Chess Endgames: 6-Man Data and Strategy
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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. -
Social Conflict and Sacrificial Rhetoric
CHRISTOPHER ROBERTS Social Conflict and Sacrificial Rhetoric Luther’s Discursive Intervention and the Religious Division of Labor Introduction ‘Sacrifice’ is a religious term whose use extends far beyond the church door. People from all walks of life speak of ‘sacrifice’ when they want to evoke an irreducible conflict in the relations between self, family, and soci- ety. In America, hardly a speech goes by without political leaders insisting upon the necessity and virtue of sacrifice, but rarely will they clarify who is sacrificing what, and to whom. Indeed, this is not only an American phenomenon, as a number of recent texts examining ‘sacrifice’ as a term in various national discourses have shown.1 Such a political and economic deployment of a religious figure demands interpretation, for not only does the rhetoric of sacrifice span the globe,2 it constitutes a problem with a long genealogy. As a key moment in the Western segment of this genealogy, this article will examine the way that Luther’s exegetical work rhetoricalized sacrifice, and, in doing so, constructed a new discursive position, the pas- tor as anti-sophist, or parrhesiast, in the religious division of labor. The overarching question for this inquiry is how did a particular re- ligious ritual like sacrifice come to serve as such a widespread rhetorical figure? When faced with the immense historical distance between, first, the public destruction of wealth or butchering of an animal, and, last, a speech act describing non-ritual phenomena as a sacrifice, one measures the distance not only in years but also in religious and cultural transform- ation. -
CONTENTS Contents
CONTENTS Contents Symbols 5 Preface 6 Introduction 9 1 Glossary of Attacking and Strategic Terms 11 2 Double Attack 23 2.1: Double Attacks with Queens and Rooks 24 2.2: Bishop Forks 31 2.3: Knight Forks 34 2.4: The Í+Ì Connection 44 2.5: Pawn Forks 45 2.6: The Discovered Double Attack 46 2.7: Another Type of Double Attack 53 Exercises 55 Solutions 61 3 The Role of the Pawns 65 3.1: Pawn Promotion 65 3.2: The Far-Advanced Passed Pawn 71 3.3: Connected Passed Pawns 85 3.4: The Pawn-Wedge 89 3.5: Passive Sacrifices 91 3.6: The Kamikaze Pawn 92 Exercises 99 Solutions 103 4 Attacking the Castled Position 106 4.1: Weakness in the Castled Position 106 4.2: Rooks and Files 112 4.3: The Greek Gift 128 4.4: Other Bishop Sacrifices 133 4.5: Panic on the Long Diagonal 143 4.6: The Knight Sacrifice 150 4.7: The Exchange Sacrifice 162 4.8: The Queen Sacrifice 172 Exercises 176 Solutions 181 5 Drawing Combinations 186 5.1: Perpetual Check 186 5.2: Repetition of Position 194 5.3: Stalemate 197 5.4: Fortress and Blockade 202 5.5: Positional Draws 204 Exercises 207 Solutions 210 6 Combined Tactical Themes 213 6.1: Material, Endings, Zugzwang 214 6.2: One Sacrifice after Another 232 6.3: Extraordinary Combinations 242 6.4: A Diabolical Position 257 Exercises 260 Solutions 264 7 Opening Disasters 268 7.1: Open Games 268 7.2: Semi-Open Games 274 7.3: Closed Games 288 8 Tactical Examination 304 Test 1 306 Test 2 308 Test 3 310 Test 4 312 Test 5 314 Test 6 316 Hints 318 Solutions 320 Index of Names 331 Index of Openings 335 THE ROLE OF THE PAWNS 3 The Role of the Pawns Ever since the distant days of the 18th century 3.1: Pawn Promotion (let us call it the time of the French Revolution, or of François-André Danican Philidor) we have known that “pawns are the soul of chess”. -
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. -
No. 123 - (Vol.VIH)
