Finding Checkmate in N Moves in Chess Using Backtracking And
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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. -
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. -
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. -
IVAN II Operating Manual Model 712
IVAN II Operating Manual Model 712 Congratulations on your purchase of Excalibur Electronics’ IVAN! You’ve purchased both your own personal chess trainer and a partner who’s always ready for a game—and who can improve as you do! Talking and audio sounds add anoth- Play a Game Right Away er dimension to your IVAN computer for After you have installed the batteries, the increased enjoyment and play value. display will show the chess board with all the pieces on their starting squares. Place Find the Pieces the plastic chess pieces on their start Turn Ivan over carefully with his chess- squares using the LCD screen as a guide. board facedown. Find the door marked The dot-matrix display will show “PIECE COMPARTMENT DOOR”. 01CHESS. This indicates you are at the Open it and remove the chess pieces. first move of the game and ready to play Replace the door and set the pieces aside chess. for now. Unless you instruct it otherwise, IVAN gives you the White pieces—the ones at Install the Batteries the bottom of the board. White always With Ivan facedown, find the door moves first. You’re ready to play! marked “BATTERY DOOR’. Open it and insert four (4) fresh, alkaline AA batteries Making your move in the battery holder. Note the arrange- Besides deciding on a good move, you ment of the batteries called for by the dia- have to move the piece in a way that Ivan gram in the holder. Make sure that the will recognize what's been played. Think positive tip of each battery matches up of communicating your move as a two- with the + sign in the battery compart- step process--registering the FROM ment so that polarity will be correct. -
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. -
Proposal to Encode Heterodox Chess Symbols in the UCS Source: Garth Wallace Status: Individual Contribution Date: 2016-10-25
Title: Proposal to Encode Heterodox Chess Symbols in the UCS Source: Garth Wallace Status: Individual Contribution Date: 2016-10-25 Introduction The UCS contains symbols for the game of chess in the Miscellaneous Symbols block. These are used in figurine notation, a common variation on algebraic notation in which pieces are represented in running text using the same symbols as are found in diagrams. While the symbols already encoded in Unicode are sufficient for use in the orthodox game, they are insufficient for many chess problems and variant games, which make use of extended sets. 1. Fairy chess problems The presentation of chess positions as puzzles to be solved predates the existence of the modern game, dating back to the mansūbāt composed for shatranj, the Muslim predecessor of chess. In modern chess problems, a position is provided along with a stipulation such as “white to move and mate in two”, and the solver is tasked with finding a move (called a “key”) that satisfies the stipulation regardless of a hypothetical opposing player’s moves in response. These solutions are given in the same notation as lines of play in over-the-board games: typically algebraic notation, using abbreviations for the names of pieces, or figurine algebraic notation. Problem composers have not limited themselves to the materials of the conventional game, but have experimented with different board sizes and geometries, altered rules, goals other than checkmate, and different pieces. Problems that diverge from the standard game comprise a genre called “fairy chess”. Thomas Rayner Dawson, known as the “father of fairy chess”, pop- ularized the genre in the early 20th century. -
Kasparov's Nightmare!! Bobby Fischer Challenges IBM to Simul IBM
California Chess Journal Volume 20, Number 2 April 1st 2004 $4.50 Kasparov’s Nightmare!! Bobby Fischer Challenges IBM to Simul IBM Scrambles to Build 25 Deep Blues! Past Vs Future Special Issue • Young Fischer Fires Up S.F. • Fischer commentates 4 Boyscouts • Building your “Super Computer” • Building Fischer’s Dream House • Raise $500 playing chess! • Fischer Articles Galore! California Chess Journal Table of Con tents 2004 Cal Chess Scholastic Championships The annual scholastic tourney finishes in Santa Clara.......................................................3 FISCHER AND THE DEEP BLUE Editor: Eric Hicks Contributors: Daren Dillinger A miracle has happened in the Phillipines!......................................................................4 FM Eric Schiller IM John Donaldson Why Every Chess Player Needs a Computer Photographers: Richard Shorman Some titles speak for themselves......................................................................................5 Historical Consul: Kerry Lawless Founding Editor: Hans Poschmann Building Your Chess Dream Machine Some helpful hints when shopping for a silicon chess opponent........................................6 CalChess Board Young Fischer in San Francisco 1957 A complet accounting of an untold story that happened here in the bay area...................12 President: Elizabeth Shaughnessy Vice-President: Josh Bowman 1957 Fischer Game Spotlight Treasurer: Richard Peterson One game from the tournament commentated move by move.........................................16 Members at -
Checkmate Bobby Fischer's Boys' Life Columns
Bobby Fischer’s Boys’ Life Columns Checkmate Bobby Fischer’s Boys’ Life Columns by Bobby Fischer Foreword by Andy Soltis 2016 Russell Enterprises, Inc. Milford, CT USA 1 1 Checkmate Bobby Fischer’s Boys’ Life Columns by Bobby Fischer ISBN: 978-1-941270-51-6 (print) ISBN: 978-1-941270-52-3 (eBook) © Copyright 2016 Russell Enterprises, Inc. & Hanon W. Russell All Rights Reserved No part of this book may be used, reproduced, stored in a retrieval system or transmitted in any manner or form whatsoever or by any means, electronic, electrostatic, magnetic tape, photocopying, recording or otherwise, without the express written permission from the publisher except in the case of brief quotations embodied in critical articles or reviews. Chess columns written by Bobby Fischer appeared from December 1966 through January 1970 in the magazine Boys’ Life, published by the Boy Scouts of America. Russell Enterprises, Inc. thanks the Boy Scouts of America for its permission to reprint these columns in this compilation. Published by: Russell Enterprises, Inc. P.O. Box 3131 Milford, CT 06460 USA http://www.russell-enterprises.com [email protected] Editing and proofreading by Peter Kurzdorfer Cover by Janel Lowrance 2 Table of Contents Foreword 4 April 53 by Andy Soltis May 59 From the Publisher 6 Timeline 60 June 61 July 69 Timeline 7 Timeline 70 August 71 1966 September 77 December 9 October 78 November 84 1967 February 11 1969 March 17 February 85 April 19 March 90 Timeline 22 May 23 April 91 June 24 July 31 May 98 Timeline 32 June 99 August 33 July 107 September 37 August 108 Timeline 38 September 115 October 39 October 116 November 46 November 122 December 123 1968 February 47 1970 March 52 January 128 3 Checkmate Foreword Bobby Fischer’s victory over Emil Nikolic at Vinkovci 1968 is one of his most spectacular, perhaps the last great game he played in which he was the bold, go-for-mate sacrificer of his earlier years.