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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. -
1999/6 Layout
Virginia Chess Newsletter 1999 - #6 1 The Chesapeake Challenge Cup is a rotating club team trophy that grew out of an informal rivalry between two Maryland clubs a couple years ago. Since Chesapeake then the competition has opened up and the Arlington Chess Club captured the cup from the Fort Meade Chess Armory on October 15, 1999, defeating the 1 1 Challenge Cup erstwhile cup holders 6 ⁄2-5 ⁄2. The format for the Chesapeake Cup is still evolving but in principle the idea is that a defense should occur about once every six months, and any team from the “Chesapeake Bay drainage basin” is eligible to issue a challenge. “Choosing the challenger is a rather informal process,” explained Kurt Eschbach, one of the Chesapeake Cup's founding fathers. “Whoever speaks up first with a credible bid gets to challenge, except that we will give preference to a club that has never played for the Cup over one that has already played.” To further encourage broad participation, the match format calls for each team to field players of varying strength. The basic formula stipulates a 12-board match between teams composed of two Masters (no limit), two Expert, and two each from classes A, B, C & D. The defending team hosts the match and plays White on odd-numbered boards. It is possible that a particular challenge could include additional type boards (juniors, seniors, women, etc) by mutual agreement between the clubs. Clubs interested in coming to Arlington around April, 2000 to try to wrest away the Chesapeake Cup should call Dan Fuson at (703) 532-0192 or write him at 2834 Rosemary Ln, Falls Church VA 22042. -
2009 U.S. Tournament.Our.Beginnings
Chess Club and Scholastic Center of Saint Louis Presents the 2009 U.S. Championship Saint Louis, Missouri May 7-17, 2009 History of U.S. Championship “pride and soul of chess,” Paul It has also been a truly national Morphy, was only the fourth true championship. For many years No series of tournaments or chess tournament ever held in the the title tournament was identi- matches enjoys the same rich, world. fied with New York. But it has turbulent history as that of the also been held in towns as small United States Chess Championship. In its first century and a half plus, as South Fallsburg, New York, It is in many ways unique – and, up the United States Championship Mentor, Ohio, and Greenville, to recently, unappreciated. has provided all kinds of entertain- Pennsylvania. ment. It has introduced new In Europe and elsewhere, the idea heroes exactly one hundred years Fans have witnessed of choosing a national champion apart in Paul Morphy (1857) and championship play in Boston, and came slowly. The first Russian Bobby Fischer (1957) and honored Las Vegas, Baltimore and Los championship tournament, for remarkable veterans such as Angeles, Lexington, Kentucky, example, was held in 1889. The Sammy Reshevsky in his late 60s. and El Paso, Texas. The title has Germans did not get around to There have been stunning upsets been decided in sites as varied naming a champion until 1879. (Arnold Denker in 1944 and John as the Sazerac Coffee House in The first official Hungarian champi- Grefe in 1973) and marvelous 1845 to the Cincinnati Literary onship occurred in 1906, and the achievements (Fischer’s winning Club, the Automobile Club of first Dutch, three years later. -
Chess2vec: Learning Vector Representations for Chess
Chess2vec: Learning Vector Representations for Chess Berk Kapicioglu Ramiz Iqbal∗ Tarik Koc OccamzRazor MD Anderson Cancer Center OccamzRazor [email protected] [email protected] [email protected] Louis Nicolas Andre Katharina Sophia Volz OccamzRazor OccamzRazor [email protected] [email protected] Abstract We conduct the first study of its kind to generate and evaluate vector representations for chess pieces. In particular, we uncover the latent structure of chess pieces and moves, as well as predict chess moves from chess positions. We share preliminary results which anticipate our ongoing work on a neural network architecture that learns these embeddings directly from supervised feedback. 