavedra 17 – Chapter Seven: Volpert, Zatulovskaya and an incredible pawn endgame 21 – Chapter Eight: My home is my castle, but I can’t castle 27 – Intermezzo: Orthodox problems 31 – Chapter Nine: Cooperation 35 – Chapter Ten: Flourish, Knightingale 38 – Chapter Eleven: Endgames 42 – Chapter Twelve: MatPlus 53 – Chapter 13: Problem Paradise and NONA 56 – Chapter 14: Knight Rush 62 – Chapter 15: An idea of symmetry and an Indian mystery 67 – Information: Logic and purity of aim (economy of aim) 72 – Chapter 16: Make the piece go away 77 – Chapter 17: Failure of the attack and the romantic chess as we knew it 82 – Chapter 18: Positional draw (what is it, anyway?) 86 – Chapter 19: Battle for the promotion 91 – Chapter 20: Book Ends 93 – Dessert: Heterodox problems 97 – Appendix: The simple things in life 148 – Epilogue 149 – Thanks 150 – Author index 152 – Bibliography 154 – License - 2 - Legal Information Partial reprint only with permission.
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• Grand Prix Proves to Be Right Formula
7.Ng1–f3 0–0 22... e7-e6 A better idea was 7...Bc8-g4, 23.Qg6-h7+ Kg8-f7 CHESS getting rid of the light-squared 24.f5xe6+ Bc8xe6 July 5th 2008 bishop which is hard to ﬁnd 25.Rh3-h6 Qc7-e5 a good post for. Another 26.Qh7-g6+ Kf7-g8 Michael interesting option was 7...c5-c4, 27.Rf1xf6 Qe5-d4+ trying to create counterplay. 28.Rf6-f2 Adams Even with what feels like 8.0–0 b7-b6 an overwhelming position, Black doesn't sense any danger it is important to maintain and makes some quiet moves, concentration. The rook retreat but he should have paid more forced resignation but the attention to White’s plans. blunder 28.Kg1–h1 Qd4xf6 Grand Prix As we shall see he can quickly 29.Qg6xf6 Rd8-f8 would lead develop a strong initiative on to a roughly level position. the kingside. proves to be 1–0 9.Qd1–e1 Bc8-g4 right formula The worst possible moment The 2nd edition of Secrets of for this move as the knight is Spectacular Chess by Jonathan no longer pinned. 9...Nf6-d7 Levitt and David Friedgood Gawain Jones is the latest in was preferable although, after (Everyman, £14.99) is a slightly a long line of English players 10.f4-f5 there is trouble ahead expanded version of the 1999 who have specialised in for the Black monarch. original, in which they analysed meeting the Sicilian in an the beauty in chess. oﬀ-beat manner. He has 10.Nf3-e5 Qd8-c7 The book is especially shared his expertise in his 11.Qe1–h4 Bg4-e6 interesting to players with little ﬁrst book, Starting Out: 12.Ne5-f3 h7-h6 experience of studies who will Sicilian Grand Prix Attack 12...Be6-c8 13.f4-f5 is no discover many paradoxical (Everyman, £14.99).
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• I Make This Pledge to You Alone, the Castle Walls Protect Our Back That I Shall Serve Your Royal Throne
AMERA M. ANDERSEN Battlefield of Life “I make this pledge to you alone, The castle walls protect our back that I shall serve your royal throne. and Bishops plan for their attack; My silver sword, I gladly wield. a master plan that is concealed. Squares eight times eight the battlefield. Squares eight times eight the battlefield. With knights upon their mighty steed For chess is but a game of life the front line pawns have vowed to bleed and I your Queen, a loving wife and neither Queen shall ever yield. shall guard my liege and raise my shield Squares eight times eight the battlefield. Squares eight time eight the battlefield.” Apathy Checkmate I set my moves up strategically, enemy kings are taken easily Knights move four spaces, in place of bishops east of me Communicate with pawns on a telepathic frequency Smash knights with mics in militant mental fights, it seems to be An everlasting battle on the 64-block geometric metal battlefield The sword of my rook, will shatter your feeble battle shield I witness a bishop that’ll wield his mystic sword And slaughter every player who inhabits my chessboard Knight to Queen’s three, I slice through MCs Seize the rook’s towers and the bishop’s ministries VISWANATHAN ANAND “Confidence is very important—even pretending to be confident. If you make a mistake but do not let your opponent see what you are thinking, then he may overlook the mistake.” Public Enemy Rebel Without A Pause No matter what the name we’re all the same Pieces in one big chess game GERALD ABRAHAMS “One way of looking at chess development is to regard it as a fight for freedom.
