Mathematics In The Game Of Chess Maths Essay

Mathematics In The Game Of deceiver Maths EssayINTRODUCTION beguiler is a dickens- wanton awayer get on bouncing froliced on a swindleboard, a squ be- harbourered board with 64squ bes arranged in an eight-by-eight grid. Each thespian begins the granulose with sixteen blames iness poof, star queen, deuce rooks, two knights, two bishops, and eight hocks. The object of the jeopardize is to master the opp whizznts top executive, whereby the king is on a lower floor immediate attack (in hindrance) and there is no way to remove or def dismiss it from attack on the next move. The gimpys present form emerged in Europe during the second half of the 15th century, an evolution of an honest-to-god Indian game, Shatranj. Theoreticians absorb real extensive cheater strategies and tactics since the games inception. computing devices hurl been used for many spacious clock time to create cheat-playing programs, and their abilities and insights have contri unlessed signif i basistly to sophisticated darnel game opening. One, Deep Blue, was the premier machine to beat a reigning World cheater Champion when it defeated Garry Kasparov in 1997.Matches between individuals took place as betimes as the 9th century. The tradition of organized competitive cheater show uped during the 16th century. The first official World bearded darnel Champion, Wilhelm Steinitz, claimed his title in 1886 the circulating(prenominal) World Champion is Viswanathan Anand from India. In addition to the World Championship, there is in addition the WomenHYPERLINK http//en.wikipedia.org/wiki/Womens_World_ swindle_ChampionshipHYPERLINK http//en.wikipedia.org/wiki/Womens_World_ trickster_Championships World Championship, the Junior World Championship, the World Senior Championship, the Correspondence Chess World Championship, the World Computer Chess Championship, and Blitz and Rapid World Championships (see fast tare). The Chess Olympiad is a popular competition among t eams from distinct nations. Online chess has opened amateur and professional competition to a wide and varied group of imposters. Chess is a recognized sport of the International Olympic Committee and global chess competition is clear by the FIDE. Today, chess is one of the foundations intimately popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tour ringnts. Some other(a) popular forms of chess atomic number 18 fast chess and computer chess. There ar too many chess variants which have variant finds, different pieces, different boards, etc.HistoryIranian chess piece, glazed fritware, 12th century. New York Metropolitan Museum of Art.Knights Templar playing chess, Libro de los juegos, 1283.Chess is commonly believed to have originated in North-West India during the Gupta empire, where its early form in the 6th century was cognize as caturaga (Sanskrit iv divisions of the military infantry, cavalry, elephants, an d chariotry, represented by the pieces that would evolve into the modern souse, knight, bishop, and rook, respectively). The earliest evidence of Chess is found in the neighboring Sassanid Persia around 600 where the game came to be known under the name chatrang. Chatrang is evoked in fount trinity epic romances written in Pahlavi (Medium Persian). Chatrang was draw backn up by the Muslim world after the Islamic conquest of Persia (633-644) where it was then named shatranj, with the pieces largely retaining their Persian names. In Spanish shatranj was rendered as ajedrez, in Portuguese as xadrez, and in Greek as zatrikion (which directly comes from Persian chatrang), except in the lodge of Europe it was replaced by versions of the Persian shh (king), which was familiar as an exclamation and became the English words check and chess. Murray theorized that this change happened from Muslim traders glide slope to European seaports with ornamental chess kings as curios before they brought the game of chess. The game r apieceed Western Europe and Russia by at least triad routes, the earliest being in the 9th century. By the year 1000 it had spreadhead throughout Europe. Introduced into the Iberian Peninsula by the Moors in the 10th century, it was described in a famous 13th-century manuscript covering shatranj, backgammon, and dice named the Libro de los juegos. A nonher theory contends that chess arose from the game xiangqi (Chinese Chess) or one of its predecessors, although this has been contested.___________________________________________________Mathematics In The Game Of ChessLegend has it that the game was invented by a mathematician in India who elicited a huge reward for its creation. The King of India was so impressed with the game that he asked the mathematician to name a prize as reward. Not wishing to appear greedy, the mathematician asked for one grain of rice to be placed on the first square of the chess board, two grains on the second, four o n the trey and so on. The number of grains of rice should be doubled each time.The King thought that hed got away light sourcely, but little did he realise the power of doubling to make things big very quickly. By the 16th square there was already a kilo of rice on the chess board. By the ordinal square his servant needed to bring in a wheelbarrow of rice. He never reached the 64th and locomote square on the board. By that point the rice on the board would have totalled a dumbfounding 18,446,744,073,709,551,615 grains.Playing chess has strong resonances with doing mathematics. There are simple rules for the way each