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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. -
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. -
View 2020 Circular
2020 South African Junior Chess Championships 2020 Wild Card Chess Championship 2020 South Africa Junior Blitz Chess Championships 2020 South Africa Doubles Chess Championships 2020 Inter Regional Team Chess Championship 3 to 12 January 2021 Hosted by 4 Knights International Events Company CIRCULAR 1 Version 1.0 26 September 2020 Table of Contents 1. LOCAL ORGANIZING COMMITTEE (LOC) 5 1. CONVENER................................................................................................................................................. 5 2. TREASURER ................................................................................................................................................ 5 3. TECHNICAL DIRECTOR .................................................................................................................................. 5 4. CHIEF ARBITER ........................................................................................................................................... 5 5. ACCOMMODATION...................................................................................................................................... 5 6. MEDIA AND PHOTO’S .................................................................................................................................. 5 7. PUBLIC RELATIONS ...................................................................................................................................... 5 8. LOGISTICS ................................................................................................................................................. -
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. -
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 ............................................................................................................ -
2016 Year in Review
The Gambit Nebraska State Chess Archives Nebraska State Chess 2016 The Year in Review. XABCDEFGHY 8Q+-+-mK-mk( 7+-+-+-+-' 6L+-sn-+-+& 5+-+-+-sN-% 4-+-+-+-+$ 3+-+-+n+-# 2-+-+-+-+" 1+-+-+-+-! xabcdefghy White to play & mate in 2 moves. (Composed by Bob Woodworth) Hint: After White’s keymove & depending on Black’s reply, find all of the ‘long-distance’ checkmates. Gambit Editor- Kent Nelson The Gambit serves as the official publication of the Nebraska State Chess Association and is published by the Lincoln Chess Foundation. Send all games, articles, and editorial materials to: Kent Nelson 4014 “N” St Lincoln, NE 68510 [email protected] NSCA Officers President John Hartmann Treasurer Lucy Ruf Historical Archivist Bob Woodworth Secretary Gnanasekar Arputhaswamy Webmaster Kent Smotherman Regional VPs NSCA Committee Members Vice President-Lincoln- John Linscott Vice President-Omaha- Michael Gooch Vice President (Western) Letter from NSCA President John Hartmann January 2017 Hello friends! Our beloved game finds itself at something of a crossroads here in Nebraska. On the one hand, there is much to look forward to. We have a full calendar of scholastic events coming up this spring and a slew of promising juniors to steal our rating points. We have more and better adult players playing rated chess. If you’re reading this, we probably (finally) have a functional website. And after a precarious few weeks, the Spence Chess Club here in Omaha seems to have found a new home. And yet, there is also cause for concern. It’s not clear that we will be able to have tournaments at UNO in the future. -
An Arbiter's Notebook
10.2 Again Purchases from our shop help keep ChessCafe.com freely accessible: Question: Dear, Mr. Gijssen. I was playing in a tournament and the board next to me played this game: 1.Nf3 Nf6 2.Ng1 Ng8 3.Nf3 Nf6 4.Ng1 Ng8. When a draw was claimed, the arbiter demanded that both players replay the game. When one of them refused, the arbiter forfeited them. Does the opening position count for purposes of threefold repetition? Matthew Larson (UK) Answer In my opinion, the arbiter was right not to accept this game. I refer to Article 12.1 of the Laws of Chess: An Arbiter’s The players shall take no action that will bring the game of chess into disrepute. Notebook To produce a "game" as mentioned in your letter brings the game of chess The Greatest Tournaments into disrepute. The only element in your letter that puzzles me is the fact that Geurt Gijssen 2001-2009 the arbiter forfeited both players, although only one refused to play a new by Chess Informant game. The question of the threefold repetition is immaterial in this case. Question Greetings, Mr. Gijssen. I acted as a member of the appeals committee in a rapid chess tournament (G60/sudden death). I also won that tournament, but I am not a strong player, just 2100 FIDE, with a good understanding of the rules. The incident is as follows: A player lost a game and signed the score sheet, and then he appealed the decision of the arbiter to the committee with regards to some bad rulings during the game. -
Regulations for the Chess Olympiad
D.II. Chess Olympiad D.II.01 Regulations for the Chess Olympiad 1. General 1.1 The Chess Olympiad is the principal team contest organized by FIDE. 1.1.1 The Olympiad is held regularly at two year intervals in the autumn of the even numbered years (2006, 2008, etc.) 1.1.2 The Olympiad for both the open section and the women section must be held, if possible, at a single venue. 1.1.3 However, in exceptional cases as determined by the FIDE General Assembly or (in between congresses) by the President - separate venues may be used for the men and women contests. 1.1.4 Organizing body: FIDE, represented by the FIDE President. 1.1.5 Administrator 1.1.5.1 The administrator is appointed through a special selection process (section 2 below). 1.1.5.2 The administrator is responsible to FIDE, and must abide by these regulations. 1.1.5.3 The administrator shall make available all necessary premises, staff and funds for the contest. The minimum requirements are laid down in individual sections of these regulations. 1.1.5.4 The administrator may utilize the services of outside bodies or private persons for the purpose of financing and running the contest. 1.1.5.5 Administrators may be proposed by the federations. 1.1.5.6 The President may also receive offers from sponsors outside the sphere of FIDE. 1.1.5.7 The tasks of the administrator are detailed in subsequent sections of these regulations. 1.1.6 FIDE Congress The administrator who undertakes the running of the Chess Olympiad must also undertake to hold the FIDE Congress for the same year. -
Finding Checkmate in N Moves in Chess Using Backtracking And
Finding Checkmate in N moves in Chess using Backtracking and Depth Limited Search Algorithm Moch. Nafkhan Alzamzami 13518132 Informatics Engineering School of Electrical Engineering and Informatics Institute Technology of Bandung, Jalan Ganesha 10 Bandung [email protected] [email protected] Abstract—There have been many checkmate potentials that has pieces of a dark color. There are rules about how pieces players seem to miss. Players have been training for finding move, and about taking the opponent's pieces off the board. checkmates through chess checkmate puzzles. Such problems can The player with white pieces always makes the first move.[4] be solved using a simple depth-limited search and backtracking Because of this, White has a small advantage, and wins more algorithm with legal moves as the searching paths. often than Black in tournament games.[5][6] Keywords—chess; checkmate; depth-limited search; Chess is played on a square board divided into eight rows backtracking; graph; of squares called ranks and eight columns called files, with a dark square in each player's lower left corner.[8] This is I. INTRODUCTION altogether 64 squares. The colors of the squares are laid out in There have been many checkmate potentials that players a checker (chequer) pattern in light and dark squares. To make seem to miss. Players have been training for finding speaking and writing about chess easy, each square has a checkmates through chess checkmate puzzles. Such problems name. Each rank has a number from 1 to 8, and each file a can be solved using a simple depth-limited search and letter from a to h.