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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. -
Little Chess Evaluation Compendium by Lyudmil Tsvetkov, Sofia, Bulgaria
Little Chess Evaluation Compendium By Lyudmil Tsvetkov, Sofia, Bulgaria Version from 2012, an update to an original version first released in 2010 The purpose will be to give a fairly precise evaluation for all the most important terms. Some authors might find some interesting ideas. For abbreviations, p will mean pawns, cp – centipawns, if the number is not indicated it will be centipawns, mps - millipawns; b – bishop, n – knight, k- king, q – queen and r –rook. Also b will mean black and w – white. We will assume that the bishop value is 3ps, knight value – 3ps, rook value – 4.5 ps and queen value – 9ps. In brackets I will be giving purely speculative numbers for possible Elo increase if a specific function is implemented (only for the functions that might not be generally implemented). The exposition will be split in 3 parts, reflecting that opening, middlegame and endgame are very different from one another. The essence of chess in two words Chess is a game of capturing. This is the single most important thing worth considering. But in order to be able to capture well, you should consider a variety of other specific rules. The more rules you consider, the better you will be able to capture. If you consider 10 rules, you will be able to capture. If you consider 100 rules, you will be able to capture in a sufficiently good way. If you consider 1000 rules, you will be able to capture in an excellent way. The philosophy of chess Chess is a game of correlation, and not a game of fixed values. -
Sample Pages
01-01 Cover -March 2021_Layout 1 17/02/2021 17:19 Page 1 03-03 Contents_Chess mag - 21_6_10 18/02/2021 09:47 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...Jorden van Foreest.......................................................7 Twitter: @CHESS_Magazine We catch up with the man of the moment after Wijk aan Zee Twitter: @TelegraphChess - Malcolm Pein Website: www.chess.co.uk Dutch Dominance.................................................................................................8 The Tata Steel Masters went ahead. Yochanan Afek reports Subscription Rates: United Kingdom How Good is Your Chess?..............................................................................18 1 year (12 issues) £49.95 Daniel King presents one of the games of Wijk,Wojtaszek-Caruana 2 year (24 issues) £89.95 3 year (36 issues) £125 Up in the Air ........................................................................................................21 Europe There’s been drama aplenty in the Champions Chess Tour 1 year (12 issues) £60 2 year (24 issues) £112.50 Howell’s Hastings Haul ...................................................................................24 3 year (36 issues) £165 David Howell ran -
Mind-Bending Analysis and Instructive Comment from a Man Who Has Participated in World Chess at the Very Highest Levels
Mind-bending analysis and instructive comment from a man who has participated in world chess at the very highest levels World championship candidate and three-times British Champion Jon Speelman annotates the best of his games. He is renowned as a great fighter and analyst, and a highly original player. This book provides entertainment and instruction in abundance. Games and stories from his: • World Championship campaigns • Chess Olympiads • Toi>level grandmaster tournaments, including the World Cup Jon Speelman is one of only two British players this century to gain a place in the world's top five. He has reached the sem>finals of the world championship and is one of the stars of the English national team, which has won the silver medals three times in the chess Olympiads. Jon Speelman's Best Games Jon Speelman B. T. Batsford Ltd, London First published 1997 © Jon Speelman 1997 ISBN 0 