Chess Obligation to Make a Move
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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. -
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. -
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). -
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. -
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. -
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”. -
CHESS INFORMANT Contain
Drawing by Bob Brandreth , The , E"..-y ail: mono. the Yuqoalav ChI .. Federation brings out a Dew book of the tin.. 1 gom.. plared dwinq the preceding baH y.ar. A unique. Dewly-deviled aystem of annotating gwu_ by coded ligna moida all languuge obetcd... 1'Ju. malt. possible a univeraally usable and yet V'Osonably-priced book which brings the neweat ideaa in the opening,; and throughout the game to every ch.. enthusiast more quickly U"m ever before. Book 6 confaina 821 gam.. played between July 1 and D.cember 31, 1968. A qreat aelectiOD of theoretically important gam_ from 28 toumcnrumta and match.. , inc1uding the Lugano Olympiad. World Student Team Cbmnpionsbip (Ybb.), Mar del Plata. Netanya, Amaterdam. Skopje, Debrecen, Sombot. Havana. Vinkovci, Belgrade, Palma d. Majorca, and Athens, S.pacial New Featurel Beginning with Book 6. each CHESS INFORMANT contain. a aection for FIDE communicati0D8, re placing the former official publication FIDE REVIEW. The FIDE section in this iau. contains comple'e Regu1ationa for the Toumamenta and Match BII for the Men'. and l.cdl·,' World CbampiC'Dlhipa. Pr.. crih n the entire competition .,atem from Zonal cmd Interzonal Toummnenta throuqb the Ccmdidatea Matches to the World Championship Match. Book 6 has aections leaturing 51 brilliant Combinations and 45 Endings from actual play during the preceding six months. Another interesting feature ia a table listing in Older the Ten Beat Gam,ea from Book 5 and showing how each of the eight Grandmastem on the jury voted. Contains an Engliah·lanquage introduction. esplanation of the annotation cod•• indez of play em and comm._tcrton. -
Chess Rules Ages 10 & up • for 2 Players
Front (Head to Head) Prints Pantone 541 Blue Chess Rules Ages 10 & Up • For 2 Players Contents: Game Board, 16 ivory and 16 black Play Pieces Object: To threaten your opponent’s King so it cannot escape. Play Pieces: Set Up: Ivory Play Pieces: Black Play Pieces: Pawn Knight Bishop Rook Queen King Terms: Ranks are the rows of squares that run horizontally on the Game Board and Files are the columns that run vertically. Diagonals run diagonally. Position the Game Board so that the red square is at the bottom right corner for each player. Place the Ivory Play Pieces on the first rank from left to right in order: Rook, Knight, Bishop, Queen, King, Bishop, Knight and Rook. Place all of the Pawns on the second rank. Then place the Black Play Pieces on the board as shown in the diagram. Note: the Ivory Queen will be on a red square and the black Queen will be on a black space. Play: Ivory always plays first. Players alternate turns. Only one Play Piece may be moved on a turn, except when castling (see description on back). All Play Pieces must move in a straight path, except for the Knight. Also, the Knight is the only Play Piece that is allowed to jump over another Play Piece. Play Piece Moves: A Pawn moves forward one square at a time. There are two exceptions to this rule: 1. On a Pawn’s first move, it can move forward one or two squares. 2. When capturing a piece (see description on back), a Pawn moves one square diagonally ahead. -
Basicxqcheckmate.Pdf
PDF created with pdfFactory Pro trial version www.pdffactory.com Preface The game of Xiangqi is similar to the deployment of forces for military operation. Though it is a battle on xiangqi board, its theory is similar to the military strategy and tactics. As it is stipulated by the xiangqi rules, the side that captures the opponent's King will be the winner of the game. Therefore, each side tries to outwit his opponent and strives to show his bravery in taking various kinds of checkmate methods and to do his best to seize every opportunity for winning the victory. The game of xiangqi is rendered with a mysterious hue. Nearly all xiangqi players or fans understand that the checkmate method takes an important position in the xiangqi game. However, some of the players believe that "the checkmate method can only play its roles in the end game." But in reality, we often see that in the heat-fought mid-game, being eager to achieve a quick success and instant benefit, one side often neglects to defend his own King, offering the opponent an opportunity for making a counterattack or winning the game. Although sometimes, a player has a chance to take a successive checkmate, as he is rusty on the checkmate methods, he bungles a chance of winning the battle, or loses the game. Such cases are often seen in actual competitions. And there are numerous examples showing that some players take advantage of checkmate methods in seizing opponent's pieces. In fact, the checkmate methods play a very important role, directly or indirectly, not only in the end game, but also in the mid-game, even in the entire game. -
Chapter 10, Different Objectives of Play
Chapter 10 Different objectives of play [The normal objective of a game of chess is to give checkmate. Some of the games which can be played with chessmen have quite different objectives, and two of them, Extinction Chess and Losing Chess, have proved to be among the most popular of all chess variants.] 10.1 Capturing or baring the king Capturing the king. The Chess Monthly than about the snobbery of Mr Donisthorpe!] hosted a lively debate (1893-4) on the suggestion of a Mr Wordsworth Donisthorpe, Baring the king. The rules of the old chess whose very name seems to carry authority, allowed a (lesser) win by ‘bare king’ and that check and checkmate, and hence stalemate, and Réti and Bronstein have stalemate, should be abolished, the game favoured its reintroduction. [I haven’t traced ending with the capture of the king. The the Bronstein reference, but Réti’s will be purpose of this proposed reform was to reduce found on page 178 of the English edition of the number of draws then (as now) prevalent Modern Ideas in Chess. It is in fact explicit in master play. Donisthorpe claimed that both only in respect of stalemate, though the words Blackburne and the American master James ‘the original rules’ within it can be read as Mason were in favour of the change, adding supporting bare king as well, and perhaps ‘I have little doubt the reform would obtain I ought to quote it in full. After expounding the support of both Universities’ which says the ancient rules, he continues: ‘Those were something about the standing of Oxford and romantic times for chess. -
New Data and Multivariate Methods Transform E-Underwriting Businesspeople Often Describe Competition in Terms of Chess, and Rightly So
Stalemate to Checkmate: New Data and Multivariate Methods Transform E-underwriting Businesspeople often describe competition in terms of chess, and rightly so. It’s a game of strategy and skill, but not of ambiguous outcomes: Only two things can happen in a chess game – a checkmate or a stalemate. The analogy effectively captures the challenges confronting U.S. life insurers as carriers seek to Bruce Bosco expand in seemingly mature markets. Vice President Business Development Consider the stalemate: the point during a chess game in which the player is left with no legal move, AURA and the game ends in a draw. The same term could describe the state of the U.S. life insurance market, where carriers confront a coverage gap worth an estimated $16 trillion. While this vast pool of under-protected potential policyholders seems to represent a tremendous opportunity, on the whole it has remained stubbornly out of reach. After investing mightily in improving the purchasing experience, insurance leaders may understandably feel as if there are no moves left. Relax underwriting assessment any further, and carriers rightly fear that a streamlined sale today may lead to widening losses tomorrow. Until recently this stalemate seemed destined to continue indefinitely. To move from stalemate to checkmate, insurers must first understand that the rules of the game have changed. New Game, New Rules Today’s life insurance consumers are looking for a buying experience befitting the digital age. They want to make quick, convenient, and affordable purchases, but this expectation is often thwarted by onerous underwriting requirements. Thankfully, the combination of new data sources and automated underwriting technologies have enabled insurers to change the rules of the game.