"ECE" Is the ENCYCLOPEDIA of CHESS ENDINGS. the Classifi- Cation System of the Twice-Yearly Yugoslav CHESS INFORMANT (
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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. -
1 Domination and the Five Queens Problem
Ordog, SWiM Graph Theory Project: Domination and The Five Queens Problem 1 Domination and The Five Queens Problem What is the smallest number of queens that we can place on a chessboard so that every space on the board is either occupied by a queen or being attacked by at least one queen? How can you use graph theory to find a suitable arrangement of queens on an n × n chessboard? To find a solution to this problem, you will learn about the dominating set of a graph. 1.1 Domination • A dominating set of a graph G is a set of vertices S such that each vertex of G is either in S or adjacent to a vertex in S. • What is the biggest dominating set of the graph below? • What is the biggest dominating set for any graph G? • Can you find a dominating set with three vertices? Two vertices? One? Give an example, or explain why not. 1.2 The domination number • The dominating number of a graph, denoted γ(G), is the smallest number of vertices in any dominating set of a graph G. • What is γ(G) for the above graph? Page 1 Ordog, SWiM Graph Theory Project: Domination and The Five Queens Problem • Recall that the complete graph on n vertices, Kn, is the graph with n vertices such that each vertex is adjacent to every other vertex (they are all connected by an edge). What is γ(Kn)? • Exercise: Find γ(G) for the following graphs ([Smi88]). Look for and discuss patterns that might help come up with algorithms for finding dominating sets. -
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. -
The Vast Majority of Practical Games Do Not Involve Stunning Visual Tactics and Combinations and Are Instead More Mundane Affairs
Institute of Chess Revision Guide to LEVEL 2 The contents were written and arranged by GM Chris Ward FM Desmond Tan. This revision guide is dedicated to the memory of IM Bob Wade OBE (1921 ~ 2008), who devoted his life to chess. (Revised) September 2010 1 Institute of Chess Level 2 Coaching Course by GM Chris Ward and FM Desmond Tan Index of Contents Page 1) Notating a Game and the Four Move Mate 2 2) Annotation Symbols 4 3) The ‘Lawnmower’ Checkmate 5 4) Checkmating with a King and Queen 8 5) Checkmating with a King and Rook 11 6) The Sacrifice 14 7) Tips on Stalemate 18 8) The Fork 20 9) The Pin 21 10) The Skewer 24 11) Discovered Check 26 12) Double Check 28 13) Doubling up 30 14) The 7th Rank 33 15) The Overloaded Piece 35 16) General Opening Principles 36 17) Advice on Practical Play 44 2 Notating a Game Writing the moves down is a very useful exercise for a few reasons. If you are prone to moving too quickly then it will help you slow your play down and if you have a record of it then you can play over it later in order to either enjoy a nice game that you may have had or else figure out where you went wrong! We all learn from our mistakes and if you have a correctly completed score sheet then you can show it to someone else who may be able to offer you help. In competitions you will write down your game on specially-provided score sheets whilst some may obtain a scorebook so that they can all be written in the same place. -
Discarding the Doctrine of Supervisory Domination: New Solutions to an Old Conflict of Interest Lynn Cox
Hastings Law Journal Volume 30 | Issue 3 Article 10 1-1979 Discarding the Doctrine of Supervisory Domination: New Solutions to an Old Conflict of Interest Lynn Cox Peter Martin Nelson Follow this and additional works at: https://repository.uchastings.edu/hastings_law_journal Part of the Law Commons Recommended Citation Lynn Cox and Peter Martin Nelson, Discarding the Doctrine of Supervisory Domination: New Solutions to an Old Conflict of Interest, 30 Hastings L.J. 763 (1979). Available at: https://repository.uchastings.edu/hastings_law_journal/vol30/iss3/10 This Note is brought to you for free and open access by the Law Journals at UC Hastings Scholarship Repository. It has been accepted for inclusion in Hastings Law Journal by an authorized editor of UC Hastings Scholarship Repository. For more information, please contact [email protected]. Discarding the Doctrine of Supervisory Domination: New Solutions to an Old Conflict of Interest By Lynn Cox* Peter Martin Nelson** Introduction Supervisors dual identity in the labor movement, in which they serve both as employees and as employer representatives, poses a per- plexing conflict of interest. Congress has attempted to ameliorate this conflict by denying to supervisors the fights guaranteed to employees2 under the National Labor Relations Act and vesting employers with plenary power to control the union activities of their supervisors. Fre- quently, however, this power remains unexercised as employers acqui- esce in the union membership of their supervisors. The National Labor * A.B., 1976, University of California at Berkeley. Member, Third Year Class. ** B.A., 1976, Williams College. Member, Third Year Class. 1. The National Labor Relations Act § 2(11), 29 U.S.C. -
The Modernized Grünfeld Defense
