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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. -
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). -
A Game of Queens
Judit Polgar Teaches Chess 3 A Game of Queens by Judit Polgar with invaluable help from Mihail Marin Quality Chess www.qualitychess.co.uk Contents Key to Symbols used 4 Preface 5 1 Kasparov 11 2 Karpov 45 3 Korchnoi 71 4 The Rapid Match with Anand 101 5 Oliver 115 6 Hanna 141 7 The Opening 167 8 The Middlegame 199 9 The Endgame 217 10 Unexpected Moves 273 11 Official Competitions 285 12 Where It All Started 365 Records and Results 382 Name Index 384 Game Index 387 126 A Game of Queens Judit Polgar – Ivan Sokolov have relied, though, on the fact that I had never before faced it in practice. Wijk aan Zee 2005 13.d5 1.e4 e5 2.¤f3 ¤c6 3.¥b5 a6 4.¥a4 ¤f6 It looks logical to block the centre after Black 5.0–0 ¥e7 6.¦e1 b5 7.¥b3 d6 8.c3 0–0 no longer has the freeing ...c7-c6. In the long Ivan has played the Ruy Lopez throughout run, Black will have to re-develop his bishop, his career, so he has had the time to try out most likely with ...¥c8-d7. all kinds of systems: the Berlin Wall and the Marshall Attack, the Open and Bird If White wishes to maintain the tension in the variations, as well as several systems in the centre, the alternatives are 13.¤f1 ¦e8 14.¤g3 closed variations. and 13.b3. Back in 1994 in Madrid, I won my first game against Ivan by somewhat restricting his 13...g6 choice with 9.d4, but by 2005 I used to stick 13...c4 is a typical reaction after d4-d5, but to the main lines. -
Electronic Funds Transfer Agreement and Disclosure VISA Checkmate and Electronic Services
Electronic Funds Transfer Agreement and Disclosure VISA CheckMate and Electronic Services This Electronic Fund Transfers Agreement and Disclosure is the contract which covers your and our rights and responsibilities concerning the electronic fund transfers (EFT) services offered to you by University of Virginia Community Credit Union (“Credit Union”). In this Agreement, the words “you,” “your,” and “yours” mean those who sign the application or account card as applicants, joint owners, or any authorized users. The words “we,” “us,” and “our” mean the Credit Union. The word “account” means any one (1) or more share and checking accounts you have with the Credit Union. Electronic fund transfers are electronically initiated transfers of money from your account through the EFT services described below. By signing an application or account card for EFT services, signing your card, or using any service, each of you, jointly and severally, agree to the terms and conditions in this Agreement and any amendments for the EFT services offered. Furthermore, electronic fund transfers that meet the definition of remittance transfers are governed by 12 C.F.R. part 1005, subpart B—Requirements for remittance transfers, and consequently, terms of this agreement may vary for those types of transactions. A “remittance transfer” is an electronic transfer of funds of more than $15.00 which is requested by a sender and sent to a designated recipient in a foreign country by a remittance transfer provider. Terms applicable to such transactions may vary from those disclosed herein and will be disclosed to you at the time such services are requested and rendered in accordance with applicable law. -
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. -
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. -
PGN/AN Verification for Legal Chess Gameplay
PGN/AN Verification for Legal Chess Gameplay Neil Shah Guru Prashanth [email protected] [email protected] May 10, 2015 Abstract Chess has been widely regarded as one of the world's most popular games through the past several centuries. One of the modern ways in which chess games are recorded for analysis is through the PGN/AN (Portable Game Notation/Algebraic Notation) standard, which enforces a strict set of rules for denoting moves made by each player. In this work, we examine the use of PGN/AN to record and describe moves with the intent of building a system to verify PGN/AN in order to check for validity and legality of chess games. To do so, we formally outline the abstract syntax of PGN/AN movetext and subsequently define denotational state-transition and associated termination semantics of this notation. 1 Introduction Chess is a two-player strategy board game which is played on an eight-by-eight checkered board with 64 squares. There are two players (playing with white and black pieces, respectively), which move in alternating fashion. Each player starts the game with a total of 16 pieces: one king, one queen, two rooks, two knights, two bishops and eight pawns. Each of the pieces moves in a different fashion. The game ends when one player checkmates the opponents' king by placing it under threat of capture, with no defensive moves left playable by the losing player. Games can also end with a player's resignation or mutual stalemate/draw. We examine the particulars of piece movements later in this paper. -
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”. -
— I Believe Hostage the Most Interesting, Exciting Variant That Can Be Played with a Standard Chess Set. Mating Attacks Are the Norm
— I believe Hostage the most interesting, exciting variant that can be played with a standard chess set. Mating attacks are the norm. Anyone can hope to discover new principles and opening lines. Grandmaster Larry Kaufman 2008 World Senior Chess Champion — Fascinating, exciting, extremely entertaining—–what a wonder- ful new game! Grandmaster Kevin Spraggett Chess World Championship Candidate — Probably the most remarkable chess variant of the last fi ft y years. Captured men are hostages that can be exchanged. Play is rarely less than exciting, sometimes with several reversals of fortune. Dramatic mates are the rule, not the exception. D.B.Pritchard author of “Th e Encyclopedia of Chess Variants” — Chess is not yet played out, but it is no longer possible to perform at a high level without a detailed knowledge of openings. In Hostage Chess creativity and imagination fl ourish, and fun returns. Peter Coast Scottish Chess Champion — With only a few rule changes, Hostage Chess creates a marvelously exciting variant on the classical game. Lawrence Day International Chess Master — Every bit as intriguing as standard chess. Beautiful roads keep branching off in all directions, and sharp eyed beginners sometimes roll right over the experts. Robert Hamilton FIDE Chess Master Published 2012 by Aristophanes Press Hostage Chess Copyright © 2012 John Leslie. All rights reserved. No part of this publication may be reproduced, stored in a re- trieval system, or transmitted in any form or by any means, digital, electronic, mechanical, photocopying, recording, or otherwise, or conveyed via the Internet or a website without prior written per- mission of the author, except in the case of brief quotations em- bedded in critical articles and reviews. -
Starting Out: the Sicilian JOHN EMMS
starting out: the sicilian JOHN EMMS EVERYMAN CHESS Everyman Publishers pic www.everymanbooks.com First published 2002 by Everyman Publishers pIc, formerly Cadogan Books pIc, Gloucester Mansions, 140A Shaftesbury Avenue, London WC2H 8HD Copyright © 2002 John Emms Reprinted 2002 The right of John Emms to be identified as the author of this work has been asserted in accordance with the Copyrights, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, electrostatic, magnetic tape, photocopying, recording or otherwise, without prior permission of the publisher. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ISBN 1 857442490 Distributed in North America by The Globe Pequot Press, P.O Box 480, 246 Goose Lane, Guilford, CT 06437·0480. All other sales enquiries should be directed to Everyman Chess, Gloucester Mansions, 140A Shaftesbury Avenue, London WC2H 8HD tel: 020 7539 7600 fax: 020 7379 4060 email: [email protected] website: www.everymanbooks.com EVERYMAN CHESS SERIES (formerly Cadogan Chess) Chief Advisor: Garry Kasparov Commissioning editor: Byron Jacobs Typeset and edited by First Rank Publishing, Brighton Production by Book Production Services Printed and bound in Great Britain by The Cromwell Press Ltd., Trowbridge, Wiltshire Everyman Chess Starting Out Opening Guides: 1857442342 Starting Out: The King's Indian Joe Gallagher 1857442296