7134 6477 I British Library Cataloguing-in-Publication Data. Contents A catalogue record for this book is available from the British Library. All rights reserved. No part of this book may be reproduced, by any means, without prior permission of the publisher. Introduction 5 Typeset and edited by First Rank Publishing, Brighton and printed in Great Britain by Redwood Books, Trowbridge, Wilts Part I Growing up as a Chess player for the publishers, B. T. Batsford Ltd, Juvenilia 7 583 Fulham Road, I JS-J.Fletcher, British U-14 Ch., Rhyl1969 9 London SW6 5BY 2 JS-E.Warren, Thames Valley Open 1970 11 3 A.Miles-JS, Islington Open 1970 14 4 JS-Hanau, Nice 1971 -
Touring Problems – a Mathematical Approach
TOURING PROBLEMS – A MATHEMATICAL APPROACH VIPUL NAIK Abstract. The article surveys “touring”, a problem of “fun” math, and employs serious techniques to attack it. The text is suitable for high school students interested in Olympiad mathematics, as well as undergraduate students studying combinatorics and discrete math- ematics. It can be used to introduce the concept of a graph. A sequel to this article, on a similar analysis for “tiling” problems, shall also appear soon. 1. Prebeginnings 1.1. The knight’s tour. Chess pieces, with their variously defined moves, are a rich source of puzzles in recreational mathematics. Chess puzzles include the following types : • Nonattacking pieces puzzle : Given a piece with some moves defined, place as many copies of this piece as possible so that no two can kill each other. The proto- typical example of this is the eight queens problem – placing eight queens on the chessboard so that no two can kill each other. • Board domination puzzle : Given a piece with some moves defined, place as few copies of the piece as possible so that every square is either covered by some copy or is under direct attack by a copy of the piece. • Touring puzzle : Given a piece with some moves defined, construct a tour of the entire chessboard with that piece. The only nontrivial case of this for a standard chess piece is the knight’s tour. Each of these problems revolves around a piece, with certain moves defined for that piece. Instead of standard chess pieces, we may sometimes be interested in defining chess pieces with somewhat different moves. -
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. -
United States Chess Federation How Many Variations?
UNITED STATES CHESS FEDERATION , ( I -• -I USCF .J •- .J America's Chess Periodical Volume XVI. Number 9 SEPTEMBER, \961 40 Cents HOW MANY VARIATIONS? 169,518,829,100,544,000,000,000,000,000 X 700 (See ~II. 253) REPORT FROM FIDE At tile ' CCClll 1'10£ COllgrefl heW at night, Mr. Hellimo has put forward the Leipzig, GrunJmmtcr M ilora V/(fmtlr 0/ Yu· original proposition to adjourn the game gruiall/6 fIIbcd mallll qlll!lIiOW} all to ,1M for a pause of 2 hours already after I adutsabilily of .Wltg lectmru In malor chaA first period of only 2 hour::, in view of event, aru:i Ille ".0. and co"", of Immlllll.re the lact that in its initial phase a game draWl by agreemlm' . J\/1 of tlw member ollcrs much less chances [or an effective C(JImlr/c1 0/ FIDE were poUcd 01 10 I/urlr analysis than later on. wcleu;JIC(!J 1111(/ idCf/iI all t/1e5e 111."0 (I I.e,· Among the federalions and persons litms and foffowllIg I.J Iflc $rUllIIllJry: who have recommended an organization of play allowing a great number or Summary of the resulh of the Inquiry on gumcs to be terminated in the sa me day the questions r.iHd by Grand-MlSler as they have been begun, certain have Vidmar. lironounced themselves in lavour of a The questions raised by Grand·Master lengthening of the [irs!: period ol play. Vidmar have aroused a rather vivid in while others wish to keep the duration terest and the number of answers pre. -
British Knockout: Adams, Howell, Jones & Mcshane
