DOCSLIB.ORG

Exhaustive Search of Piece Combinations Based on Total Shannon Value

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Exhaustive Search of Piece Combinations Based on Total Shannon Value electronic Journal of Computer Science and Information Technology (eJCSIT), Vol. 5, No. 1, 2015 Exhaustive Search of Piece Combinations Based on Total Shannon Value Shazril bin Azman1 Azlan Iqbal2 1, 2College of Information Technology, Universiti Tenaga Nasional, Putrajaya Campus, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor e-mail: [email protected], [email protected] Abstract— In chess games, the Shannon value is one way to In this paper, we demonstrate a method to produce all the represent the relative values of chess pieces. We propose a piece combinations based on a particular TSV specified. The method to perform an exhaustive search of piece combinations piece combination consist of different possible combinations based on any given total Shannon value. Nested loops are used of queens, rooks, knights, bishops and pawns that are equal to along with certain sentinel controls that comply with the basic any given TSV and they are technically ‘legal’ in the game. rules of chess. For example, there are 9 loops assigned for the In Section II, we review some related works ranging from queen, as the maximum legal number of queens on the board is 9, including the promoted pawns. Therefore, each chess piece the historical background of the concept of permutation and (queen, rook, bishop, knight, pawn) has its own specific number its utilization in modern day applications. Section III of loops which correspond to its legal number and they are describes the method towards generating the piece nested in together. The experiment performed shows that if combination, and Section IV shows the results obtained. We nested loops that represent each of the pieces are arranged conclude briefly with Section V. together along with the chess-based sentinel controls, they can produce all possible and legal chess piece combinations that II. LITERATURE REVIEW match the desired Total Shannon Value (TSV). This method can be used for a variety of purposes in chess engines and other A. Permutation games or areas with similar constructs and constraints. The concept of permutations was first reported in ancient Index terms— Shannon value, nested loops, piece India [3]. Old Indian scriptures, such as the Brihat Samhita combination, exhaustive search deals with the treatise of permutations such as making perfume by mixing various ingredients in various I. INTRODUCTION combinative ways. In the writings of Brahmagupta, there are The Shannon value is a representation of the relative passages that deal with inquisitive permutations to be made, values of the chess pieces. It originates from C. Shannon’s such as how many different ways that 8 doors could be approximate evaluation function for programming a opened if the number of apertures in all the doors are one, computer to play chess [1]. Shannon’s evaluation function two, three, four and so on. However, further details or can be used by the computer in a chess game to decide which depictions are not available in the ancient texts. probably the best move is in order to win. Any chess player, Permutation allows different combinations of a set of be it human or computer, would typically strive to maintain symbols, numbers or alphabets, for instance, to be made. For the Total Shannon Value (TSV) or reduce the other player’s example, given the numbers 1, 2, and 3, the total permutation TSV, which is basically material in the game. Each of the five number is six, in total and as shown in Fig. 1. different chess pieces has the following Shannon values: 1, 2, 3 • Queen = 9 1, 3, 2 • Rook = 5 2, 1, 3 • Bishop = 3 2, 3, 1 • Knight = 3 3, 1, 2 • Pawn = 1 3, 2, 1 The king is usually excluded in the TSV because it is Figure 1. Permutations of 1, 2 and 3. regarded as having ‘infinite’ importance in a chess game. Losing the king means losing the game. The values assigned The above example can also be calculated as 3! (3 to each chess piece typically depend on the inherent utility of factorial) or 3x2x1=6, meaning that it has six different ways a particular piece. C. James in his ‘relative strength’ approach of permuting the numbers. Permutations also have been in [2] added more refinements by assigning values to a chess widely used to protect multimedia data across the internet [4]. piece based on its ‘mobility aspect’ such as counting the Digital multimedia elements such as pixels and video signals number of squares controlled by the chess piece so that the can be permuted in a secure way to cipher the multimedia value of the piece is more reliable. For example, the relative data before it is sent to the authorized recipient. For example, strength value for the king at the corner of the board is 3, the word ‘drinking water’ could be encoded into ‘rgnkadnei because at that position, the king controls three squares in his wit’ by using a certain permutation matrix and can be safely surroundings. The queen would have more relative strength decoded by the authorized receiver who has a prior value than the other pieces because the queen has more decryption key. Digital multimedia files such as JPEG could controlled squares. S. Azman and A. Iqbal, Exhaustive Search of Piece Combinations Based on Total Shannon Value 7 electronic Journal of Computer Science and Information Technology (eJCSIT), Vol. 5, No. 1, 2015 also be encoded into blurry and randomized pixels that an Hackers are more likely to be individuals who try to gain unauthorized recipient would not understand. unauthorized access on documents, software, or computer. Permutations