1 Introduction In the last couple of years, advances in machine learning have yielded dramatic improvements in tasks as diverse as visual object classification [9], automatic speech recognition [7], machine translation [18], and natural language processing (NLP) [12]. A common thread among all these tasks is, as diverse as they may seem, they all involve processing input data, such as image, audio, and text, that have not traditionally been amenable to feature engineering. Modern machine learning methods that enabled these breakthroughs did so partly because they shifted the burden away from feature engineering, which is difficult for humans and requires domain expertise, towards designing models that automatically infer feature representations that are relevant for downstream tasks [1]. In this paper, we are interested in learning and studying feature representations of chess positions and pieces. Our work is inspired by how learning vector representation of words [12, 13], also known as word embeddings, yielded improvements in tasks such as syntactic parsing [16] and sentiment analysis [17]. -
Chess Horizons
FREE ENTRY FOR GMs & IMs 78th New England Open September 1 – 3, 2018 Location: Crowne Plaza Boston - Newton 20 USCF 320 Washington St. Grand Prix 3‐day and 2‐day options available! Newton, MA 02458 Points Prizes: $4,000 b/120 paid entries, 75% guaranteed Championship $650 – 300 – 250, top U2400 $225, top U2200 $225 U2000 $400 – 200 – 150 U1800 $400 – 200 – 150 U1600 $300 – 150 – 100, top U1400 $150, top U1200 $150 Time Control: 40/100, SD/30 d10 (2‐day rounds 1‐3 are G/45 d5) Sections: Championship Section (rated 1800+) – 3‐day only – FIDE Rated U2000 Section – 3‐day or 2‐day U1800 Section – 3‐day or 2‐day U1600 Section – 3‐day or 2‐day Round Times: 3‐day section – Saturday 11 AM & 5 PM, Sunday 11 AM & 5 PM, Monday 10 AM & 3: 5 PM 2‐day section – Sunday 1 : 0 AM, 1: 0 PM, : 0 PM, & 5 PM; Monday 10 AM & 3: 5 PM :00 :30 :00 :30 :30 4 Byes: Limit 2 byes, rounds 1‐5 in1 0 Championship Section, rounds 1‐6 in0 3 0 :30 U2000:30 to U16004 sections. Players must commit to byes in rounds 4‐6 before round 2. Entry Fee: Byes in rounds 4-6 are irrevocable. 3‐day section ‐ $75 online by 11:59 PM on 8/3 , $85 onsite 2‐day section ‐ $74 online by 11:59 PM on 8/3 , $85 onsite 0 Onsite Registration: 3‐day – Saturday 9/ from 8:0 30 to 9:30 AM; 2‐day – Sunday 9/ from 8:30 to 9:30 AM Other Information: 1 2 ‐ There is no 2‐day schedule for the Championship Section. -
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. -
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). -
Life Cycle Patterns of Cognitive Performance Over the Long
Life cycle patterns of cognitive performance over the long run Anthony Strittmattera,1 , Uwe Sundeb,1,2, and Dainis Zegnersc,1 aCenter for Research in Economics and Statistics (CREST)/Ecole´ nationale de la statistique et de l’administration economique´ Paris (ENSAE), Institut Polytechnique Paris, 91764 Palaiseau Cedex, France; bEconomics Department, Ludwig-Maximilians-Universitat¨ Munchen,¨ 80539 Munchen,¨ Germany; and cRotterdam School of Management, Erasmus University, 3062 PA Rotterdam, The Netherlands Edited by Robert Moffit, John Hopkins University, Baltimore, MD, and accepted by Editorial Board Member Jose A. Scheinkman September 21, 2020 (received for review April 8, 2020) Little is known about how the age pattern in individual perfor- demanding tasks, however, and are limited in terms of compara- mance in cognitively demanding tasks changed over the past bility, technological work environment, labor market institutions, century. The main difficulty for measuring such life cycle per- and demand factors, which all exhibit variation over time and formance patterns and their dynamics over time is related to across skill groups (1, 19). Investigations that account for changes the construction of a reliable measure that is comparable across in skill demand have found evidence for a peak in performance individuals and over time and not affected by changes in technol- potential around ages of 35 to 44 y (20) but are limited to short ogy or other environmental factors. This study presents evidence observation periods that prevent an analysis of the dynamics for the dynamics of life cycle patterns of cognitive performance of the age–performance profile over time and across cohorts. over the past 125 y based on an analysis of data from profes- An additional problem is related to measuring productivity or sional chess tournaments. -
Colorado Chess Informant