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• Do First Mover Advantages Exist in Competitive Board Games: the Importance of Zugzwang
DO FIRST MOVER ADVANTAGES EXIST IN COMPETITIVE BOARD GAMES: THE IMPORTANCE OF ZUGZWANG Douglas L. Micklich Illinois State University [email protected] ABSTRACT to the other player(s) in the game (Zagal, et.al., 2006) Examples of such games are chess and Connect-Four. The players try to The ability to move first in competitive games is thought to be secure some sort of first-mover advantage in trying to attain the sole determinant on who wins the game. This study attempts some advantage of position from which a lethal attack can be to show other factors which contribute and have a non-linear mounted. The ability to move first in competitive board games effect on the game’s outcome. These factors, although shown to has thought to have resulted more often in a situation where that be not statistically significant, because of their non-linear player, the one moving first, being victorious. The person relationship have some positive correlations to helping moving first will normally try to take control from the outset and determine the winner of the game. force their opponent into making moves that they would not otherwise have made. This is a strategy which Allis refers to as “Zugzwang”, which is the principle of having to play a move INTRODUCTION one would rather not. To be able to ensure that victory through a gained advantage In Allis’s paper “A Knowledge-Based Approach of is attained, a position must first be determined. SunTzu in the Connect-Four: The Game is Solved: White Wins”, the author “Art of War” described position in this manner: “this position, a states that the player of the black pieces can follow strategic strategic position (hsing), is defined as ‘one that creates a rules by which they can at least draw the game provided that the situation where we can use ‘the individual whole to attack our player of the red pieces does not start in the middle column (the rival’s) one, and many to strike a few’ – that is, to win the (Allis, 1992).
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• Fundamental Endings CYRUS LAKDAWALA
First Steps : Fundamental Endings CYRUS LAKDAWALA www.everymanchess.com About the Author Cyrus Lakdawala is an International Master, a former National Open and American Open Cham- pion, and a six-time State Champion. He has been teaching chess for over 30 years, and coaches some of the top junior players in the U.S. Also by the Author: Play the London System A Ferocious Opening Repertoire The Slav: Move by Move 1...d6: Move by Move The Caro-Kann: Move by Move The Four Knights: Move by Move Capablanca: Move by Move The Modern Defence: Move by Move Kramnik: Move by Move The Colle: Move by Move The Scandinavian: Move by Move Botvinnik: Move by Move The Nimzo-Larsen Attack: Move by Move Korchnoi: Move by Move The Alekhine Defence: Move by Move The Trompowsky Attack: Move by Move Carlsen: Move by Move The Classical French: Move by Move Larsen: Move by Move 1...b6: Move by Move Bird’s Opening: Move by Move Petroff Defence: Move by Move Fischer: Move by Move Anti-Sicilians: Move by Move Opening Repertoire ... c6 First Steps: the Modern 3 Contents About the Author 3 Bibliography 5 Introduction 7 1 Essential Knowledge 9 2 Pawn Endings 23 3 Rook Endings 63 4 Queen Endings 119 5 Bishop Endings 144 6 Knight Endings 172 7 Minor Piece Endings 184 8 Rooks and Minor Pieces 206 9 Queen and Other Pieces 243 4 Introduction Why Study Chess at its Cellular Level? A chess battle is no less intense for its lack of brevity. Because my messianic mission in life is to make the chess board a safer place for students and readers, I break the seal of confessional and tell you that some students consider the idea of enjoyable endgame study an oxymoron.
