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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. -
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. -
The Modern Defence: Move by Move PDF Book
THE MODERN DEFENCE: MOVE BY MOVE PDF, EPUB, EBOOK Cyrus Lakdawala | 400 pages | 20 Nov 2012 | EVERYMAN CHESS | 9781857449860 | English | London, United Kingdom The Modern Defence: Move by Move PDF Book Please try to maintain a semblance of civility at all times. When to resign - Etiquette - An honest appeal Optimissed 7 min ago. Published November 20th by Everyman Chess first published October 7th Cochrane vs Somacarana 34 Calcutta B06 Robatsch 8. Rxh7 9. Error rating book. Nc3 in the actual game. Aug 10, Chapter 1 — Introduction — initial remarks and comments. Cyrus Lakdawala. I know he is notoriously hit-and-miss as an author. Kxf7, 6. The flexibility and toughness of the Modern Defense has provoked some very aggressive responses by White, including the crudely named Monkey's Bum , a typical sequence being 1. Welcome back. Chapter 8 — The Fianchetto Variation: g3-Bg2 setups — the quiet, but no less venomous setups involving an early fianchetto of the light-squared bishop. Question feed. Bg7 3. See something that violates our rules? Please observe our posting guidelines: No obscene, racist, sexist, or profane language. Be2, Black can retreat the knight or gambit a pawn with Therefore, I find it an advantage to block these pieces by pawns. Nf3, Black can play Jul 22, 2. Numerous hours were spent analyzing, importing, commenting, fixing mistakes, fixing the fixes of mistakes, replying to beta tester comments, improving the initial version, etc. B06 Robatsch. Transpositions are possible after 2. A repertoire for my favourite opening for the Black pieces — the Modern Defence — was among them. To ask other readers questions about The Modern Defence , please sign up. -
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”. -
Of Kings and Pawns
OF KINGS AND PAWNS CHESS STRATEGY IN THE ENDGAME ERIC SCHILLER Universal Publishers Boca Raton • 2006 Of Kings and Pawns: Chess Strategy in the Endgame Copyright © 2006 Eric Schiller All rights reserved. Universal Publishers Boca Raton , Florida USA • 2006 ISBN: 1-58112-909-2 (paperback) ISBN: 1-58112-910-6 (ebook) Universal-Publishers.com Preface Endgames with just kings and pawns look simple but they are actually among the most complicated endgames to learn. This book contains 26 endgame positions in a unique format that gives you not only the starting position, but also a critical position you should use as a target. Your workout consists of looking at the starting position and seeing if you can figure out how you can reach the indicated target position. Although this hint makes solving the problems easier, there is still plenty of work for you to do. The positions have been chosen for their instructional value, and often combined many different themes. You’ll find examples of the horse race, the opposition, zugzwang, stalemate and the importance of escorting the pawn with the king marching in front, among others. When you start out in chess, king and pawn endings are not very important because usually there is a great material imbalance at the end of the game so one side is winning easily. However, as you advance through chess you’ll find that these endgame positions play a great role in determining the outcome of the game. It is critically important that you understand when a single pawn advantage or positional advantage will lead to a win and when it will merely wind up drawn with best play. -
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. -
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”. -
A Podium Select Superclass Individual Online Live Classes
CHESS A P O D I U M S E L E C T S U P E R C L A S S I N D I V I D U A L O N L I N E L I V E C L A S S E S AGE CUSTOMIZED BATCH FOR 06+ YEARS INDIVIDUAL ATTENTION FREE CANCELLATION / RESCHEDULING BY AWARD WINNING ANKITA PANDEY BEST TEACHERS. INDIVIDUALIZED LEARNING. HIGH ENGAGEMENT. MEASURED RESULTS. PODIUM IS A GLOBAL CO-CURRICULAR LEARNING PLATFORM BASED ON HOWARD GARDENER'S THEORY OF MULTIPLE INTELLIGENCES FOCUSSED ON CREATING THE ABSOLUTE BEST LEARNING ENVIRONMENT FOR BEGINNERS. ALL COURSES ARE DESIGNED USING GLOBAL BEST LEARNING TOOLS AND TECHNIQUES - FOLLOWING INTERNATIONAL BENCHMARKS BY TOP-NOTCH FACULTY. SUPERCLASS PRIVATE ONLINE CLASSES Beginners need individual attention - and we at Podium believe in it hence all our courses are designed to be customized to the development and learning needs at an individual level. Our classes have specific learning outcomes and give individual feedback as per the learning pace of the student. The classes are conducted by the best faculty chosen by Podium's education board. Chess helps build individual friendships and teaches children about sportsmanship. Children learn how to win graciously, and more importantly, how not to give up when encountering defeat. Chess encourages and rewards hard work. Children learn that those who practice and study the strategies win more games. In his celebrated work, “Frames of Mind: The Theory of Multiple Intelligences”, noted psychologist Dr. Howard Gardner uses chess as an example of visual-spatial intelligence. Indeed, visual memory plays a crucial role in chess and often manifests itself in the form of pattern recognition. -
Basicxqcheckmate.Pdf
