AUGUST 27 , 2007

Chess, kids' development and learning

Beginning at 6 months till 6 years old, the child begins to understand and appreciate spoken language.  When lecture is initiated the child is not very objective about what he reads and imposes his own his own idea and personality on what it is said.  It is "pseudoreading" or "top-down approach".
   Beginning 6 and 7 years old, when the child enters the 1rst grade at school, he is capable of some kind of coding and interpretation of what he reads.  He begins to understand really what he reads and can learn from what he reads.
   Beginning at 8 till 12 years old, during what it is called by Piaget  the stage of concrete operation, the acquisition of some concepts is done, like those of space, time and amount.  During this stage, the child is introduced to mathematics, learns arithmetics, is capable of memorizing what he reads (can "learn by heart") and can begin to play chess. Reading can then be used to acquire knowledge. While playing chess, the child can do simple combinations and inferences (at least two and at most three moves) which are applications of some logical construction . 
   During this period, children with minor learning problems or with true learning disabilities begin to be dragged behind, with less or more severity, and later, in life, may be incapable of effective abstraction. However, Chess, because it is a game, can still be appealing to them and may be of some help to prevent them from developing phobic avoidance of maths and of sciences in general. In the other hand, some of those children may have good ability to learn languages and this ability may even be amplified by their inabilty to learn and possess maths.
  AUGUST 26 , 2007

"En passant" explained

In my comments done on AUGUST 21 , 2007, I have explained mathematically, with Euclidian geometry laws, why the law of the square can be applied and is a valid one to infer the possibility of a promotion.  Now, after having seen that many kids and their parents do not understand the "en passant", I will try to explain the later also by using geometry or algebraic graph.  The capture "en passant" is done when a pawn moves two cases away from his first and original case, bypassing an opposing pawn.  The later can then capture the fugitive pawn in moving diagonally to the case this pawn would have occupied if it had moved only one case, as explained below.  En passant is the only case when a pawn can move diagonally.  Mathematically it can be represented by the intersection of two lines, the lines the captured and the capturing pawns moved respectively.

Can Chess help kids understand maths?  Can Chess be useful at school? 

(Before the battle of Waterloo, Napoleon asked his cavalry to keep contact and to harass the enemy to prevent it of mounting a huge offensive, but the cavalry failed to do so.  He argued thereafter that caused him to loose the battle, an important one in France's and Europe's history.  However, chess are not miltary battlefield where not only tactics and strategy might come into play at the beginning of the confrontation, but also the number of the soldiers and the miltary equipment of the protagonists facing each other are important.  Clearly, Napoleon was overwhelmed and his cavalry having kept contact or not might not have helped.  Nevertheless, at his time, wars were won mostly on one battlefield.)

Moving rapidly but cautiously into opponent's territory

During my last games I saw that while playing whites with my usual two first moves e4 and b3 I had a better opening in moving rapidly my light pieces on an attacking position with the knights moving first. I had then a better chance with having one knight soon dominating the opponent's territory, but I had to exchange my bishop against knights to gain this small territorial advantage. MAY 24, 2007Of the seven games I played on this day in Central Park, I won three gainst Alberto, one againsr Max, lost one against Max and had another one ending in draw with him.  I told Alberto, an old man who has been and is still a good marathon runner that the major problems with his attacks are they mobilize too few pieces to be able to build a mating net.  However, Alberto who may either suffer of Parkinson's disease or who seems to be prone to develop it may also have some problems at controling or watching all his attacking pieces and the more you have in attack the more it is difficult to watch them all in move.  In one ofthe game, he lost easily his queen in one of the attacks.

It is good to shop for a draw if you cannot buy a win

Max is really a good player.  So when I play against him I am always satisfied with a draw while he isn't. In the game I won against Max, he was attacking me with his queen, his bishop and his rook. He offered me his queen in exchange of mine but I declined his offer and retreated my queen leaving my rook at the forefront of my defense but protecting it with my queen.  Then, I decided a bold attack with the sacrifice of my bishop.  Immediately after the sacrifice, Max king was put in check by my queen and while I was in a defensive position I came now to be in an attacking one teasing the king of Max.  Suddenly, Max commited an error and lost his rook, He then resigned.  If it was not for my intelligent play, having declined the exchange of queen, Max who had a better pawn structure than me would have won the game, but really I was not looking for a win but only was after a draw by perpetual check or by three-fold repetition of the same position in order to avoid the mate.

