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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. -
FM ALISA MELEKHINA Is Currently Balancing Her Law and Chess Careers. Inside, She Interviews Three Other Lifelong Chess Players Wrestling with a Similar Dilemma
NAKAMURA WINS GIBRALTAR / SO FINISHES SECOND AT TATA STEEL APRIL 2015 Career Crossroads FM ALISA MELEKHINA is currently balancing her law and chess careers. Inside, she interviews three other lifelong chess players wrestling with a similar dilemma. IFC_Layout 1 3/11/2015 6:02 PM Page 1 OIFC_pg1_Layout 1 3/11/2015 7:11 PM Page 1 World’s biggest open tournament! 43rd annual WORLD OPEN Hyatt Regency Crystal City, near D.C. 9rounds,June30-July5,July1-5,2-5or3-5 $210,000 Guaranteed Prizes! Master class prizes raised by $10,000 GM & IM norms possible, mixed doubles prizes, GM lectures & analysis! VISIT OUR NATION’S CAPITAL SPECIAL FEATURES! 4) Provisional (under 26 games) prize The World Open completes a three 1) Schedule options. 5-day is most limits in U2000 & below. year run in the Washington area before popular, 4-day and 3-day save time & 5) Unrated not allowed in U1200 returning to Philadelphia in 2016. money.New,leisurely6-dayhas three1- though U1800;$1000 limit in U2000. $99 rooms, valet parking $6 (if full, round days. Open plays 5-day only. 6) Mixed Doubles: $3000-1500-700- about $7-15 nearby), free airport shuttle. 2) GM & IM norms possible in Open. 500-300 for male/female teams. Fr e e s hutt l e to DC Metro, minutes NOTECHANGE:Mas ters can now play for 7) International 6/26-30: FIDE norms from Washington’s historic attractions! both norms & large class prizes! possible, warm up for main event. Als o 8sections:Open,U2200,U2000, 3) Prize limit $2000 if post-event manyside events. -
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. -
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. -
UIL Text 111212
UIL Chess Puzzle Solvin g— Fall/Winter District 2016-2017 —Grades 4 and 5 IMPORTANT INSTRUCTIONS: [Test-administrators, please read text in this box aloud.] This is the UIL Chess Puzzle Solving Fall/Winter District Test for grades four and five. There are 20 questions on this test. You have 30 minutes to complete it. All questions are multiple choice. Use the answer sheet to mark your answers. Multiple choice answers pur - posely do not indicate check, checkmate, or e.p. symbols. You will be awarded one point for each correct answer. No deductions will be made for incorrect answers on this test. Finishing early is not rewarded, even to break ties. So use all of your time. Some of the questions may be hard, but all of the puzzles are interesting! Good luck and have fun! If you don’t already know chess notation, reading and referring to the section below on this page will help you. How to read and answer questions on this test Piece Names Each chessman can • To answer the questions on this test, you’ll also be represented need to know how to read chess moves. It’s by a symbol, except for the pawn. simple to do. (Figurine Notation) K King Q • Every square on the board has an “address” Queen R made up of a letter and a number. Rook B Bishop N Knight Pawn a-h (We write the file it’s on.) • To make them easy to read, the questions on this test use the figurine piece symbols on the right, above. -
Parallel Chess Searching and Bitboards
Parallel Chess Searching and Bitboards David Ravn Rasmussen August 2004 Abstract In order to make chess programs faster and thus stronger, the two approaches of parallelizing the search and of using clever data structures have been suc- cessful in the past. In this project it is examined how the use of a specific data structure called a bitboard affects the performance of parallel search. For this, a realistic bitboard chess program with important modern enhance- ments is implemented, and several experiments are done to evaluate the performance of the implementation. A maximum speedup of 9.2 on 22 pro- cessors is achieved in one experiment and a maximum speedup of 9.4 on 12 processors is achieved in another experiment. These results indicate that bitboards are a realistic choice of data structure in a parallel chess program, although the considerable difference in the two results suggests that more research could be done to clarify what factors affect such an implementation, and how. I II Contents 1 Introduction 1 2 The Game Of Chess 5 2.1 TheBoard............................. 6 2.2 TheArmies ............................ 6 2.3 TheMoves............................. 6 2.3.1 TheBishop ........................ 7 2.3.2 TheRook ......................... 7 2.3.3 TheQueen ........................ 8 2.3.4 TheKnight ........................ 8 2.3.5 TheKing ......................... 8 2.3.6 ThePawn ......................... 10 2.4 TheEnd.............................. 11 3 Game Trees and Searching 13 3.1 GameTrees ............................ 13 3.2 SearchAlgorithms ........................ 15 3.2.1 Minimax.......................... 16 3.2.2 Negamax ......................... 18 3.2.3 Evaluation......................... 18 3.2.4 Alpha-BetaSearch . 20 4 Search Algorithm Improvements 25 4.1 AspirationWindows . -