PDF created with pdfFactory Pro trial version www.pdffactory.com Preface The game of Xiangqi is similar to the deployment of forces for military operation. Though it is a battle on xiangqi board, its theory is similar to the military strategy and tactics. As it is stipulated by the xiangqi rules, the side that captures the opponent's King will be the winner of the game. Therefore, each side tries to outwit his opponent and strives to show his bravery in taking various kinds of checkmate methods and to do his best to seize every opportunity for winning the victory. The game of xiangqi is rendered with a mysterious hue. Nearly all xiangqi players or fans understand that the checkmate method takes an important position in the xiangqi game. However, some of the players believe that "the checkmate method can only play its roles in the end game." But in reality, we often see that in the heat-fought mid-game, being eager to achieve a quick success and instant benefit, one side often neglects to defend his own King, offering the opponent an opportunity for making a counterattack or winning the game. Although sometimes, a player has a chance to take a successive checkmate, as he is rusty on the checkmate methods, he bungles a chance of winning the battle, or loses the game. Such cases are often seen in actual competitions. And there are numerous examples showing that some players take advantage of checkmate methods in seizing opponent's pieces. In fact, the checkmate methods play a very important role, directly or indirectly, not only in the end game, but also in the mid-game, even in the entire game. -
A GUIDE to SCHOLASTIC CHESS (11Th Edition Revised June 26, 2021)
A GUIDE TO SCHOLASTIC CHESS (11th Edition Revised June 26, 2021) PREFACE Dear Administrator, Teacher, or Coach This guide was created to help teachers and scholastic chess organizers who wish to begin, improve, or strengthen their school chess program. It covers how to organize a school chess club, run tournaments, keep interest high, and generate administrative, school district, parental and public support. I would like to thank the United States Chess Federation Club Development Committee, especially former Chairman Randy Siebert, for allowing us to use the framework of The Guide to a Successful Chess Club (1985) as a basis for this book. In addition, I want to thank FIDE Master Tom Brownscombe (NV), National Tournament Director, and the United States Chess Federation (US Chess) for their continuing help in the preparation of this publication. Scholastic chess, under the guidance of US Chess, has greatly expanded and made it possible for the wide distribution of this Guide. I look forward to working with them on many projects in the future. The following scholastic organizers reviewed various editions of this work and made many suggestions, which have been included. Thanks go to Jay Blem (CA), Leo Cotter (CA), Stephan Dann (MA), Bob Fischer (IN), Doug Meux (NM), Andy Nowak (NM), Andrew Smith (CA), Brian Bugbee (NY), WIM Beatriz Marinello (NY), WIM Alexey Root (TX), Ernest Schlich (VA), Tim Just (IL), Karis Bellisario and many others too numerous to mention. Finally, a special thanks to my wife, Susan, who has been patient and understanding. Dewain R. Barber Technical Editor: Tim Just (Author of My Opponent is Eating a Doughnut and Just Law; Editor 5th, 6th and 7th editions of the Official Rules of Chess). -
Chess Pieces – Left to Right: King, Rook, Queen, Pawn, Knight and Bishop
CCHHEESSSS by Wikibooks contributors From Wikibooks, the open-content textbooks collection Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". Image licenses are listed in the section entitled "Image Credits." Principal authors: WarrenWilkinson (C) · Dysprosia (C) · Darvian (C) · Tm chk (C) · Bill Alexander (C) Cover: Chess pieces – left to right: king, rook, queen, pawn, knight and bishop. Photo taken by Alan Light. The current version of this Wikibook may be found at: http://en.wikibooks.org/wiki/Chess Contents Chapter 01: Playing the Game..............................................................................................................4 Chapter 02: Notating the Game..........................................................................................................14 Chapter 03: Tactics.............................................................................................................................19 Chapter 04: Strategy........................................................................................................................... 26 Chapter 05: Basic Openings............................................................................................................... 36 Chapter 06: -
The Power of Pawns Chess Structure Fundamentals for Post-Beginners
Jörg Hickl The Power of Pawns Chess Structure Fundamentals for Post-beginners New In Chess 2016 Contents Explanation of Symbols ........................................... 6 Introduction ................................................... 7 Part 1 - Pieces and pawns . 11 Chapter 1 The bishop..........................................12 Chapter 2 The knight ..........................................24 Chapter 3 The rook ...........................................36 Part II - Basic pawn structures . 49 Chapter 4 Hanging pawns ......................................50 Chapter 5 Isolated pawns .......................................62 Chapter 6 Backward pawns......................................86 Chapter 7 Passed pawns .......................................106 Chapter 8 Doubled pawns .....................................123 Chapter 9 Weak squares .......................................141 Chapter 10 Pawn chains ........................................162 Index of Games ............................................... 181 Index of Openings............................................. 183 Bibliography ................................................. 185 5 Introduction What every club player desires is to reach an acceptable playing level with a reasonable expenditure of time and effort. That is the point of the present book ‘The power of the pawns’. An overview of basic pawn structures, together with a lot of practical hints, helps to improve one’s understanding of chess at a deep level. Chess players require a broad spectrum of knowledge.