No. 123 - (Vol.VIH) January 1997 Editorial Board editors John Roycrqfttf New Way Road, London, England NW9 6PL Edvande Gevel Binnen de Veste 36, 3811 PH Amersfoort, The Netherlands Spotlight-column: J. Heck, Neuer Weg 110, D-47803 Krefeld, Germany Opinions-column: A. Pallier, La Mouziniere, 85190 La Genetouze, France Treasurer: J. de Boer, Zevenenderdrffi 40, 1251 RC Laren, The Netherlands EDITORIAL achievement, recorded only in a scientific journal, "The chess study is close to the chess game was not widely noticed. It was left to the dis- because both study and game obey the same coveries by Ken Thompson of Bell Laboratories rules." This has long been an argument used to in New Jersey, beginning in 1983, to put the boot persuade players to look at studies. Most players m. prefer studies to problems anyway, and readily Aside from a few upsets to endgame theory, the give the affinity with the game as the reason for set of 'total information' 5-raan endgame their preference. Your editor has fought a long databases that Thompson generated over the next battle to maintain the literal truth of that ar- decade demonstrated that several other endings gument. It was one of several motivations in might require well over 50 moves to win. These writing the final chapter of Test Tube Chess discoveries arrived an the scene too fast for FIDE (1972), in which the Laws are separated into to cope with by listing exceptions - which was the BMR (Board+Men+Rules) elements, and G first expedient. Then in 1991 Lewis Stiller and (Game) elements, with studies firmly identified Noam Elkies using a Connection Machine with the BMR realm and not in the G realm. -
Chess Endgame News
Chess Endgame News Article Published Version Haworth, G. (2014) Chess Endgame News. ICGA Journal, 37 (3). pp. 166-168. ISSN 1389-6911 Available at http://centaur.reading.ac.uk/38987/ It is advisable to refer to the publisher’s version if you intend to cite from the work. See Guidance on citing . Publisher: The International Computer Games Association All outputs in CentAUR are protected by Intellectual Property Rights law, including copyright law. Copyright and IPR is retained by the creators or other copyright holders. Terms and conditions for use of this material are defined in the End User Agreement . www.reading.ac.uk/centaur CentAUR Central Archive at the University of Reading Reading’s research outputs online 166 ICGA Journal September 2014 CHESS ENDGAME NEWS G.McC. Haworth1 Reading, UK This note investigates the recently revived proposal that the stalemated side should lose, and comments further on the information provided by the FRITZ14 interface to Ronald de Man’s DTZ50 endgame tables (EGTs). Tables 1 and 2 list relevant positions: data files (Haworth, 2014b) provide chess-line sources and annotation. Pos.w-b Endgame FEN Notes g1 3-2 KBPKP 8/5KBk/8/8/p7/P7/8/8 b - - 34 124 Korchnoi - Karpov, WCC.5 (1978) g2 3-3 KPPKPP 8/6p1/5p2/5P1K/4k2P/8/8/8 b - - 2 65 Anand - Kramnik, WCC.5 (2007) 65. … Kxf5 g3 3-2 KRKRB 5r2/8/8/8/8/3kb3/3R4/3K4 b - - 94 109 Carlsen - van Wely, Corus (2007) 109. … Bxd2 == g4 7-7 KQR..KQR.. 2Q5/5Rpk/8/1p2p2p/1P2Pn1P/5Pq1/4r3/7K w Evans - Reshevsky, USC (1963), 49. -
Multilinear Algebra and Chess Endgames
Games of No Chance MSRI Publications Volume 29, 1996 Multilinear Algebra and Chess Endgames LEWIS STILLER Abstract. This article has three chief aims: (1) To show the wide utility of multilinear algebraic formalism for high-performance computing. (2) To describe an application of this formalism in the analysis of chess endgames, and results obtained thereby that would have been impossible to compute using earlier techniques, including a win requiring a record 243 moves. (3) To contribute to the study of the history of chess endgames, by focusing on the work of Friedrich Amelung (in particular his apparently lost analysis of certain six-piece endgames) and that of Theodor Molien, one of the founders of modern group representation theory and the first person to have systematically numerically analyzed a pawnless endgame. 1. Introduction Parallel and vector architectures can achieve high peak bandwidth, but it can be difficult for the programmer to design algorithms that exploit this bandwidth efficiently. Application performance can depend heavily on unique architecture features that complicate the design of portable code [Szymanski et al. 1994; Stone 1993]. The work reported here is part of a project to explore the extent to which the techniques of multilinear algebra can be used to simplify the design of high- performance parallel and vector algorithms [Johnson et al. 1991]. The approach is this: Define a set of fixed, structured matrices that encode architectural primitives • of the machine, in the sense that left-multiplication of a vector by this matrix is efficient on the target architecture. Formulate the application problem as a matrix multiplication. -