are also useful to reduce storage Crackers, on the other hand, are the individuals who try to requirements and disk transfer rates in video-on-demand find security loopholes to bypass certain firewalls via the (VOD) systems. In video broadcasting, the management of network [10]. video block storage in the set-top box (see Fig. 2) is An example of a computer program that utilizes brute important. A set-top box is another name for the video force is Chinook. Chinook is a checker program that uses a decoder [5]. In Malaysia, for example, the video decoder deep brute force search algorithm with its own evaluation device provided by AstroTM to the users is a set-top box per se function to play against human player. Chinook was played [6]. against human player in an actual checker tournament in 1992 (World Checkers Champion) but lost at the hands of Dr. Marion Tinsley, the defending champion. J. Schaeffer pointed out that there comes a point where deep brute force search is not cost effective. Certain factors such as high processing and hardware consumption should also be considered in brute force approach [11, 12]. Otherwise known as diminishing returns. C. Shannon also argued that game strategies should not rely too much on brute force. Instead, logical analyses of the piece’s position should be focused upon. Brute force is also used in password recovery tools that permute all possible combinations of digits, alphabets and Figure 2. Astro Video Decoder. symbols to recover the forgotten password. However, since the recovery task is arduous, and could take millions of years, While buffering, part of the video block is initially stored the tools provide settings to narrow down the exhaustive in the device before being displayed, just like a YoutubeTM search, such as recovering a password that might contain a video’s buffering grey bar at the bottom of the flash video possible word or character that the user can remember, or is player that is progressively increasing throughout the contained in a dictionary [13]. playback, indicating that the video block is stored in the computer progressively [7]. C. Recursion A method called recursion was studied. Recursion can be roughly translated as ‘call back’ [14]. It enables the computer to call back a previous instruction or code line. For example, the computer is reading code line number four, and then at the next code line, it is instructed to go back to code line number two, so the computer goes back to read code line number two. This can be done repetitively until it fulfills certain conditions. Recursion in programming can perhaps better be described as a function that calls itself in order to solve a simpler version of the problem before ‘scaling up’ to the final answer. Figure 3. YoutubeTM buffering bar, as shown by the red arrow. D. Programming Language Used We used the Python Programming Language to generate High bandwidth video transmission will give smooth the piece combinations. Python was developed by Guido von streaming, but it increases the storage requirement and this Rossum in 1990 [15]. It is known for its short, clear and easy could cause latency in the transmission traffic. If there are syntax, high level dynamic data types and portability. Its thousands of users being given high bandwidth video outputs can be easily copied and pasted into a spreadsheet transmission simultaneously, it would bottleneck the program such as Microsoft Excel for further analysis. transmission traffic. This will cause latency. Charu et al. in [8] introduced a permutation-based pyramid broadcasting scheme, which transmits video blocks in a pre-specified III. METHODOLOGY cyclic permutation and it substantially reduces the latency, We coin the term ‘piece combination’ as a reference to the storage and disk transfer rate. combination of chess pieces that matches the desired TSV when each of their Shannon values is summed up together. B. Brute Force The piece combination concept is inspired by the concepts of permutation, brute force and recursion, even though it does The other common name for exhaustive search is ‘brute not follow those concepts exactly.
Load more

Recommended publications
  • Recovering and Rendering Vital Blueprint for Counter Education At
    Recovering and Rendering Vital clash that erupted between the staid, conservative Board of Trustees and the raucous experimental work and atti- Blueprint for Counter Education tudes put forth by students and faculty (the latter often- times more militant than the former). The full story of the at the California Institute of the Arts Institute during its frst few years requires (and deserves) an entire book,8 but lines from a 1970 letter by Maurice Paul Cronin Stein, founding Dean of the School of Critical Studies, written a few months before the frst students arrived on campus, gives an indication of the conficts and delecta- tions to come: “This is the most hectic place in the world at the moment and promises to become even more so. At heart of the California Institute of Arts’ campus is We seem to be testing some complex soap opera prop- a vast, monolithic concrete building, containing more osition about the durability of a marriage between the than a thousand rooms. Constructed on a sixty-acre site radical right and left liberals. My only way of adjusting to thirty-fve miles north of Los Angeles, it is centered in the situation is to shut my eyes, do my job, and hope for what at the end of the 1960s was the remote outpost the best.”9 of sun-scorched Valencia (a town “dreamed up by real estate developers to receive the urban sprawl which is • • • Los Angeles”),1 far from Hollywood, a town that was—for many students at the Institute—the belly of the beast.
