The Complete Guide to Chess
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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. -
The London System Is a Chess Opening That Usually Arises After 1.D4 and 2.Bf4, Or 2.Nf3 and 3.Bf4
ICC presents: The London System by GM Damian Lemos This is a guide that comes with the video course “The London System”. We highly recommend you first watch the video series before completing these exercises. To watch the videos, click here. The London System is a chess opening that usually arises after 1.d4 and 2.Bf4, or 2.Nf3 and 3.Bf4. It is a "system" opening that can be used against virtually any black defense and thus comprises a smaller body of opening theory than many other openings. The London is a set of solid lines where after 1.d4 White quickly develops his dark- squared bishop to f4 and normally bolsters his center with pawns on c3 and e3 rather than expanding. Although it has the potential for a quick kingside attack, the white forces are generally flexible enough to engage in a battle anywhere on the board. Historically it developed into a system mainly from three variations: 1.d4 d5 2.Nf3 Nf6 3.Bf4 1.d4 Nf6 2.Nf3 e6 3.Bf4 1.d4 Nf6 2.Nf3 g6 3.Bf4 "There is one opening that shines above all others when comparing reward payout to the input effort," says Zhigen Lin. "It is relatively quick to learn and obscure enough that even titled opponents may not have a proper antidote lined up." He is - of course - talking about the London System, popularized by the London BCF Congress Tournament of 1922. ICC presents: The London System by GM Damian Lemos Learning the London system is not hard, and it can be an essential arrow in your quiver! All you need is a set of videos by an experienced GM and, of course, a lot of practice! Damian Lemos became a chess Grandmaster at 18 and won the Gold Medal at the Pan-American Games U-20 in Colombia. -
Games Ancient and Oriental and How to Play Them, Being the Games Of
CO CD CO GAMES ANCIENT AND ORIENTAL AND HOW TO PLAY THEM. BEING THE GAMES OF THE ANCIENT EGYPTIANS THE HIERA GRAMME OF THE GREEKS, THE LUDUS LATKUNCULOKUM OF THE ROMANS AND THE ORIENTAL GAMES OF CHESS, DRAUGHTS, BACKGAMMON AND MAGIC SQUAEES. EDWARD FALKENER. LONDON: LONGMANS, GEEEN AND Co. AND NEW YORK: 15, EAST 16"' STREET. 1892. All rights referred. CONTENTS. I. INTRODUCTION. PAGE, II. THE GAMES OF THE ANCIENT EGYPTIANS. 9 Dr. Birch's Researches on the games of Ancient Egypt III. Queen Hatasu's Draught-board and men, now in the British Museum 22 IV. The of or the of afterwards game Tau, game Robbers ; played and called by the same name, Ludus Latrunculorum, by the Romans - - 37 V. The of Senat still the modern and game ; played by Egyptians, called by them Seega 63 VI. The of Han The of the Bowl 83 game ; game VII. The of the Sacred the Hiera of the Greeks 91 game Way ; Gramme VIII. Tlie game of Atep; still played by Italians, and by them called Mora - 103 CHESS. IX. Chess Notation A new system of - - 116 X. Chaturanga. Indian Chess - 119 Alberuni's description of - 139 XI. Chinese Chess - - - 143 XII. Japanese Chess - - 155 XIII. Burmese Chess - - 177 XIV. Siamese Chess - 191 XV. Turkish Chess - 196 XVI. Tamerlane's Chess - - 197 XVII. Game of the Maharajah and the Sepoys - - 217 XVIII. Double Chess - 225 XIX. Chess Problems - - 229 DRAUGHTS. XX. Draughts .... 235 XX [. Polish Draughts - 236 XXI f. Turkish Draughts ..... 037 XXIII. }\'ci-K'i and Go . The Chinese and Japanese game of Enclosing 239 v. -
Prusaprinters
Chinese Chess - Travel Size 3D MODEL ONLY Makerwiz VIEW IN BROWSER updated 6. 2. 2021 | published 6. 2. 2021 Summary This is a full set of Chinese Chess suitable for travelling. We shrunk down the original design to 60% and added a new lid with "Chinese Chess" in traditional Chinese characters. We also added a new chess board graphics file suitable for printing on paper or laser etching/cutting onto wood. Enjoy! Here is a brief intro about Chinese Chess from Wikipedia: 8C 68 "Xiangqi (Chinese: 61 CB ; pinyin: xiàngqí), also called Chinese chess, is a strategy board game for two players. It is one of the most popular board games in China, and is in the same family as Western (or international) chess, chaturanga, shogi, Indian chess and janggi. Besides China and areas with significant ethnic Chinese communities, xiangqi (cờ tướng) is also a popular pastime in Vietnam. The game represents a battle between two armies, with the object of capturing the enemy's general (king). Distinctive features of xiangqi include the cannon (pao), which must jump to capture; a rule prohibiting the generals from facing each other directly; areas on the board called the river and palace, which restrict the movement of some pieces (but enhance that of others); and placement of the pieces on the intersections of the board lines, rather than within the squares." Toys & Games > Other Toys & Games games chess Unassociated tags: Chinese Chess Category: Chess F3 Model Files (.stl, .3mf, .obj, .amf) 3D DOWNLOAD ALL FILES chinese_chess_box_base.stl 15.7 KB F3 3D updated 25. -