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• Sarajevo 1967 ° "' 1 '"
Grondmaster ayme, lefl, explafntnq the qallle 01 d»eu to 80"011, c.nter, and USSR Champion Stein, Byrne later floated SteIn 10 anOfher leuon o"er the board. accountmq tor Sleln's only lou 01 lhe lournamenl, SARAJEVO 1967 I 2 3 4 5 6 7 8 A 10 11 12 13 14 15 16 W L D !: ~~::: :::::::::::::::::::::.:.... .::: :' .' ...: . ~ ~~, ---.-~;.-.::~;--:~;-"~,==~: =~~f. =~"tl =j~~=;~t="ii"'\'----;.~:;:--;"-;-·I - ::- -;:===-;~'----;~'---";:""~=- 10 ~ .4- ~ 3. tknko , If.! Y.i: % 0 I 0 1 1 I ~ I \ _ ;-1 _~'~ ,;--;;-, - \1)-5 x 1h 'h ':-l - '--'' 1 I I 1 'h I 0 I ,';-,,'c-- -:';-_-- 1().5_ °1 '""' 1h x 0 0 n 1 n I ¥, I 1 1 I ,..' .....;:3_ ~ 9Ik.5 ~ h 1 x I,i h ~ 1 n h I I,i 1;.--:1_ _ 5 1 9 9h . ~~ ° "1 h 1 I,i x 0 I 'h 0 1 "':"''-''''7----:-1 t 6" 5'- - 8'7 .6% o o lit liz 1 x 1,1: .., .., 1 "':t I t ¥l -.' , 2 ~ 81.1 f1lh 1 0 0 n 0 If. :< 0 0 1 J I n _ -;-I _ ';--;-6_ ,_ _ ,.. - 11 Duc1n tcin .. .. .... ... n ~ ~ ~ ~ : ~ "~'- : : ~ ~ ~ --,~,,-:~:-~ ----.-~ :: ~! 12. Ja.noS('vic .... ... ... ... .. ~_-;";... _~ ~ _Ifl "1 ;;:0'--;,;..0 _ 0,,-:"':-"''7--;;:''--''''' 1 ~"''-.;.I _ _.;:-' _ ;!i 8 f.. 9 13. Pict%.Sch ................................... \o!t Vr 'tit;. _ ";. ,-~O:- 0 n 'fl 0 0 . __1 'h x 0 1:'.1 0 1 6 --;8- - - 5- 10 14. Bogdanuvic .. .................. Y.t 0 0 0 0 lit Yt 0 0 Yt 1 0 I x 0 h 2 8 5 _ _ " "1.100" :~ : ~:~;:~.
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• Dvoretsky Lessons 12
The Instructor Tragicomedies in Pawn Endgames “Pawn endgames are rare birds in practice. Players avoid them, because they do not like them, because they do not understand them. It’s certainly no secret that pawn endings are ‘terra incognita’ - even for many masters, right up to the level of grandmasters and world champions.” N. Grigoriev Herewith, I offer proof that these words, spoken by a famous expert on pawn endings, are true. Without commentary, I give below the final moves of some actual games, and offer the readers the chance to comment on them, to uncover all the mistakes committed by both players. The endgames you will be dealing with here are not all that difficult; but still, the players on both sides have The provided you with plenty of opportunities for critical commentary. 1...Kf8 2. Qf5+ Qxf5 3. gf Kg7 4. c4 f3 5. h6+ Kxh6 6. c5 dc 7. f6 Kg6 Instructor White resigned. Mark Dvoretsky 1...g5 2. Kf3 Kd5 3. c6 Kd6 4. Ke4 a6 5. ba Kxc6 6. Kf3 Kb6 7. h4 gh 8. Kg4 Kxa6 9. Kxh4 Kb6 10. Kg4 Kc6 11. h4 Kd6. White resigned. file:///C|/Cafe/Dvoretsky/dvoretsky.htm (1 of 9) [9/11/2001 7:09:02 AM] The Instructor 1. Kh7 Kf7 2. Kh8 Kf8 3. g5. Black resigned. 1. Kg5 Kf8 2. Kxf5 Kf7 3. Kg4 Kf6 4. Kf4 Kf7 5. Kf5 Ke7 6. Ke5 Kf7 7. Kd6 Kf6 8. Kd7 Kf7 9. h6 Kg6 10. f4 Kf7 11. f5 Kf6 Drawn Gazic - Petursson European Junior Championship, Groningen 1978/79 The draw is obvious after 1...Kh8! Black mistakenly allowed the trade of queens.
