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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. -
Computer Analysis of World Chess Champions 65
Computer Analysis of World Chess Champions 65 COMPUTER ANALYSIS OF WORLD CHESS CHAMPIONS1 Matej Guid2 and Ivan Bratko2 Ljubljana, Slovenia ABSTRACT Who is the best chess player of all time? Chess players are often interested in this question that has never been answered authoritatively, because it requires a comparison between chess players of different eras who never met across the board. In this contribution, we attempt to make such a comparison. It is based on the evaluation of the games played by the World Chess Champions in their championship matches. The evaluation is performed by the chess-playing program CRAFTY. For this purpose we slightly adapted CRAFTY. Our analysis takes into account the differences in players' styles to compensate the fact that calm positional players in their typical games have less chance to commit gross tactical errors than aggressive tactical players. Therefore, we designed a method to assess the difculty of positions. Some of the results of this computer analysis might be quite surprising. Overall, the results can be nicely interpreted by a chess expert. 1. INTRODUCTION Who is the best chess player of all time? This is a frequently posed and interesting question, to which there is no well founded, objective answer, because it requires a comparison between chess players of different eras who never met across the board. With the emergence of high-quality chess programs a possibility of such an objective comparison arises. However, so far computers were mostly used as a tool for statistical analysis of the players' results. Such statistical analyses often do neither reect the true strengths of the players, nor do they reect their quality of play. -
2020-21 Candidates Tournament ROUND 9
2020-21 Candidates Tournament ROUND 9 CATALAN OPENING (E05) easy to remove and will work together with the GM Anish Giri (2776) other pieces to create some long-term ideas. GM Wang Hao (2763) A game between two other top players went: 2020-2021 Candidates Tournament 14. Rac1 Nb4 15. Rfd1 Ra6 (15. ... Bxf3! 16. Bxf3 Yekaterinburg, RUS (9.3), 04.20.2021 c6 is the most solid approach in my opinion. I Annotations by GM Jacob Aagaard cannot see a valid reason why the bishop on f3 for Chess Life Online is a strong piece.) 16. Qe2 Nbd5 17. Nb5 Ne7 18. The Game of the Day, at least in terms of Nd2 Bxg2 19. Kxg2 Nfd5 20. Nc4 Ng6 21. Kh1 drama, was definitely GM Ding Liren versus Qe7 22. b3 Rd8 23. Rd2 Raa8 24. Rdc2 Nb4 25. GM Maxime Vachier-Lagrave. Drama often Rd2 Nd5 26. Rdc2, and the game was drawn in Ivanchuk – Dominguez Perez, Varadero 2016. means bad moves, which was definitely the case there. Equally important for the tournament 14. ... Bxg2 15. Kxg2 c6 16. h3!N 8. ... Bd7 standings was the one win of the day. GM Anish Giri moves into shared second place with this The bishop is superfluous and will be The real novelty of the game, and not a win over GM Wang Hao. exchanged. spectacular one. The idea is simply that the king The narrative of the game is a common one hides on h2 and in many situations leaves the 9. Qxc4 Bc6 10. Bf4 Bd6 11. -
From Los Angeles to Reykjavik
FROM LOS ANGELES CHAPTER 5: TO REYKJAVIK 1963 – 68 In July 1963 Fridrik Ólafsson seized a against Reshevsky in round 10 Fridrik ticipation in a top tournament abroad, Fridrik spent most of the nice opportunity to take part in the admits that he “played some excellent which occured January 1969 in the “First Piatigorsky Cup” tournament in games in this tournament”. Dutch village Wijk aan Zee. five years from 1963 to Los Angeles, a world class event and 1968 in his home town the strongest one in the United States For his 1976 book Fridrik picked only Meanwhile from 1964 the new bian- Reykjavik, with law studies since New York 1927. The new World this one game from the Los Angeles nual Reykjavik chess international gave Champion Tigran Petrosian was a main tournament. We add a few more from valuable playing practice to both their and his family as the main attraction, and all the other seven this special event. For his birthday own chess hero and to the second best priorities. In 1964 his grandmasters had also participated at greetings to Fridrik in “Skák” 2005 Jan home players, plus provided contin- countrymen fortunately the Candidates tournament level. They Timman showed the game against Pal ued attention to chess when Fridrik Benkö from round 6. We will also have Ólafsson competed on home ground started the new biannual gathered in the exclusive Ambassador Hotel in Los Angeles for a complete a look at some critical games which against some famous foreign players. international tournament double round event of 14 rounds. -