    [Show full text]
  • Chess Camp Volume 3: Checkmates with Many Pieces Contents Note for Coaches, Parents, Teachers, and Trainers
    Igor Sukhin Chess Camp Volume 3: Checkmates with Many Pieces Contents Note for Coaches, Parents, Teachers, and Trainers ........................................................................ 5 Mate in One in the Opening Approaching the Opening ............................................................................................................... 7 Silly Games ......................................................................................................................................13 Open Games ...................................................................................................................................17 Semi-Open Games ...........................................................................................................................40 Closed Games ................................................................................................................................ 49 Mate in One in the Middlegame Pins .................................................................................................................................................55 Silly Pin Positions ............................................................................................................................57 Double Check .................................................................................................................................58 Discovered Check ...........................................................................................................................60 Attacking
    [Show full text]
  • 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
    [Show full text]
  • Virginia Chess Federation 2008 - #6
    VIRGINIA CHESS Newsletter The bimonthly publication of the Virginia Chess Federation 2008 - #6 Grandmaster Larry Kaufman See page 1 VIRGINIA CHESS Newsletter 2008 - Issue #6 Editor: Circulation: Macon Shibut Ernie Schlich 8234 Citadel Place 1370 South Braden Crescent Vienna VA 22180 Norfolk VA 23502 [email protected] [email protected] k w r Virginia Chess is published six times per year by the Virginia Chess Federation. Membership benefits (dues: $10/yr adult; $5/yr junior under 18) include a subscription to Virginia Chess. Send material for publication to the editor. Send dues, address changes, etc to Circulation. The Virginia Chess Federation (VCF) is a non-profit organization for the use of its members. Dues for regular adult membership are $10/yr. Junior memberships are $5/yr. President: Mike Hoffpauir, 405 Hounds Chase, Yorktown VA 23693, mhoffpauir@ aol.com Treasurer: Ernie Schlich, 1370 South Braden Crescent, Norfolk VA 23502, [email protected] Secretary: Helen Hinshaw, 3430 Musket Dr, Midlothian VA 23113, jallenhinshaw@comcast. net Scholastics Coordinator: Mike Hoffpauir, 405 Hounds Chase, Yorktown VA 23693, [email protected] VCF Inc. Directors: Helen Hinshaw (Chairman), Rob Getty, John Farrell, Mike Hoffpauir, Ernie Schlich. otjnwlkqbhrp 2008 - #6 1 otjnwlkqbhrp Larry Kaufman, of Maryland, is a familiar face at Virginia tournaments. Among others he won the Virginia Open in 1969, 1998, 2000, 2006 and 2007! Recently Larry achieved a lifelong goal by attaining the title of International Grandmaster, and agreed to tell VIRGINIA CHESS readers how it happened. -ed World Senior Chess Championship by Larry Kaufman URING THE LAST FIVE YEARS OR SO, whenever someone asked me Dif I still hoped to become a GM, I would reply something like this: “I’m too old now to try to do it the normal way, but perhaps when I reach 60 I will try to win the World Senior, which carries an automatic GM title.