chess piece moves but beyond these basic constraints, the pieces end roam freely across the board. Mathematics in like manner paying back by taking self-evident truths (called axioms) about properties of numbers and geometry and then by applying basic rules of logic you be active to move mathematics from its starting point to deduce new statements about numbers and geometry. For eccentric, using the moves allowed by mathematics the eighteenth-century mathematician Lagrange reached an endgame that showed that every number can be written as the sum of four square numbers, a far from obvious fact. For example, 310 = 172 +42 + 22 + 12.Some mathematicians have turned their analytical skills on the game of chess itself. A classic problem called the Knights Tour asks whether it is possible to use a knight to jump around the chess board visiting each square once only. The first examples were documented in a 9th-century Arabic manuscript. It is only within the past decade that mathematical techniques have been developed to count exactly how many such tours are possible.It isnt just mathematicians and chess impostors who have been fascinate by the Knights Tour. The highly styled Sanskrit poem Kavyalankara presents the Knights Tour in verse form. And in the 20th century, the French occasion Georges Perecs novel Life A Users Manual describes an a breakment with 100 rooms arranged in a 1010 grid. In the novel the order that the author visits the rooms is determined by a Knights Tour on a 1010 chessboard.Mathematicians have also analysed just how many games of chess are possible. If you were to line up chessboards brass by side, the number of them you would need to reach from one side of the observable universe to the other would rent only 28 digits. Yet Claude Shannon, the mathematician credited as the father of the digital age, estimated that the number of unique games you could play was of the order of 10120 (a 1 followed by 120 0s). Its this level of complexity that makes chess such an attractive game and ensures that at the Olympiad in Russia in 2010, local spectators pull up stakes witness games of chess never before seen by the human eye, change surface if the winning team turns out to have familiar names.________________________________________________________RulesThe official rules of chess are maintained by th e World Chess Federation. Along with information on official chess tournaments, the rules are described in the FIDE Hand record, section Laws of Chess.2SetupPieces at the start of a gameAbCdefgh8877665544332211AbCDefghInitial position first row rook, knight, bishop, queen, king, bishop, knight, and rook second row overchargesChess is played on a square board of eight rows (called social out-and-out(a)s and denoted with numbers 1 to 8) and eight columns (called cross- saddles and denoted with letters a to h) of squares. The colorise of the sixty-four squares alternate and are referred to as light squares and dark squares. The chessboard is placed with a light square at the right hand end of the rank nearest to each player, and the pieces are set out as shown in the diagram, with each queen on its own color.The pieces are divided, by convention, into clean-living and black sets. The players are referred to as White and Black, and each begins the game with sixteen pieces of the s pecified color. These consist of one king, one queen, two rooks, two bishops, two knights and eight plumes.___________________________________________________________________________MovementWhite always moves first. After the initial move, the players alternately move one piece at a time (with the censure of move, when two pieces are move). Pieces are moved to either an unoccupied square, or one occupied by an opponents piece, capturing it and removing it from play. With the sole exception of en passant, all pieces capture opponents pieces by moving to the square that the opponents piece occupies. A player may not make any move which would put or leave his king under attack. If the player to move has no legal moves, the game is over it is either a copulate-if the king is under attack-or a stalemate-if the king is not.Each chess piece has its own style of moving. In the diagrams, the dots mark the squares where the piece can move if no other pieces (including ones own piece) ar e on the squares between the pieces initial position and its cultivation.The king moves one square in any direction, the king has also a special move which is called castle and also involves a rook.The rook can move any number of squares on any rank or file, but may not derail over other pieces. Along with the king, the rook is also involved during the kings castling move.The bishop can move any number of squares diagonally, but may not leap over other pieces.The queen combines the power of the rook and bishop and can move any number of squares along rank, file, or diagonal, but it may not leap over other pieces.The knight moves to any of the close squares which are not on the alike(p) rank, file or diagonal, thus the move forms an L-shape two squares long and one square wide. The knight is the only piece which can leap over other pieces.The pawn may move forward to the unoccupied square immediately in front of it on the same file, or on its first move it may advance two squar es along the same file provided both squares are unoccupied, or it may move to a square occupied by an opponents piece, which is diagonally in front of it on an adjacent file, capturing that piece. The pawn has two