FIDE Laws of Chess
FIDE Laws of Chess FIDE Laws of Chess cover over-the-board play. The Laws of Chess have two parts: 1. Basic Rules of Play and 2. Competition Rules. The English text is the authentic version of the Laws of Chess (which was adopted at the 84th FIDE Congress at Tallinn (Estonia) coming into force on 1 July 2014. In these Laws the words ‘he’, ‘him’, and ‘his’ shall be considered to include ‘she’ and ‘her’. PREFACE The Laws of Chess cannot cover all possible situations that may arise during a game, nor can they regulate all administrative questions. Where cases are not precisely regulated by an Article of the Laws, it should be possible to reach a correct decision by studying analogous situations which are discussed in the Laws. The Laws assume that arbiters have the necessary competence, sound judgement and absolute objectivity. Too detailed a rule might deprive the arbiter of his freedom of judgement and thus prevent him from finding a solution to a problem dictated by fairness, logic and special factors. FIDE appeals to all chess players and federations to accept this view. A necessary condition for a game to be rated by FIDE is that it shall be played according to the FIDE Laws of Chess. It is recommended that competitive games not rated by FIDE be played according to the FIDE Laws of Chess. Member federations may ask FIDE to give a ruling on matters relating to the Laws of Chess. BASIC RULES OF PLAY Article 1: The nature and objectives of the game of chess 1.1 The game of chess is played between two opponents who move their pieces on a square board called a ‘chessboard’. -
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. -
More About Checkmate
MORE ABOUT CHECKMATE The Queen is the best piece of all for getting checkmate because it is so powerful and controls so many squares on the board. There are very many ways of getting CHECKMATE with a Queen. Let's have a look at some of them, and also some STALEMATE positions you must learn to avoid. You've already seen how a Rook can get CHECKMATE XABCDEFGHY with the help of a King. Put the Black King on the side of the 8-+k+-wQ-+( 7+-+-+-+-' board, the White King two squares away towards the 6-+K+-+-+& middle, and a Rook or a Queen on any safe square on the 5+-+-+-+-% same side of the board as the King will give CHECKMATE. 4-+-+-+-+$ In the first diagram the White Queen checks the Black King 3+-+-+-+-# while the White King, two squares away, stops the Black 2-+-+-+-+" King from escaping to b7, c7 or d7. If you move the Black 1+-+-+-+-! King to d8 it's still CHECKMATE: the Queen stops the Black xabcdefghy King moving to e7. But if you move the Black King to b8 is CHECKMATE! that CHECKMATE? No: the King can escape to a7. We call this sort of CHECKMATE the GUILLOTINE. The Queen comes down like a knife to chop off the Black King's head. But there's another sort of CHECKMATE that you can ABCDEFGH do with a King and Queen. We call this one the KISS OF 8-+k+-+-+( DEATH. Put the Black King on the side of the board, 7+-wQ-+-+-' the White Queen on the next square towards the middle 6-+K+-+-+& and the White King where it defends the Queen and you 5+-+-+-+-% 4-+-+-+-+$ get something like our next diagram. -
A Feast of Chess in Time of Plague – Candidates Tournament 2020
A FEAST OF CHESS IN TIME OF PLAGUE CANDIDATES TOURNAMENT 2020 Part 1 — Yekaterinburg by Vladimir Tukmakov www.thinkerspublishing.com Managing Editor Romain Edouard Assistant Editor Daniël Vanheirzeele Translator Izyaslav Koza Proofreader Bob Holliman Graphic Artist Philippe Tonnard Cover design Mieke Mertens Typesetting i-Press ‹www.i-press.pl› First edition 2020 by Th inkers Publishing A Feast of Chess in Time of Plague. Candidates Tournament 2020. Part 1 — Yekaterinburg Copyright © 2020 Vladimir Tukmakov 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, mechanical, photocopying, recording or otherwise, without the prior written permission from the publisher. ISBN 978-94-9251-092-1 D/2020/13730/26 All sales or enquiries should be directed to