    [Show full text]
  • Duchamp, Chess and the Avant-Garde
    ENDGAME: DUCHAMP, CHESS AND THE AVANT-GARDE Press kit 29.10.2016—22.01.2017 Fundació Joan Miró Now I am content to just play. I am still a victim of chess. It has all the beauty of art – and much more. It cannot be commercialized. Chess is much purer than art in its social position. The chess pieces are the block alphabet which shapes thoughts; and these thoughts, although making a visual design on the chess board, express their beauty abstractly, like a poem. […] I have come to the conclusion that while all artists are not chess players, all chess players are artists. Marcel Duchamp. Address at the banquet of the New York State Chess Association in 1952 1 Contents Press release 3 Curator 9 Exhibition layout 12 Sections of the exhibition and selection of works 13 Full list of works 28 Artists and sources of the works 35 Publication 38 Activities 39 General information 41 2 Press release Endgame. Duchamp, Chess and the Avant-Garde Fundació Joan Miró 29 October 2016 – 22 January 2017 Opening: 28 October 2016, 7 pm Curator: Manuel Segade Sponsored by the BBVA Foundation The Fundació Joan Miró presents Endgame: Duchamp, Chess and the Avant-Garde, an exhibition that re-reads the history of modern art through the lens of its relationship to chess. The exhibition, sponsored by the BBVA Foundation and curated by Manuel Segade, looks at chess as a leitmotif that runs through the avant-garde, and metaphorically offers an innovative and playful insight into the history of modern art. Endgame: Duchamp, Chess and the Avant-Garde brings together around eighty works, including paintings and sculptures – some of which have never been shown before in Spain – by some of the key artists of the twentieth century, drawn from major public and private collections in Europe, America, and Middle East.
    [Show full text]
  • The Reviled Art Stuart Rachels
    The Reviled Art Stuart Rachels “If chess is an art, it is hardly treated as such in the United States. Imagine what it would be like if music were as little known or appreciated. Suppose no self-respecting university would offer credit courses in music, and the National Endowment for the Arts refused to pay for any of it. A few enthusiasts might compose sonatas, and study and admire one another’s efforts, but they would largely be ignored. Once in a while a Mozart might capture the public imagination, and like Bobby Fischer get written about in Newsweek. But the general attitude would be that, while this playing with sound might be clever, and a great passion for those who care about it, still in the end it signifies nothing very important.” —James Rachels1 Bragging and Whining When I was 11, I became the youngest chess master in American history. It was great fun. My picture was put on the cover of Chess Life; I appeared on Shelby Lyman’s nationally syndicated chess show; complete strangers asked me if I was a genius; I got compared to my idol, Bobby Fischer (who was not a master until he was 13); and I generally enjoyed the head-swelling experience of being treated like a king, as a kid among adults. When I wasn’t getting bullied at school, I felt special. And the fact that I was from Alabama, oozing a slow Southern drawl, must have increased my 2 mystique, since many northeastern players assumed that I lived on a farm, and who plays chess out there? In my teens, I had some wonderful experiences.
    [Show full text]
  • Mapping Chess Aesthetics Onto Procedurally Generated Chess-Like Games
    Mapping Chess Aesthetics onto Procedurally Generated Chess-like Games Jakub Kowalski1?, Antonios Liapis2, and Łukasz Żarczyński3 1 Institute of Computer Science, University of Wrocław, [email protected] 2 Institute of Digital Games, University of Malta, [email protected] 3 Institute of Computer Science, University of Wrocław, [email protected] Abstract. Variants of chess have been generated in many forms and for several reasons, such as testbeds for artificial intelligence research in gen- eral game playing. This paper uses the visual properties of chess pieces as inspiration to generate new shapes for other chess-like games, targeting specific visual properties which allude to the pieces’ in-game function. The proposed method uses similarity measures in terms of pieces’ strate- gic role and movement in a game to identify the new pieces’ closest representatives in chess. Evolution then attempts to minimize the dis- tance from chess pieces’ visual properties, resulting in new shapes which combine one or more chess pieces’ visual identities. While experiments in this paper focus on two chess-like games from previous publications, the method can be used for broader generation of game visuals based on functional similarities of components to known, popular games. Keywords: Procedural Content Generation, Chess Variants, Digital Aes- thetics, Evolutionary Algorithms, Simplified Boardgames 1 Introduction For over a decade, digital games have been the domain of choice for research in computational and artificial intelligence, culminating in several handbooks on the topic [1, 2]. The vast majority of the research output on this domain has been treating digital games as systems, focusing on their functional aspects.