MAY 22, 2007,  ABOUT INFERENCESIt is no enough to play chess; it is also to make inferences.  Making inferences help you to get stronger in life.  It is easy to build new projects; it is not easy to  foresee those of your adversaries.   It is easy to make inferences, it is no easy to ''see" what is in the mind of your mate.  In playing chess you should be able to do many inferences.  While shorter inferences may well succeed against easier chess players longer ones may not work against stronger chess players. Let us begin a game and see the inferences that can be made during it.   The opening was like that: 1.e4 d6 2.d4 Nf6 3.f3.  However the inference that has been made by Blacks, was that Whites' next move after they have played Ng8-f6 would be Nb1-c3 to what they would answer by Bc8-g4 and Whites would then play Ng1-f3 and they Nb8-d7.  This inference is said to be of depth 5  because it has 5 members and has been made before Blacks did their second move.  This a relatively short inference but not the shortest one.  However, the Whites did not fill the expectation of the Blacks and played instead f3 putting more accent on defense than on attack.
     Let us take another opening: 1.e4 e6 2.d4 d5 3.e5 c5 *.  The inference made by Blacks after Whites' third move was: Pc7-c5 Ng1-f3 Nb8-c6 Bf1-b5 Bc8-d7. Blacks thought that by moving their pawn to c5 Whites would come with their knight to protect it, but then they will attack it again with their knight to what Whites would conterattack by threatening the knight with its bishop. Then, Blacks would move their bishop to protect the knight and their king.  Whites would have thus been taken in the attacking trap of Blacks that would have used to develop their pieces and have a stronger control of the center. Blacks expectations were almost fulfill but Whites thought that after moving its knight to f3 they would rather move their other bishop to e3 and put stronger emphasis on defense to what Blacks would answer by moving their queen to b6 to give some support to their pawn in c5.  Whites would have then move their pawn to b3 in order to have, at their next move, the bishop in position to support their pawn in d4.  The inference was written: Ng1-f3 Nb8-c6 Bc1-e3 Qd8-b6 Pb2-b3. Blacks keeping their expectations thought at moving then their bishop to d7 in order to protect the knight in c6 and their king. Whites having expected that also decided that they would have to move their knight to c3 in order to protect their king against Blacks' queen coming in a3.  Pursuing their plan, Blacks next intention was to have an exchange of pawns then of their kinight against bishop in d4 and to be in position to take Whites' pawn in b2 in order to either take Whites' rook in a1 or the queen's knight which would have moved to either a3 or c3;  it is a fork.  Having moved to c3, Blacks' queen would have put in check Whites' king which would have required the protection of the queen leaving alone the rook to be taken by Blacks' queen which would have checked again Whites' king.  Intelligent tactical moves and good inferences by Blacks!  This inference by black at the 5th move can be written partly: Qd8-b6 Pb2-b3 Bc8-d7 Nb1-c3 Pc5xd4 Be3xd4 Nc6xd4 Nf3xd4 and is in prolongation of the previous inference.   At the end of the 5th move, the opening seemed to have ended in favor of the Blacks.  The middle of the game would decide which would be victorious but Blacks would have acquired a sizable advantage and, as chess obeys to Bayesian statistics with its conditional probabilities, they would probably be the winer. Overhead is a picture of the board at the end of the 5th moves.



MAY 21, 2007, COMPUTER ANALYSIS OF OPENINGS OF PAST GAMES

In this first game that Whites have lost they wanted to open with the Queen's Gambit (a bold opening) and played 1.e4, 2.Bd3, and 3.c4 while Blacks played 1.Nf6, 2.e6, and 3.Nc6.  Computer analysis showed that since the third move Whites have been at a disadvantage and that Whites should have opened with 1.e4, 2.Nc3 and possibly 3.Bc4 after that.  Computer simulation beginning at the third move showed with a mean inference of 5 moves ahead that the game would have ben level at the end of the opening and that Whites would have not lost probably the game although they scored less points at the beginning.