The Modernized Grünfeld Defense First edition 2020 by Thinkers Publishing Copyright © 2020 Yaroslav Zherebukh 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, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission from the publisher. All sales or enquiries should be directed to Thinkers Publishing, 9850 Landegem, Belgium. Email: [email protected] Website: www.thinkerspublishing.com Managing Editor: Romain Edouard Assistant Editor: Daniël Vanheirzeele Typesetting: Mark Haast Proofreading: Bob Bolliman Software: Hub van de Laar Cover Design: Iwan Kerkhof Graphic Artist: Philippe Tonnard Production: BESTinGraphics ISBN: 9789492510792 D/2020/13730/7 The Modernized Grünfeld Defense Yaroslav Zherebukh Thinkers Publishing 2020 Key to Symbols ! a good move ⩲ White stands slightly better ? a weak move ⩱ Black stands slightly better !! an excellent move ± White has a serious advantage ?? a blunder ∓ Black has a serious advantage !? an interesting move +- White has a decisive advantage ?! a dubious move -+ Black has a decisive advantage □ only move → with an attack N novelty ↑ with initiative ⟳ lead in development ⇆ with counterplay ⨀ zugzwang ∆ with the idea of = equality ⌓ better is ∞ unclear position ≤ worse is © with compensation for the + check sacrificed material # mate Table of Contents Key to Symbols ......................................................................................................... -
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 Endgames: 6-Man Data and Strategy
CORE Metadata, citation and similar papers at core.ac.uk Provided by Central Archive at the University of Reading Chess endgames: 6-man data and strategy M.S. Bourzutschky, J.A. Tamplin, and G.McC. Haworth [email protected], [email protected], [email protected]; http:// http://www.jaet.org/jat/ Abstract While Nalimov’s endgame tables for Western Chess are the most used today, their Depth-to-Mate metric is not the most efficient or effective in use. The authors have developed and used new programs to create tables to alternative metrics and recommend better strategies for endgame play. Key words: chess: conversion, data, depth, endgame, goal, move count, statistics, strategy 1 Introduction Chess endgames tables (EGTs) to the ‘DTM’ Depth to Mate metric are the most commonly used, thanks to codes and production work by Nalimov [10,7]. DTM data is of interest in itself, even if conversion, i.e., change of force, is more often adopted as an interim objective in human play. However, more effective endgame strategies using different metrics can be adopted, particularly by computers [3,4]. A further practical disadvantage of the DTM metric is that, as maxDTM increases, the EGTs take longer to generate and are less compressible. 1 2 Here, we focus on metrics DTC, DTZ and DTZ50 ; the first two were effectively used by Thompson [19], Stiller [14], and Wirth [20]. New programs by Tamplin [15] and Bourzutschky [2] have already enabled a complete suite of 3-to-5-man DTC/Z/Z50 EGTs to be produced [18]. This note is an update, focusing solely on Tamplin’s continuing work, assisted by Bourzutschky, with the latter code on 6-man, pawnless endgames for which DTC ≡ DTZ and DTC50 ≡ DTZ50. -
How I Beat Fischer's Record
Judit Polgar Teaches Chess 1 How I Beat Fischer’s Record by Judit Polgar with invaluable help from Mihail Marin Quality Chess www.qualitychess.co.uk Contents Key to Symbols used 4 Preface 5 1 Tricks 9 2 Mating Net 41 3 Trapping the Queen 57 4 Zwischenzug 63 5 Tales with an Unexpected End 69 6 Improving Piece Placement 77 7 Pawn Play 95 8 Piece Domination 103 9 A Lead in Development 121 10 Attacking the Uncastled King 133 11 The Art of Simplifying & Elements of Endgame Technique 163 12 Attacking without Queens 199 13 Decisive Games 227 14 Memorable Games 251 15 Amsterdam 1989 OHRA Tournament Diary 315 Records and Results 376 Game Index 378 Name Index 381 Preface I started flirting with the idea of publishing a collection of my best games a long time ago. For years, I was aware that the moment when I could fulfil my dream was far away. As a professional player, I spent most of my time and energy playing in tournaments and training, so each time the idea of my book popped up, I had to say to myself “Later, later...” By coincidence, several publishers approached me during this period. And although I was not prepared to embark on any definite project yet, I could feel that the whole idea was, little by little, starting to take shape. The critical moment The 2009 World Cup proved to be a decisive moment in the birth of my book. In the third round I played Boris Gelfand, a very strong opponent who eventually went on to win the event. -
History, Comparative Law, and Bona Fide Purchases P
Louisiana Law Review Volume 29 | Number 2 The Work of the Louisiana Appellate Courts for the 1967-1968 Term: A Symposium February 1969 Sales of Another's Movables - History, Comparative Law, and Bona Fide Purchases P. Michael Hebert James R. Pettway Repository Citation P. Michael Hebert and James R. Pettway, Sales of Another's Movables - History, Comparative Law, and Bona Fide Purchases, 29 La. L. Rev. (1969) Available at: https://digitalcommons.law.lsu.edu/lalrev/vol29/iss2/19 This Comment is brought to you for free and open access by the Law Reviews and Journals at LSU Law Digital Commons. It has been accepted for inclusion in Louisiana Law Review by an authorized editor of LSU Law Digital Commons. For more information, please contact [email protected]. COMMENTS SALES OF ANOTHER'S MOVABLES-HISTORY, COMPARATIVE LAW, AND BONA FIDE PURCHASERS Certain recurring conflicts arise between men that any system of law must seek to resolve. When justice and reason fail to indicate one best solution to such a conflict, different legal systems may well reach different results. Although these different results are often supported in the technical terms or theory of the legal system involved, the actual decision to favor one party over the other in such a situation is basically one of policy.' This comment deals with the often arising conflict be- tween one who is owner of a movable and one who has acquired it without the owner's consent. Under some circumstances, jus- tice and reason clearly favor one party and in these situations the different legal systems have no difficulty reaching common results.