PRESS RELEASE For immediate release BRITISH KNOCKOUT: ADAMS, HOWELL, JONES & MCSHANE INTO SEMIS England top 4 Mickey Adams, David Howell, Gawain Jones and Luke McShane all negotiate their way through a tough quarter-final stage to qualify for the British Knockout Championship semi-finals. David Howell triumphs eventually over IM Ravi Haria in a rapid playoff, despite almost coming to grief in the first Classical game. Semi-Finals pit Adams vs McShane and Howell vs Jones. Live coverage of the Semi-Final matches, starting Tuesday at 11:00 UTC, is available on the London Chess Classic website. LONDON (December 10, 2018) – Despite valiant efforts from the underdogs in the British Knockout, England Olympiad team members Mickey Adams, David Howell, Gawain Jones and Luke McShane all managed to win their Quarter-Final matches – although not without a struggle. Qtr Fina1 1 1 2 3 4 A Simon Williams 2466 ½ 0 - - - ½ Mickey Adams 2706 ½ 1 - - - 1½ Qtr Fina1 2 1 2 3 4 A David Howell 2697 ½ ½ 1 1 - 3 Ravi Haria 2436 ½ ½ 0 0 - 1 Qtr Fina1 3 1 2 3 4 A Gawain Jones 2683 1 ½ - - - 1½ Alan Merry 2429 0 ½ - - - ½ Qtr Fina1 4 1 2 3 4 A Jonathan Hawkins 2579 ½ 0 - - - ½ Luke McShane 2667 ½ 1 - - - 1½ David Howell had the closest shave of all the top seeds, only managing to qualify for the Semi-Finals after winning a nail-biting playoff match 2-0 against IM Ravi Haria. Elsewhere, Mickey Adams enjoyed a convincing victory in Game 2 of his match, after putting GM Simon Williams’s central king position under pressure in a double-edged Sicilian Richter-Rauzer. -
Illinois Chess Bulletin Volume 28, Issue 2 March April 2005
Illinois Chess Bulletin Volume 28, Issue 2 March April 2005 Illinois Youth Shine at Nationals I NSIDE T HIS I S S U E 7 Ill youth shine at Nationals 24 2005 IHSA Championship Boris Spassky makes appearance 26 out west AboutAdvertisement the Illinois Chess Bulletin and the Illinois Chess Association 2005 Illinois Amateur Championships Lincolnwood, IL (immediately north of Chicago) 5-round Swiss, March 19-20, 2005 $4,000 Projected Prizes (b/125), $2,000 minimum Guaranteed. 5-SS , 40/90 SD/30. Sat : 9:30, 2, 6:30. Sun : 12, 4:30. Location: Purple Hotel, 4500 W. Touhy Ave. (1 mile east of I-94), Lincolnwood, IL 60712. Prizes: $4,000 based on 125 paid entries (special EF counts as ½ entry). In 6 sections – you face only those in your section. Class A (1800-1999): $400, $300, $200, $100 Class B (1600-1799): $400, $300, $200, $100 Class C (1400-1599): $300, $200, $100, $50 Class D (1200-1399): $300, $200, $100, $50 Class E/F (1199 and below): $200, $100, $50, $50 Unrated: $150, $100, $50 Registration: Reg. ends 9am SHARP! Entries after 9am must take 1st round ½ bye. EF: Adults - $60 mailed by 3/1/05; Juniors (18-20) $55 mailed by 3/1/05; All $70 onsite. Special EF: Scholastic Players under the age of 18 receive a free 1 year membership to the ICA or a $14 discount off of the Junior Early EF (if they are already ICA members) either mailed entry or onsite. All: USCF membership required. ICA membership required for IL players. -
Efficiency of the Application of Some Exercises of Tactical Combinations
International Journal of Sport, Exercise and Health Research 2019; 3(2): 49-53 Research Article Efficiency of The Application of Some Exercises of Tactical IJSEHR 2019; 3(2): 49-53 © 2019, All rights reserved Combinations to Improve Student's Calculation Capacity in www.sportscienceresearch.com Received: 15-10-2019 Chess Classes at HCMC University of Technology and Accepted: 04-12-2019 Education Nguyen Duc Thanh1 1 Center for Physical and Defense Education, Ho Chi Minh City University of Technology and Education, Ho Chi Minh City, Viet Nam Abstract Background: Through the research process, the topic has selected a number of tactical coordination exercises, then applied them to chess classes at Ho Chi Minh City University of Technology and Education (UTE). Methodsː 66 male students in their 20s are divided into 2 groups of experiments (34 students) and control (32 students) all participating in the