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• Dvoretsky Lessons 5
The Instructor Averbakh I AM IN THE PROCESS of writing an instructional endgame book. In the course of my work on this book, besides the rather extensive materials I had already accumulated, I of course made use of works by other authors, including the multi-volumed endgame set by Yuri Averbakh. Upon testing this material I found that an amazing number of endgames, including some well-known ones which have migrated from book to book, have been poorly analyzed and incorrectly evaluated. The following example must set some sort of record. Yuri Averbakh, Chess Endings (Rook) Page 299, Position No. 734 (See The Diagram) Instructor Black to move First, I will give Averbakh’s commentaries. Mark Dvoretsky 1... Ra2! "The only move! 1...h5 is a mistake, because of 2. Kd6! (2. Re8 Ra6+! 3. Kxf5 Rxa7 4. Kg5 Ra5+ 5. Kf4 Ra2 is only a draw) 2... Kh7 3. Ke7 Kg7 4. Ke6 Ra2 5. Kxf5 Rxf2+ (5...Ra5+ 6. Kf4 Kh7 7. Rf8! Rxa7 8. Kg5 Ra5+ 9. Rf5 and wins) 6. Kg5 Ra2 7. Kxh5 Ra4 8. Re8 Rxa7 9. Kxg4, and White wins." 2. Kxf5 Rxf2+ 3. Kxg4 Ra2 Draw Before reading what follows, I propose that the reader perform the following exercise (in the style of the outstanding John Nunn’s Chess Puzzle Book): How many of the moves that Averbakh gives as best - or at least normal - are really mistakes that change the outcome of the game? And now, let us begin our analysis. After 1...Ra2, White wins: instead of 2. Kxf5? [1 mistake], he plays 2.
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• This Multi-Media Resource List, Compiled by Gina Blume Of
Delve Deeper into Brooklyn Castle A film by Katie Dellamaggiore This list of fiction and Lost Generation-- and What Eight-time National Chess nonfiction books, compiled We Can Do About It. New Champion as a youth and by Erica Bess, Susan Conlon York: Harper Perennial, subject of the film Searching for and Hanna Lee of Princeton 2013. Froymovich discusses the Bobby Fischer (1993), Josh Public Library, provides a impact of the 2008 recession on Waitzkin later expanded his range of perspectives on the millennials (defined as people horizons and studied martial issues raised by the POV being born between 1976 and arts, eventually earning several documentary Brooklyn 2000) and presents ideas such National and World Castle. as political activism and creative Championship titles. In this entrepreneurship as potential book, he shares his personal Brooklyn’s I.S. 318, a solutions to the long-term side journey to the top—twice—and powerhouse in junior high chess effects of financial crisis. his reflections on principles of competitions, has won more learning and performance. than 30 national championships, Kozol, Jonathan. Savage the most of any school in the Inequalities: Children in Weinreb, Michael. The Kings country. Its 85-member squad America’s Schools. New of New York: A Year Among boasts so many strong players York: Crown, 1991. National the Geeks, Oddballs, and that the late Albert Einstein, a Book Award-winning author Geniuses Who Make Up dedicated chess maven, would Jonathan Kozol presents his America’s Top High School rank fourth if he were on the shocking account of the Chess Team.
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