    [Show full text]
  • Mapping Chess Aesthetics Onto Procedurally Generated Chess-Like Games
    Mapping Chess Aesthetics onto Procedurally Generated Chess-like Games Jakub Kowalski, Antonios Liapis,Lukasz Zarczy´nski_ University of Wroc law, Poland University of Malta, Malta EvoGAMES 05.04.2018 Jakub Kowalski, Antonios Liapis,Lukasz Zarczy´nski_ Mapping Chess Aesthetics onto Procedurally Generated Chess-like Games Background Jakub Kowalski, Antonios Liapis,Lukasz Zarczy´nski_ Mapping Chess Aesthetics onto Procedurally Generated Chess-like Games Procedural Content Generation (PCG) Jakub Kowalski, Antonios Liapis,Lukasz Zarczy´nski_ Mapping Chess Aesthetics onto Procedurally Generated Chess-like Games General Game Playing (GGP) Jakub Kowalski, Antonios Liapis,Lukasz Zarczy´nski_ Mapping Chess Aesthetics onto Procedurally Generated Chess-like Games Simplified Boardgames (Bj¨ornsson,2012) P (0,1,e) + (-1,1,p) + (1,1,p) + (0,1,e)(0,5,e)(0,-4,e) + ... & N (2,1,e) + (2,-1,e) + (-2,1,e) + (-2,-1,e) + (1,2,e)... & R (0,1,e)^* + (0,1,e)^*(0,1,p) + (0,-1,e)^* + ... & Jakub Kowalski, Antonios Liapis,Lukasz Zarczy´nski_ Mapping Chess Aesthetics onto Procedurally Generated Chess-like Games Motivation Jakub Kowalski, Antonios Liapis,Lukasz Zarczy´nski_ Mapping Chess Aesthetics onto Procedurally Generated Chess-like Games Procedural Content Generation for GDL Descriptions of Simplified Boardgames (Kowalski, Szykula; 2015) Jakub Kowalski, Antonios Liapis,Lukasz Zarczy´nski_ Mapping Chess Aesthetics onto Procedurally Generated Chess-like Games Evolving Chesslike Games Using Relative Algorithm Performance Profiles (Kowalski, Szyku la; 2016) Jakub Kowalski, Antonios Liapis,Lukasz Zarczy´nski_ Mapping Chess Aesthetics onto Procedurally Generated Chess-like Games Evaluating Chess-like Games Using Generated Natural Language Descriptions (Kowalski, Zarczy´nski,Kisielewicz;_ 2017) Jakub Kowalski, Antonios Liapis,Lukasz Zarczy´nski_ Mapping Chess Aesthetics onto Procedurally Generated Chess-like Games Goal The shapes evolved for one game should look similar, so that they are easily identified as parts of a whole.
    [Show full text]
  • Pages 116-128
    Appendix A: Two personal appreciations Flere follow translations of the original introductions to 64 studii z oboru vdioUich a pdicovlich koncovek and Studie. To 64 studii z oboru vdiovllch a pdicovlich koncovek by Bediich Thelen (1905-72). Thelen was little known outside his own country, but was among the leading players within it; he had a first place in an international tourney (Tapolcza Fiirdo 1926) to his credit, he achieved second place in a wartime championship of Bohemia and Moravia, and he was the captain of tl.re Czechoslovak team at the 1964 Olympiad. He published a textbook, "A detailed treatise on chess". in 1929. I have known the author of this little book for more than 40 years. Of coune, I first met him behind a chessboard. I already knew that he was a friend of the chess master Richard Rdti. And that fact in itself said a great deal to me, a very great deal... Dr Artur Mandler is a master of the chess study. A renowned rnaster! His works have something to say to chess enthusiasts, and he knows irow to say it. So I advised him to select for this collection those of his studies which would be of the greatest value to practical players, namely some of his rook and pawn studies. Was this good advice? Do not practical players find all that they need in endgame textbooks, which in any case are larger and more comprehensive? The practical player seeks usefulness, not beauty! But why, in that case, do textbooks contain so many studies? Because the effect ofan artistic work is stronger and longer-lasting than that of exhaustive notes in a textbook.