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. -
Of Kings and Pawns
OF KINGS AND PAWNS CHESS STRATEGY IN THE ENDGAME ERIC SCHILLER Universal Publishers Boca Raton • 2006 Of Kings and Pawns: Chess Strategy in the Endgame Copyright © 2006 Eric Schiller All rights reserved. Universal Publishers Boca Raton , Florida USA • 2006 ISBN: 1-58112-909-2 (paperback) ISBN: 1-58112-910-6 (ebook) Universal-Publishers.com Preface Endgames with just kings and pawns look simple but they are actually among the most complicated endgames to learn. This book contains 26 endgame positions in a unique format that gives you not only the starting position, but also a critical position you should use as a target. Your workout consists of looking at the starting position and seeing if you can figure out how you can reach the indicated target position. Although this hint makes solving the problems easier, there is still plenty of work for you to do. The positions have been chosen for their instructional value, and often combined many different themes. You’ll find examples of the horse race, the opposition, zugzwang, stalemate and the importance of escorting the pawn with the king marching in front, among others. When you start out in chess, king and pawn endings are not very important because usually there is a great material imbalance at the end of the game so one side is winning easily. However, as you advance through chess you’ll find that these endgame positions play a great role in determining the outcome of the game. It is critically important that you understand when a single pawn advantage or positional advantage will lead to a win and when it will merely wind up drawn with best play. -
1 Domination and the Five Queens Problem
Ordog, SWiM Graph Theory Project: Domination and The Five Queens Problem 1 Domination and The Five Queens Problem What is the smallest number of queens that we can place on a chessboard so that every space on the board is either occupied by a queen or being attacked by at least one queen? How can you use graph theory to find a suitable arrangement of queens on an n × n chessboard? To find a solution to this problem, you will learn about the dominating set of a graph. 1.1 Domination • A dominating set of a graph G is a set of vertices S such that each vertex of G is either in S or adjacent to a vertex in S. • What is the biggest dominating set of the graph below? • What is the biggest dominating set for any graph G? • Can you find a dominating set with three vertices? Two vertices? One? Give an example, or explain why not. 1.2 The domination number • The dominating number of a graph, denoted γ(G), is the smallest number of vertices in any dominating set of a graph G. • What is γ(G) for the above graph? Page 1 Ordog, SWiM Graph Theory Project: Domination and The Five Queens Problem • Recall that the complete graph on n vertices, Kn, is the graph with n vertices such that each vertex is adjacent to every other vertex (they are all connected by an edge). What is γ(Kn)? • Exercise: Find γ(G) for the following graphs ([Smi88]). Look for and discuss patterns that might help come up with algorithms for finding dominating sets. -
Chess Openings
Chess Openings PDF generated using the open source mwlib toolkit. See http://code.pediapress.com/ for more information. PDF generated at: Tue, 10 Jun 2014 09:50:30 UTC Contents Articles Overview 1 Chess opening 1 e4 Openings 25 King's Pawn Game 25 Open Game 29 Semi-Open Game 32 e4 Openings – King's Knight Openings 36 King's Knight Opening 36 Ruy Lopez 38 Ruy Lopez, Exchange Variation 57 Italian Game 60 Hungarian Defense 63 Two Knights Defense 65 Fried Liver Attack 71 Giuoco Piano 73 Evans Gambit 78 Italian Gambit 82 Irish Gambit 83 Jerome Gambit 85 Blackburne Shilling Gambit 88 Scotch Game 90 Ponziani Opening 96 Inverted Hungarian Opening 102 Konstantinopolsky Opening 104 Three Knights Opening 105 Four Knights Game 107 Halloween Gambit 111 Philidor Defence 115 Elephant Gambit 119 Damiano Defence 122 Greco Defence 125 Gunderam Defense 127 Latvian Gambit 129 Rousseau