chess experiment program. Resultsː After the time of applying tactical coordination exercises, the results of tests performed by the experimental groups and control groups both increased, but the experimental group’s growth was more superior than control group’s (Means of of all 6 tests were significant difference with P <0.05). It shows that the rationality and effectiveness of the tactics coordination exercises selected to be included in the chess curriculum to improve the calculating capacity for students after a period of 4 months of experiment. Keywords: Calculations, Chess, Coordination, Exercises, Tactics. 1. INTRODUCTION Chess is an intellectual sport that hides extremely fascinating mysteries, so it attracts up to 600 million people worldwide to play every day [6, 10]. -
Sample Pages
01-01 July Cover_Layout 1 18/06/2017 21:25 Page 1 02-02 NIC advert_Layout 1 18/06/2017 19:54 Page 1 03-03 Contents_Chess mag - 21_6_10 18/06/2017 20:32 Page 3 Chess Contents Founding Editor: B.H. Wood, OBE. M.Sc † Executive Editor: Malcolm Pein Editorial.................................................................................................................4 Editors: Richard Palliser, Matt Read Malcom Pein on the latest developments in the game Associate Editor: John Saunders Subscriptions Manager: Paul Harrington 60 Seconds with...John Bartholomew....................................................7 We catch up with the IM and CCO of Chessable.com Twitter: @CHESS_Magazine Twitter: @TelegraphChess - Malcolm Pein Not a Classic .......................................................................................................8 Website: www.chess.co.uk Steve Giddins wasn’t overly taken with the Moscow Grand Prix Subscription Rates: How Good is Your Chess? ..........................................................................11 United Kingdom Daniel King features a game from the in-form Mamedyarov 1 year (12 issues) £49.95 2 year (24 issues) £89.95 Bundesliga Brilliance.....................................................................................14 3 year (36 issues) £125 Matthew Lunn presents two creative gems from the Bundesliga Europe 1 year (12 issues) £60 Find the Winning Moves .............................................................................18 2 year (24 issues) £112.50 Can you do as well as some leading -
1967 U.S. Women's Champion
1967 U.S. WOMEN'S CHAMPION Edith Lude Wear:!, lelt, pr.Hnllnq 11M cup .... hkh .hc donal~ In 1951. /9$1 U.s. Wornetn'. Champion Mrs. G/Hla Gro"er accept. lhe ClIp Im~kIfely followlno lhe toumomcml. S •• p. 190. ~ UNITED STATES ~ ._-- - - - --- -~ - ------ ---- -- -- . -- - - --~ -_. - Volume XXII Number 6 July, 1967 EDITOR: Burt Hochberg ------- --- --- --- -- CONTENTS Sarajevo 1967, by Dimitrije Bjelica .... ... ... ...... ... ...... .... ........... .............. 184 PRESIDENT Marshall Rohland Twa Games Fram Sara jevo, by Robert Byrne ... ... ......... ... ...... ................ 185 VICI·PRESIDENT Dutch Treat, by Bernard Zuckerman ............................ .... .................... 188 Isaac Kashdan REGIONAL VICE·PRESIDENTS Chess Life, Here and There, compiled by Wm. Go ichberg ......... ... 189. 203, 204, 207, 215 NEW ENCJLAND James Bolton Harold Dolldls Ell Buurdon Women's Chess, by Kothryn Slater ..... ......... ... ...... ............ .... ..... ............ 190 EASTERN Ii Obl'M LaBeU" Lewis E. Wood MIchael Raimo The College Column, by Mark L. Schwarcz ... ...... ...... ........................... 191 MID-ATLANTIC Earl Clary Steve Carruthers RObert Erk",. Observation Point, by Miro Rodojcic ... ...... .... ... ... .. ... ...... ... ... ............... 193 SOUTHERN Phlllp Lamb I-'w t H Lah.de Carroll M. Crull U. S. Open ... ..... ... ... ..... .. .. .. ........... .. ... ... .. ...................... ..... .................... 197 GREAT LAKES Donald W. Hlldlng Dr. Harvey M~ Clellan V. E. Vandenbur g Lorry Evans on Chess ...