1 Najdorf Sicilian Focus on the Critical D5 Squar One the Most Common Openings in the Past 50 Years Is the Najdorf Variation Of
1 Najdorf Sicilian will try to keep full control over the d5 Focus on the Critical d5 Squar square, and try to maintain the possibility of placing and keeping a piece One the most common openings in the on d5. Fully controlling the d5 square past 50 years is the Najdorf variation of allows white to affect both sides of the the Sicilian Defense. The Najdorf offers board. In order to assure that control, many different possibilities, starting from white wants to trade off black pieces extremely sharp, poison pawn variation that can control d5. For example, he (1. e4, c5 2. nf3 d6 3. d4 cxd4 4. Nxd4 wants to play with Bg5, in order to trade Nf6 5. Nc3 a6 6. Bg5 e6 7. f4 Qb6 8. off the Knight on f6. He also will Qd2 Qxb2! ) to extremely positional lines increase the number of his own pieces (1. e4, c5 2. nf3 d6 3. d4 cxd4 4. Nxd4 that can control d5, with maneuvers like Nf6 5. Nc3 a6 6. Be2 e5 7. Nb3 ... ) bishop to c4, then b3, and the knight on Somewhere between those two lines is f3 going to d2-c4-e3. It seems that white the following position, which I will try to has full control of the situation. So why explain. 1.e4 c5 2.Nf3 d6 3.d4 cxd4 does black choose to create this pawn 4.Nxd4 Nf6 5.Nc3 a6 6.Be3 e5 7.Nf3 structure? The answer is because this is Diagram one of the rare Sicilian pawn structures abcdef gh that gives the black side a slight space advantage. -
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). -
How to Setup Chess Board - Easy
How to setup Chess Board - Easy By G Bud Games https://gbud.in July 24, 2021 Contents 1 How to setup Chess Board - Easy 3 1.1 Squares in chess board .................... 3 1.2 Ranks and files of chess board ................ 8 1.2.1 Rank in chess ..................... 8 1.2.2 File in Chess ..................... 10 1.3 Piece arrangement ...................... 12 1.4 Colors of chess pieces ..................... 12 1.5 Initial setup of chess board .................. 12 1.6 Staunton chess set ...................... 17 1 List of Figures 1.1 Squares in a chess board ................... 4 1.2 Column names at chess board ................ 4 1.3 Row numbers at at chess board ............... 5 1.4 Names of Chess squares ................... 5 1.5 Default position of white king at chess board ........ 6 1.6 Default position of black queen at chess board ....... 6 1.7 a1 square at chess board ................... 7 1.8 h8 square at chess board ................... 7 1.9 Rank in a chess board .................... 8 1.10 Rank 1 in a chess board ................... 9 1.11 Rank 8 in a chess board ................... 9 1.12 File in a chess board ..................... 10 1.13 A file in a chess board .................... 11 1.14 H file in a chess board .................... 11 1.15 Height of chess pieces ..................... 12 1.16 Initial setup of chess board .................. 13 1.17 Queen’s position at chess board ............... 14 1.18 King’s position at chess board ................ 14 1.19 Knight’s position at chess board ............... 15 1.20 Rook’s position at chess board ................ 15 1.21 Bishop’s position at chess board .............. -
Chess Strategies for Beginners II Top Books for Beginners Chess Thinking
Chess Strategies for Beginners II Stop making silly Moves! Learn Chess Strategies for Beginners to play better chess. Stop losing making dumb moves. "When you are lonely, when you feel yourself an alien in the world, play Chess. This will raise your spirits and be your counselor in war." Aristotle Learn chess strategies first at Chess Strategies for Beginners I. After that come back here. Chess Formation Strategy I show you now how to start your game. Before you start to play you should know where to place your pieces - know the right chess formation strategy. Where do you place your pawns, knights and bishops, when do you castle and what happens to the queen and the rooks. When should you attack? Or do you have to attack at all? Questions over questions. I will give you a rough idea now. Please study the following chess strategies for beginners carefully. Read the Guidelines: Chess Formation Strategy. WRITE YOUR REVIEW ASK QUESTIONS HERE! Top Books For Beginners For beginners I recommend Logical Chess - Move by Move by Chernev because it explains every move. Another good book is the Complete Idiot's Guide to Chess that received very good reviews. Chess Thinking Now try to get mentally into the real game and try to understand some of the following positions. Some are difficult to master, but don't worry, just repeat them the next day to get used to chess thinking. Your brain has to adjust, that's all there is to it. Win some Positions here! - Chess Puzzles Did you manage it all right? It is necessary that you understand the following basic chess strategies for beginners called - Endgames or Endings, using the heavy pieces.(queen and rook are called heavy pieces) Check them out now! Rook and Queen Endgames - Basic Chess Strategies How a Beginner plays Chess Replay the games of a beginner. -
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.