special moves, the en passant capture, and pawn promotion.Moves of a kingaBcDefgh8877665544332211aBcDefghMoves of a rookaBcDefgh8877665544332211aBcDefghMoves of a bishopaBcDefgh8877665544332211aBcDefghMoves of a queenaBcDefgh8877665544332211aBcDefghMoves of a knightaBcDefgh8877665544332211aBcDefghMoves of a pawnaBcDefgh8877665544332211aBcDefgh* Pawns can optionally move two squares forward instead of one on their first move only. They capture diagonally (black xs) they cannot capture with their normal move (black circles). Pawns are also involved in the special move en passant (below).CheckWhen a king is under immediate attack by one or two of the opponents pieces, it is said to be in check. A response to a check is a legal move if it results in a position where the king is no longer under direct attack (i.e. not in check). This can involve capturing the checking piece, interposing a piece between the checking piece and the king (which is possible only if the attacking piece is a queen, rook, or bishop and there is a square between it and the king), or moving the king to a square where it is not under attack. Castling is not a permissible response to a check. The object of the game is to checkmate the opponent this occurs when the opponents king is in check, and there is no legal way to remove it from attack.End of the gameAlthough the objective of the game is to checkmate the opponent, chess games do not have to end in checkmate-either player may resign if the situation looks abject. It is selected bad etiquette to continue playing when in a truly hopeless position. If it is a timed game a player may run out of time and lose, even with a much superior position. Games also may end in a draw (tie). A draw can occur in several situations, including draw by agreement, stalemate, threefold repetition of a position, the fifty-move rule, or a draw by impossibility of checkmate ( unremarkably because of insufficient bodily to checkmate). As checkmate from approximately positions cannot be forced in less than 50 moves (see e.g. pawnless chess endgame and two knights endgame), the fifty-move rule is not applied everywhere,6 particularly in correspondence chess.White is in checkmateaBcDefgh8877665544332211aBcdefghWhite is in checkmate. He cannot escape from being attacked by the Black king and bishops.StalemateaBcdefgh8877665544332211aBcdefghStalemate if Black is to move. The position is not checkmate, and since Black cannot move, the game is a draw.Time crackA modern digital chess clockBesides casual games without any time restriction, chess is also played with a time control, mostly by club and professional players. If a players time runs out before the game is completed, the game is automatically lost (provided his opponent has enough pieces left to write checkmate). The duration of a game ranges from long games played up to seven hours to shorter rapid chess games undestroyable normally 30 minutes or one hour per game. Even shorter is blitz chess with a time control of three to fifteen minutes for each player, or bullet chess (under three minutes). In tournament play, time is controlled using a game clock which has two displays, one for each players remaining time.________________________________________________________Notation for recording movesNaming the squares in algebraic chess notationChess games and positions are recorded using a special notation, most often algebraic chess notation. Abbreviated (or short) algebraic notation generally records moves in the format abbreviation of the piece moved file where it moved rank where it moved, e.g. Qg5 means queen moves to the g-file and 5th rank (that is, to the square g5). If there are two pieces of the same image that can move to the same square, one much letter or number is added to indicate the file or rank from which the piece moved, e.g. Ngf3 means knight from the g-file moves to the square f3. The letter P indicating a pawn is not used, so that e4 means pawn moves to the square e4.If the piece makes a capture, x is inserted before the destination square, e.g. Bxf3 means bishop captures on f3. When a pawn makes a capture, the file from which the pawn departed is used in place of a piece initial, and ranks may be omitted if unambiguous. For example, exd5 (pawn on the e-file captures the piece on d5) or exd (pawn on e-file captures something on the d-file).ScholarHYPERLINK http//en.wikipedia.org/wiki/Scholars_mateHYPERLINK http//en.wikipedia.org/wiki/Scholars_mates mateIf a pawn moves to its last rank, achieving promotion, the piece chosen is indicated after the move, for example e1Q or e1=Q. Castling is indicated by the special notations 0-0 for kingside castling and 0-0-0 for queenside castling. A move which places the opponents king in check usually has the notation + added. Checkmate can be indicated by (occasionally ++, although this is sometimes used for a double check instead). At the end of the game, 1-0 means White won, 0-1 means Black won and - indicates a draw.Chess moves can be annotated with punctuation marks and other symbols. For example indicates a good move, an excellent move, ? a mistake, a blunder, ? an interesting move that may not be best or ? a dubious move, but not easily refuted.1For example, one variant of a simple trap known as the ScholarHYPERLINK http//en.wikipedia.org/wiki/Scholars_mateHYPERLINK http//en.wikipedia.org/wiki/Scholars_mates mate, stir in the picture to the right, can be recordede4 e5Qh5? Nc6Bc4 Nf6Qxf7 1-0________________________________________________________Strategy