Chess-Training-Guide.Pdf
Q Chess Training Guide K for Teachers and Parents Created by Grandmaster Susan Polgar U.S. Chess Hall of Fame Inductee President and Founder of the Susan Polgar Foundation Director of SPICE (Susan Polgar Institute for Chess Excellence) at Webster University FIDE Senior Chess Trainer 2006 Women’s World Chess Cup Champion Winner of 4 Women’s World Chess Championships The only World Champion in history to win the Triple-Crown (Blitz, Rapid and Classical) 12 Olympic Medals (5 Gold, 4 Silver, 3 Bronze) 3-time US Open Blitz Champion #1 ranked woman player in the United States Ranked #1 in the world at age 15 and in the top 3 for about 25 consecutive years 1st woman in history to qualify for the Men’s World Championship 1st woman in history to earn the Grandmaster title 1st woman in history to coach a Men's Division I team to 7 consecutive Final Four Championships 1st woman in history to coach the #1 ranked Men's Division I team in the nation pnlrqk KQRLNP Get Smart! Play Chess! www.ChessDailyNews.com www.twitter.com/SusanPolgar www.facebook.com/SusanPolgarChess www.instagram.com/SusanPolgarChess www.SusanPolgar.com www.SusanPolgarFoundation.org SPF Chess Training Program for Teachers © Page 1 7/2/2019 Lesson 1 Lesson goals: Excite kids about the fun game of chess Relate the cool history of chess Incorporate chess with education: Learning about India and Persia Incorporate chess with education: Learning about the chess board and its coordinates Who invented chess and why? Talk about India / Persia – connects to Geography Tell the story of “seed”. -
Chess Mag - 21 6 10 18/09/2020 14:01 Page 3
01-01 Cover - October 2020_Layout 1 18/09/2020 14:00 Page 1 03-03 Contents_Chess mag - 21_6_10 18/09/2020 14:01 Page 3 Chess Contents Founding Editor: B.H. Wood, OBE. M.Sc † Executive Editor: Malcolm Pein Editorial....................................................................................................................4 Editors: Richard Palliser, Matt Read Malcolm Pein on the latest developments in the game Associate Editor: John Saunders Subscriptions Manager: Paul Harrington 60 Seconds with...Peter Wells.......................................................................7 Twitter: @CHESS_Magazine The acclaimed author, coach and GM still very much likes to play Twitter: @TelegraphChess - Malcolm Pein Website: www.chess.co.uk Online Drama .........................................................................................................8 Danny Gormally presents some highlights of the vast Online Olympiad Subscription Rates: United Kingdom Carlsen Prevails - Just ....................................................................................14 1 year (12 issues) £49.95 Nakamura pushed Magnus all the way in the final of his own Tour 2 year (24 issues) £89.95 Find the Winning Moves.................................................................................18 3 year (36 issues) £125 Can you do as well as the acclaimed field in the Legends of Chess? Europe 1 year (12 issues) £60 Opening Surprises ............................................................................................22 2 year (24 issues) £112.50 -
Chess & Bridge
2013 Catalogue Chess & Bridge Plus Backgammon Poker and other traditional games cbcat2013_p02_contents_Layout 1 02/11/2012 09:18 Page 1 Contents CONTENTS WAYS TO ORDER Chess Section Call our Order Line 3-9 Wooden Chess Sets 10-11 Wooden Chess Boards 020 7288 1305 or 12 Chess Boxes 13 Chess Tables 020 7486 7015 14-17 Wooden Chess Combinations 9.30am-6pm Monday - Saturday 18 Miscellaneous Sets 11am - 5pm Sundays 19 Decorative & Themed Chess Sets 20-21 Travel Sets 22 Giant Chess Sets Shop online 23-25 Chess Clocks www.chess.co.uk/shop 26-28 Plastic Chess Sets & Combinations or 29 Demonstration Chess Boards www.bridgeshop.com 30-31 Stationery, Medals & Trophies 32 Chess T-Shirts 