Gambit 133 Petrov's Defence 136 e4 Openings – Sicilian Defence 140 Sicilian Defence 140 Sicilian Defence, Alapin Variation 159 Sicilian Defence, Dragon Variation 163 Sicilian Defence, Accelerated Dragon 169 Sicilian, Dragon, Yugoslav attack, 9.Bc4 172 Sicilian Defence, Najdorf Variation 175 Sicilian Defence, Scheveningen Variation 181 Chekhover Sicilian 185 Wing Gambit 187 Smith-Morra Gambit 189 e4 Openings – Other variations 192 Bishop's Opening 192 Portuguese Opening 198 King's Gambit 200 Fischer Defense 206 Falkbeer Countergambit 208 Rice Gambit 210 Center Game 212 Danish Gambit 214 Lopez Opening 218 Napoleon Opening 219 Parham Attack 221 Vienna Game 224 Frankenstein-Dracula Variation 228 Alapin's Opening 231 French Defence 232 Caro-Kann Defence 245 Pirc Defence 256 Pirc Defence, Austrian Attack 261 Balogh Defense 263 Scandinavian Defense 265 Nimzowitsch Defence 269 Alekhine's Defence 271 Modern Defense 279 Monkey's Bum 282 Owen's Defence 285 St. -
Chess Strategies for Beginners II Top Books for Beginners Chess Thinking
Chess Strategies for Beginners II Stop making silly Moves! Learn Chess Strategies for Beginners to play better chess. Stop losing making dumb moves. "When you are lonely, when you feel yourself an alien in the world, play Chess. This will raise your spirits and be your counselor in war." Aristotle Learn chess strategies first at Chess Strategies for Beginners I. After that come back here. Chess Formation Strategy I show you now how to start your game. Before you start to play you should know where to place your pieces - know the right chess formation strategy. Where do you place your pawns, knights and bishops, when do you castle and what happens to the queen and the rooks. When should you attack? Or do you have to attack at all? Questions over questions. I will give you a rough idea now. Please study the following chess strategies for beginners carefully. Read the Guidelines: Chess Formation Strategy. WRITE YOUR REVIEW ASK QUESTIONS HERE! Top Books For Beginners For beginners I recommend Logical Chess - Move by Move by Chernev because it explains every move. Another good book is the Complete Idiot's Guide to Chess that received very good reviews. Chess Thinking Now try to get mentally into the real game and try to understand some of the following positions. Some are difficult to master, but don't worry, just repeat them the next day to get used to chess thinking. Your brain has to adjust, that's all there is to it. Win some Positions here! - Chess Puzzles Did you manage it all right? It is necessary that you understand the following basic chess strategies for beginners called - Endgames or Endings, using the heavy pieces.(queen and rook are called heavy pieces) Check them out now! Rook and Queen Endgames - Basic Chess Strategies How a Beginner plays Chess Replay the games of a beginner. -
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. -
Super Human Chess Engine
SUPER HUMAN CHESS ENGINE FIDE Master / FIDE Trainer Charles Storey PGCE WORLD TOUR Young Masters Training Program SUPER HUMAN CHESS ENGINE Contents Contents .................................................................................................................................................. 1 INTRODUCTION ....................................................................................................................................... 2 Power Principles...................................................................................................................................... 4 Human Opening Book ............................................................................................................................. 5 ‘The Core’ Super Human Chess Engine 2020 ......................................................................................... 6 Acronym Algorthims that make The Storey Human Chess Engine ......................................................... 8 4Ps Prioritise Poorly Placed Pieces ................................................................................................... 10 CCTV Checks / Captures / Threats / Vulnerabilities ...................................................................... 11 CCTV 2.0 Checks / Checkmate Threats / Captures / Threats / Vulnerabilities ............................. 11 DAFiii Attack / Features / Initiative / I for tactics / Ideas (crazy) ................................................. 12 The Fruit Tree analysis process ............................................................................................................