and tacticsChess strategy consists of stage setting and achieving long-term goals during the game for example, where to place different pieces while tactics concentrate on immediate manoeuvre. These two parts of chess thinking cannot be completely separated, because strategic goals are mostly achieved by the means of tactics, while the tactical opportunities are based on the previous strategy of play.A game of chess is normally divided into three phases origin, typically the first 10 to 25 moves, when players move their pieces into useful positions for the coming battle middlegame, usually the fiercest part of the game and endgame, when most of the pieces are gone, kings typically take a more active part in the struggle, and pawn promotion is often decisive.OpeningA chess opening is the group of initial moves of a game (the opening moves). Recognized sequences of opening moves are referred to as openings and have been given names such as the Ruy Lopez or Sicilian Defence. They are catalogued in reference whole shebang such as the Encyclopaedia of Chess Openings. There are dozens of different openings, varying widely in character from quiet positional play (e .g. the Rti Opening) to very aggressive (e.g. the Latvian Gambit). In some opening lines, the exact sequence considered best for both sides has been worked out to more than 30 moves. Professional players spend years studying openings, and continue doing so throughout their careers, as opening theory continues to evolve.The fundamental strategic aims of most openings are similarDevelopment To place (develop) the pieces (particularly bishops and knights) on useful squares where they pass on have an optimal impact on the game.Control of the center Control of the central squares allows pieces to be moved to any part of the board relatively easily, and can also have a cramping effect on the opponent.King safety Keeping the king safe from dangerous possibilities. A correct timing for castling can often enhance this.Pawn structure Players strive to avoid the creation of pawn weaknesses such as isolated, doubled or backward pawns, and pawn islands and to force such weaknesses in the oppon ents position.Most players and theoreticians consider that White, by virtue of the first move, begins the game with a small advantage. This initially gives White the initiative. Black usually strives to neutralize Whites advantage and achieve equality, or to develop dynamic counterplay in an unbalanced position.MiddlegameThe middlegame is the part of the game which starts after the opening. There is no clear line between the opening and the middlegame, but typically the middlegame will start when most pieces have been developed. (Similarly, there is no clear transition from the middlegame to the endgame, see start of the HYPERLINK http//en.wikipedia.org/wiki/Chess_endgameThe_start_of_the_endgameendgame.) Because the opening theory has ended, players have to form plans based on the features of the position, and at the same time to take into account the tactical possibilities in the position. The middlegame is also the phase in which most combinations occur. Combinations are a series of tactical moves executed to achieve some gain. Middlegame combinations are often connected with an attack against the opponents king some typical patterns have their own names, for example the BodenHYPERLINK http//en.wikipedia.org/wiki/Bodens_MateHYPERLINK http//en.wikipedia.org/wiki/Bodens_Mates Mate or the Lasker-Bauer combination.Specific plans or strategic themes will often arise from particular groups of openings which result in a specific type of pawn structure. For example, the minority attack, that is the attack of queenside pawns against an opponent who has more pawns on the queenside. The study of openings should accordingly be connected with the preparation of plans that are typical of the resulting middlegames.Another important strategic question in the middlegame is whether and how to reduce material and transform into an endgame (i.e. simplify). For example, minor material advantages can generally be transformed into victory only in an endgame, and therefore the s tronger side moldiness choose an appropriate way to achieve an result. Not every reduction of material is good for this purpose for example, if one side keeps a light-squared bishop and the opponent has a dark-squared one, the transformation into a bishops and pawns ending is usually advantageous for the weaker side only, because an endgame with bishops on opposite colors is likely to be a draw, even with an advantage of a pawn, or sometimes with a two-pawn advantage._____________________________________________________________________________________EndgameaBcDefgh8877665544332211aBcdefghAn example of zugzwang the side which is to make a move is at a disadvantage.The endgame (or end game or ending) is the stage of the game when there are few pieces left on the board. There are three main strategic differences between earlier stages of the game and endgameDuring the endgame, pawns become more important endgames often revolve around attempting to promote a pawn by advancing it to th e eighth rank.The king, which has to be protect in the middlegame owing to the threat of checkmate, becomes a strong piece in the endgame. It is often brought to the center of the board where it can protect its own pawns, attack the pawns of opposite color, and hinder movement of the opponents king.Zugzwang, a disadvantage because the player has to