33-37 Chess DVDs Post the order form to: 38-39 Chess Software: Playing Programs 40 Chess Software: ChessBase 12` Chess & Bridge 41-43 Chess Software: Fritz Media System 44 Baker Street 44-45 Chess Software: from Chess Assistant 46 Recommendations for Junior Players London, W1U 7RT 47 Subscribe to Chess Magazine 48-49 Order Form 50 Subscribe to BRIDGE Magazine REASONS TO SHOP ONLINE 51 Recommendations for Junior Players - New items added each and every week 52-55 Chess Computers - Many more items online 56-60 Bargain Chess Books 61-66 Chess Books - Larger and alternative images for most items - Full descriptions of each item Bridge Section - Exclusive website offers on selected items 68 Bridge Tables & Cloths 69-70 Bridge Equipment - Pay securely via Debit/Credit Card or PayPal 71-72 Bridge Software: Playing Programs 73 Bridge Software: Instructional 74-77 Decorative Playing Cards 78-83 Gift Ideas & Bridge DVDs 84-86 Bargain Bridge Books 87 Recommended Bridge Books 88-89 Bridge Books by Subject 90-91 Backgammon 92 Go 93 Poker 94 Other Games 95 Website Information 96 Retail shop information page 2 TO ORDER 020 7288 1305 or 020 7486 7015 cbcat2013_p03to5_woodsets_Layout 1 02/11/2012 09:53 Page 1 Wooden Chess Sets A LITTLE MORE INFORMATION ABOUT OUR CHESS SETS.. -
TACTICAL IDEA 4: ATTACKS on F7/F2
TACTICAL IDEA 4: ATTACKS ON f7/f2 You’ve already seen that f7 is Black’s weak point at the start of the game, and that you can sometimes win quickly by going for SCHOLAR’S MATE. You’ve also seen that if your opponent knows what to do you may well end up in trouble. There are other ways you can win quickly by using the weakness on f7. There are several reasons why you might want to SACRIFICE a piece on f7. You might also be able to SACRIFICE a piece at the other end of the board in order to capture on f7 and CHECKMATE your opponent. Some of the tactics are quite complicated. Let’s look at a few examples. 1. e4 c5 Black chooses the very popular SICILIAN DEFENCE. White decides to give up a pawn for rapid development. 2. d4 cxd4 3. c3 dxc3 4. Nxc3 d6 5. Bc4 Nf6 6. e5 White sets a trap, and Black falls right into it. The best move now is 6… Nfd7 6… dxe5 7. Bxf7+ A simple DEFLECTION. The black king is an OVERWORKED PIECE and White’s bishop forces him away from defending the queen. Black’s only move now is 7… Kxf7 when White just plays 8. Qxd8. 1. e4 Nc6 2. Nf3 d6 3. Bc4 Bg4 Black PINS the white Now White can move the knight, but it’s a mistake. PINNED knight with CHECK, White can play a SACRIFICE opening up a DISCOVERED on f7 to DECOY the black ATTACK. king. 5. -
Sicilian Warfare Ilya Smirin
Sicilian Warfare By Ilya Smirin Quality Chess www.qualitychess.co.uk Contents Key to Symbols used 4 Preface 5 1 Attacking the King in the Centre 7 2 The Killer Knight on f5 33 3 Pawn Breaks 59 4 Opposite-side Castling 101 5 The Exchange Sacrifice 131 6 Positional Elements 167 7 Hedgehog Strategy 207 8 Endgames 241 9 Imagination 269 10 Typical Attacks 299 Game Index 324 Name Index 331 Preface The two most exciting openings in chess are beyond doubt the King’s Indian Defence and the Sicilian Defence. Not everyone feels comfortable playing these openings, but from the viewpoint of chess fans, these two fighting systems lead to the most spectacular and interesting games. The Sicilian Defence is truly the choice of champions. Although Karpov only played it rarely, it has been a cornerstone in the Black repertoires of most of the world champions in my lifetime. Kasparov relied heavily upon it and played little else for most of his career. Kramnik was the great champion of the Sveshnikov Variation in the Sicilian Defence, until he came up with the Berlin Defence to frustrate Kasparov and claim the crown. Later on, he turned to the Najdorf, though this time without so much success. Topalov is a natural Sicilian player, as is Anand, although 1...e5 has also been a standard for these two champions. Magnus Carlsen is a truly versatile player, who played the Najdorf and the Dragon on his way up, while he recently returned to the Sveshnikov Variation against Caruana in the 2018 title defence – an opening he had not played since his junior days.