Volume 39, Number 3 July 2012 / $3.00 Colorado State Chess Association COLORADO CHESS INFORMANT Photo by Michael Wokurka Grandmaster Tejas Bakre receiving his prize winnings from Organizer, Joe Fromme. Grandmaster In The House! Bobby Fischer Saluted www.colorado-chess.com Volume 39, Number 3 Colorado Chess Informant July 2012 From The Editor Whew, it has been a busy past few months for chess in Colorado. When the membership voted to go to an all electronic issue of the Informant, that gave me the ability to expand an issue as The Colorado State Chess Junior Representative: much as the number of articles allowed without incurring any Association, Inc., is a Section Rhett Langseth cost to the CSCA. 501(C)(3) tax exempt, non- 15282 Paddington Circle 44 pages of chess in Colorado awaits you in this issue! That profit educational corporation Colorado Springs, CO 80921 should keep you busy for the next three months. The feature of formed to promote chess in [email protected] this issue is the wonderful “Salute to Bobby Fischer Chess Tour- Colorado. Contributions are Members at Large: nament” that was held in early May and which I was once again tax deductible. Dues are $15 a Frank Deming honored by the Organizer, Joe Fromme, in having selected me as year or $5 a tournament. Youth 7906 Eagle Ranch Road the Tournament Director. Again a premier event all around and (under 21) and Senior (65 or Fort Collins, CO 80528 even more so when we had the pleasure of hosting Grandmaster older) memberships are $10. [email protected] Tejas Bakre from India, who decided to play. -
No. 123 - (Vol.VIH)
No. 123 - (Vol.VIH) January 1997 Editorial Board editors John Roycrqfttf New Way Road, London, England NW9 6PL Edvande Gevel Binnen de Veste 36, 3811 PH Amersfoort, The Netherlands Spotlight-column: J. Heck, Neuer Weg 110, D-47803 Krefeld, Germany Opinions-column: A. Pallier, La Mouziniere, 85190 La Genetouze, France Treasurer: J. de Boer, Zevenenderdrffi 40, 1251 RC Laren, The Netherlands EDITORIAL achievement, recorded only in a scientific journal, "The chess study is close to the chess game was not widely noticed. It was left to the dis- because both study and game obey the same coveries by Ken Thompson of Bell Laboratories rules." This has long been an argument used to in New Jersey, beginning in 1983, to put the boot persuade players to look at studies. Most players m. prefer studies to problems anyway, and readily Aside from a few upsets to endgame theory, the give the affinity with the game as the reason for set of 'total information' 5-raan endgame their preference. Your editor has fought a long databases that Thompson generated over the next battle to maintain the literal truth of that ar- decade demonstrated that several other endings gument. It was one of several motivations in might require well over 50 moves to win. These writing the final chapter of Test Tube Chess discoveries arrived an the scene too fast for FIDE (1972), in which the Laws are separated into to cope with by listing exceptions - which was the BMR (Board+Men+Rules) elements, and G first expedient. Then in 1991 Lewis Stiller and (Game) elements, with studies firmly identified Noam Elkies using a Connection Machine with the BMR realm and not in the G realm. -
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. -
Yale Yechiel N. Robinson, Patent Attorney Email: [email protected]
December 16, 2019 From: Yale Yechiel N. Robinson, Patent Attorney Email: [email protected] To: United States Patent and Trademark Office (USPTO) Email: [email protected] Re: Request for Comments on Intellectual Property Protection for Artificial Intelligence Innovation, Docket number: PTO-C-2019-0038 To the USPTO and Members of the Public: My name is Yale Robinson. In addition to my professional work as a patent attorney and in other legal matters, I have for years enjoyed the intergenerational conversation within the game of chess, which originated many centuries ago and spread across Europe and North America around the middle of the 19th century, and has since reached every major country in the world. I will direct my comments regarding issues of intellectual property for artificial intelligence innovations based on the history of traditional western chess. Early innovators in computing, including Alan Turing and Claude Shannon, tried to calculate the value of certain chess positions using the 1950-era equivalent of a present-day handheld calculator. Their work launched the age of computer chess, where the strongest present-day computers can consistently (but not always) defeat or draw elite human grandmasters. The quality of human-versus-human play has increased in part because of computer analysis of opening and middle-game positions that strong players can analyze and practice playing on their home computer device before trying the idea against a human player in competition. In addition to the development of chess theory for the benefit of chess players (human and electronic alike), the impact of chess computing has arguably extended beyond the limits of the game itself.