    [Show full text]
  • VARIANTIM Bulletin of the Israel Chess Composition Society
    VARIANTIM Bulletin of The Israel Chess Composition Society P.O. Box 637 Petach-Tikva 49106 Israel www.variantim.org No. 58 - December 2012 Editors Paz Einat, 45a Moshe Levi St., Nes Ziona 74207 [email protected] Shaul Shamir, 3 Dror St., Rishon Lezion 75305 [email protected] Ofer Comay, 213 Bney Efrayim St., Tel Aviv 69984 [email protected] Original problems Regular: Evgeny Bourd, Haazmaut 55/15, Ashdod 77452 [email protected] Fairy: Michael Grushko, P.O.Box 363, Kiryat Beyalik 27019 [email protected] Studies: Ofer Comay [email protected] In this issue: Pat aidé super-complet - Kummer 2-3 Israeli Successes Abroad - Navon 11-12 Philip Stamma and the Modern Study – Costeff 3-5 Originals 13-17 Working out an old Rukhlis mechanism – Einat 5-6 Selected Problems – Bourd 18-19 IRT - Threemovers 2009-11- Kuhlmann 7-8 Haymann 80 Birthday meeting 19 Storisteanu corrections 8 Israeli successes in Kobe 20-21 IRT - Fairies 2011- Gordian 9-10 Kobe Congress report – Einat 22 Ettinger 90 Memorial Tourney announcement 10 Editorial 23 1/4 Solving Championship 2013 23 Menachem Witztum & Mark Erenburg, our new International Master and FIDE Master 1 Pat aidé super-complet Eckart Kummer, Berlin (Germany) (Translated & shortened version of an article first published in Die Schwalbe, August 2012) Variantim readers will probably have heard of those feats which in 1964 the French problemist Romeo Bédoni proposed labelling aidé complet. In addition to the "normal" solution there have to be (in a helpmate or helpstalemate in 2) three tries which fail for lack of a tempo at B1, B2 and W1 respectively.
    [Show full text]
  • Lasker's Manual of Chess
    Lasker’s Manual of Chess by Emanuel Lasker Foreword by Mark Dvoretsky 2008 Russell Enterprises, Inc. Milford, CT USA 3 Lasker’s Manual of Chess © Copyright 2008 Russell Enterprises, Inc. 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. ISBN: 978-1-888690-50-7 Published by: Russell Enterprises, Inc. PO Box 5460 Milford, CT 06460 USA http://www.chesscafe.com [email protected] Cover design by Zygmunt Nasiolkowski and Janel Lowrance Editing and Proofreading: Taylor Kingston, David Kaufmann, Hanon Russell Production: Mark Donlan Printed in the United States of America 4 Table of Contents Foreword 14 Editor’s Preface 16 Dr. Lasker’s Tournament Record 18 Dr. Lasker’s Match Record 19 Preface to the Original German Edition 20 Book I: The Elements of Chess 21 Book II: The Theory of the Openings 50 Book III. The Combination 102 Book IV: Position Play 140 Book V: The Aesthetic Effect in Chess 199 Book VI: Examples and Models 216 Final Reflections 247 Analytical Endnotes 250 Index of Players 275 Index of Openings 277 Analytical Contents First Book The Elements of Chess 21 Brief Account of the Origin of the Game 21 The Chess Board 21 The Pieces 23 The Rules for Moving: a. the King 23 b. the Rook 23 c.
    [Show full text]
  • Catalogue 2017 POLISH Chess Sets CONTENTS
    since 1996 catalogue 2017 POLISH CHess Sets CONTENTS About us /3 CHESSBOARDS AND TABLES /49 wooden /49 wholesale /4 plastic /53 Production /5 e-boards /57 Wooden chess sets /6 tables /65 Amateur /6 DEMO CHESSBOARDS, ACCESSORIES /67 Decorative /17 three players /30 CHESS CLOCKS /70 tournament /31 ANALOG /70 travel /37 DIGITAL /72 Multi-game sets CHESS PIECES /40 /74 wooden /40 backgammon sets /76 indian /42 CHECKERS (DRAUGHTS) /78 plastic /46 2 About us We are a Polish based company engaged in the production and sale of hand-made We invite you to shop both online store and visit our warehouse near Lublin, Poland: wooden games such as chess sets, checkers or backgammon. Marysin, Szarugi 59A street, where you can also see and buy our chess. Our company was established in 1996 in Poland and has beensteadily growing. We We encourage everyone to play chess. This great game develops a lot of skills, helps currently export to most European countries, as well as to the United States, Canada, to improve memory, ability to concentrate practices in attention and stimulates the Australia and Japan. imagination to the youngest as well as oldest players. In the production process we use only carefully selected high quality wood species. All If you need help in making the purchases, please call us +48 81 7409614 we speak our products are manufactured in Poland by the best polish craftsmen working with us. English and French. The effort that they put into their work and creativity, makes our chess sets an interesting alternative for the modern mass production.
    [Show full text]