Th inkers Publishing, 9850 Landegem, Belgium. e-mail: [email protected] website: www.thinkerspublishing.com TABLE OF CONTENTS KEY TO SYMBOLS 5 INTRODUCTION 7 PRELUDE 11 THE PLAY Round 1 21 Round 2 44 Round 3 61 Round 4 80 Round 5 94 Round 6 110 Round 7 127 Final — Round 8 141 UNEXPECTED CONCLUSION 143 INTERIM RESULTS 147 KEY TO SYMBOLS ! a good move ?a weak move !! an excellent move ?? a blunder !? an interesting move ?! a dubious move only move =equality unclear position with compensation for the sacrifi ced material White stands slightly better Black stands slightly better White has a serious advantage Black has a serious advantage +– White has a decisive advantage –+ Black has a decisive advantage with an attack with initiative with counterplay with the idea of better is worse is Nnovelty +check #mate INTRODUCTION In the middle of the last century tournament compilations were ex- tremely popular. -
OCTOBER 25, 2013 – JULY 13, 2014 Object Labels
OCTOBER 25, 2013 – JULY 13, 2014 Object Labels 1. Faux-gem Encrusted Cloisonné Enamel “Muslim Pattern” Chess Set Early to mid 20th century Enamel, metal, and glass Collection of the Family of Jacqueline Piatigorsky Though best known as a cellist, Jacqueline’s husband Gregor also earned attention for the beautiful collection of chess sets that he displayed at the Piatigorskys’ Los Angeles, California, home. The collection featured gorgeous sets from many of the locations where he traveled while performing as a musician. This beautiful set from the Piatigorskys’ collection features cloisonné decoration. Cloisonné is a technique of decorating metalwork in which metal bands are shaped into compartments which are then filled with enamel, and decorated with gems or glass. These green and red pieces are adorned with geometric and floral motifs. 2. Robert Cantwell “In Chess Piatigorsky Is Tops.” Sports Illustrated 25, No. 10 September 5, 1966 Magazine Published after the 1966 Piatigorsky Cup, this article celebrates the immense organizational efforts undertaken by Jacqueline Piatigorsky in supporting the competition and American chess. Robert Cantwell, the author of the piece, also details her lifelong passion for chess, which began with her learning the game from a nurse during her childhood. In the photograph accompanying the story, Jacqueline poses with the chess set collection that her husband Gregor Piatigorsky, a famous cellist, formed during his travels. 3. Introduction for Los Angeles Times 1966 Woman of the Year Award December 20, 1966 Manuscript For her efforts in organizing the 1966 Piatigorsky Cup, one of the strongest chess tournaments ever held on American soil, the Los Angeles Times awarded Jacqueline Piatigorsky their “Woman of the Year” award. -
CHESS FEDERATION Newburgh, N.Y
Announcing an important new series of books on CONTEMPORARY CHESS OPENINGS Published by Chess Digest, Inc.-General Editor, R. G. Wade The first book in this current series is a fresh look at 's I IAN by Leonard Borden, William Hartston, and Raymond Keene Two of the most brilliant young ployers pool their talents with one of the world's well-established authorities on openings to produce a modern, definitive study of the King's Indian Defence. An essen tial work of reference which will help master and amateur alike to win more games. The King's Indian Defence has established itself as one of the most lively and populor openings and this book provides 0 systematic description of its strategy, tactics, and variations. Written to provide instruction and under standing, it contains well-chosen illustrative games from octuol ploy, many of them shown to the very lost move, and each with an analysis of its salient features. An excellent cloth-bound book in English Descriptive Notation, with cleor type, good diagrams, and an easy-to-follow format. The highest quality at a very reasonable price. Postpaid, only $4.40 DON'T WAIT-ORDER NOW-THE BOOK YOU MUST HAVE! FLA NINGS by Raymond Keene Raymond Keene, brightest star in the rising galaxy of young British players, was undefeated in the 1968 British Championship and in the 1968 Olympiad at Lugano. In this book, he posses along to you the benefit of his studies of the King's Indian Attack and the Reti, Catalan, English, and Benko Larsen openings. The notation is Algebraic, the notes comprehensive but easily understood and right to the point. -
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.