make a move, is often a factor in endgames but rarely in other stages of the game. For example, the diagram on the right is zugzwang for both sides, as with Black to move he must play 1Kb7 and let White promote a pawn after 2.Kd7 and with White to move he must allow a draw by 1.Kc6 stalemate or lose his last pawn by any other legal move.Endgames can be classified according to the type of pieces that remain on board. Basic checkmates are positions in which one side has only a king and the other side has one or two pieces and can checkmate the opposing king, with the pieces working together with their king. For example, king and pawn endga mes involve only kings and pawns on one or both sides and the task of the stronger side is to promote one of the pawns. Other more complicated endings are classified according to the pieces on board other than kings, such as the rook and pawn versus rook endgame.Origins of the modern game (1000-1850)A tactical puzzle from LucenaHYPERLINK http//en.wikipedia.org/wiki/Luis_Ramirez_de_LucenaHYPERLINK http//en.wikipedia.org/wiki/Luis_Ramirez_de_Lucenas 1497 bookAround 1200, rules of shatranj started to be modified in southern Europe, and around 1475, several major changes made the game essentially as it is known today. These modern rules for the basic moves had been adopted in Italy and Spain. Pawns gained the option of advancing two squares on their first move, while bishops and queens acquired their modern abilities. The queen replaced the earlier vizier chess piece towards the end of the 10th century and by the 15th century, had become the most powerful piece consequently modern chess was referred to as Queens Chess or Mad Queen Chess. These new rules quickly spread throughout western Europe, with the exception of the rules about stalemate, which were finalized in the early 19th century. To distinguish it from its predecessors, this version of the rules is sometimes referred to as western chess or international chess.Writings about the theory of how to play chess began to appear in the 15th century. The Repeticin de Amores y Arte de Ajedrez (Repetition of Love and the Art of Playing Chess) by Spanish churchman Luis Ramirez de Lucena was published in Salamanca in 1497. Lucena and afterwards masters like Portuguese Pedro Damiano, Italians Giovanni Leonardo Di Bona, Giulio Cesare Polerio and Gioachino Greco or Spanish bishop Ruy Lpez de Segura developed elements of openings and started to analyze simple endgames.Franois-Andr Danican Philidor, 18th-century French chess MasterIn the 18th century the center of European chess life moved from the Southern European coun tries to France. The two most important French masters were Franois-Andr Danican Philidor, a musician by profession, who discovered the importance of pawns for chess strategy, and later Louis-Charles Mah de La Bourdonnais who won a famous series of matches with the Irish master Alexander McDonnell in 1834. Centers of chess activity in this period were coffee houses in big European cities like Caf de la Rgence in Paris and SimpsonHYPERLINK http//en.wikipedia.org/wiki/Simpsons-in-the-StrandHYPERLINK http//en.wikipedia.org/wiki/Simpsons-in-the-Strands Divan in London.As the 19th century progressed, chess organization developed quickly. Many chess clubs, chess books and chess journals appeared. There were correspondence matches between cities for example the London Chess Club played against the Edinburgh Chess Club in 1824. Chess problems became a regular part of 19th-century newspapers Bernhard Horwitz, Josef Kling and Samuel Loyd unruffled some of the most influential problems. In 18 43, von der Lasa published his and BilguerHYPERLINK http//en.wikipedia.org/wiki/Paul_Rudolf_von_BilguerHYPERLINK http//en.wikipedia.org/wiki/Paul_Rudolf_von_Bilguers Handbuch des Schachspiels (Handbook of Chess), the first comprehensive manual of chess theory.________________________________________________________Competitive playContemporary chess is an organized sport with structured international and national leagues, tournaments and congresses. Chesss international governing body is FIDE (Fdration Internationale des checs). Most countries have a national chess organization as well (such as the US Chess Federation and English Chess Federation), which in turn is a member of FIDE. FIDE is a member of the International Olympic Committee, but the game of chess has never been part of the Olympic Games chess does have its own Olympiad, held every two years as a team event.The current World Chess Champion Viswanathan Anand (left) playing chess against his predecessor Vladimir Kramnik.Th e current World Chess Champion is Viswanathan Anand of India. The reigning Womens World Champion is Alexandra Kosteniuk from Russia but the worlds highest rated female person player, Judit Polgr, has never participated in the WomenHYPERLINK http//en.wikipedia.org/wiki/Womens_World_Chess_ChampionshipHYPERLINK http//en.wikipedia.org/wiki/Womens_World_Chess_Championships World Chess Championship, instead preferring to compete with the leading men and maintaining a ranking among the top male players.Other competitions for individuals include the World Junior Chess Championship, the European Individual Chess Championship and the case Chess Championships. Invitation-only tournaments regularly attract the worlds strongest players and these include Spains Linares event, Monte Carlos Melody Amber tournament, the Dortmund Sparkassen meeting, Sofias M-tel Masters and Wijk aan Zees Corus tournament.Regular