In this second game that has begun like that: 1.e4 c5 2.c4 Nc6 3.d3 g6 4.Bd2 Bg7 5.Bc3 Nf6 6.Nf3 d6 7.Be2 O-O 8.Qd2 Re8m9.O-O b6 10.Na3 Bg4, computer simulation and analysis with a mean inferential depth of 5 moves ahead showed that whites by playing 1.e4 c5 2.c4 Nc6 3.Nf3 d6 4.Nc3 Nf6 5.d4 Bg4 6.dxc5 dxc5 7.Bg5 Qb6 8.Rb1 Rd8 9.Bd3 Bxf3 10.gxf3 Ne5 would have a better chance of wining the game although the computer deemed the game to be indecisive till the 40th moves. However, Whites would have broken the pawn structure of Blacks since the 15th move and again at the 32nd move and would have gained thus an advantage long before the 40th move. At the end of the 42nd move, Blacks would have been in a very bad position and would have resigned before loosing their only bishop.  In this simulated game, Whites opened the game with the intention of offering the queen's pawn as a gambit,  Even after Blacks has refused the gambit at the 5th move, there was an exchange of pawns at the 6th moves that allowed Whites to open a breach in the defence line of Blacks,  After having checked Blacks' king at the 11th move, Whites exchanged their queen with Blacks' queen, then exchanged a bishop against a Blacks' knight forcing them at doubling their first pawn and creating more breaches in Blacks' defence line.  Although the analyis made by the computer did not give the victory to the Whites for the opening, Whites by moving their knights to f3 and to c3 at the third and fourth moves had gained the control of one case more over Blacks at the (rectangular) center, had been able to play their gambit by moving their queen's pawn to d4 and had found substantially much space to lay out (deploy) their strategy. (At the end of 5th move, the two Whites' bishop controled together 9 cases, the queen 9 also, the knights together 8 ahead in the middle of the board, and the three adavanced pawns 5 cases ahead also in the middle of the board: a huge advantage) .  Thus Whites by playing the Queen's gambit moved aggressively since the opening; what the computer mistook for imprudence and gave bad scores to Whites till the 40th move when Blacks' defence crumbled.

MAY 20, 2007, PREPARING THE NEXT GAMES AT THE CHESS & CHECKERS' HOUSE IN CENTRAL PARK

Analysis of an opening, with computer simulation beginning at the 5th move, and having in mind the control of the rectangular area of 8 cases at the center (c to f line and 4th to 5th column)

To have the control of the center, the four first moves of Whites have been: 1.e4 2.b3 3.Nc3 4.Bb2.  Blacks answer with: 1.e5 2.Nf6 3.Bb4 4.d6. Whites' intention was to have the control of the center over Blacks and to increase or maintain it as the game progressed. As its knights could move easily to the center, Whites' second preoccupation after having opened for its queen and king's bishop was to free it queen's bishop by moving its pawn to b2, but before that it needed to protect its queen's rook by moving its queen's knight to c3 .   At the end of the 4th move, the situation of the protagonists were as follows: 1.e4 e5 2.b3 Nf6 3.Nc3 Bb4 4.Bb2 d6 with Blacks having the control of 5 cases at the center and Withes 4.  To avoid losing totallly the control of the center, Whites' next move should be 5.Nge2 instead of 5.Ngf3 and have its king's knight in control of f4 and, at the same time, protecting its queen's knight.   Indeed, Blacks next move would have led to an exchange of pieces of almost equal value with Whites and the taking of their central pawn e4.  At the end of the fifth move, the situation was like this on the board: 1.e4 e5 2.b3 Nf6 3.Nc3 Bb4 4.Bb2 d6 5.Nge2 O-O *, with an equal number of cases controled at the center by both sides (respectively d5, e4, f5, d4 and f4 by Whites, c5, d4, f4, d5 and e4 by Blacks) and the game was considered as being level by the computer's mind.  Whites' next intention was to remove the threat set by Blacks' bishop at the center by attacking it with its pawn moving to a3 and, at the same time, to prevent the next move of the Blacks' queen that could lead to a difficult situation and even a mate for any small error by moving another pawn to g3.   Blacks then castled on the king side trying to increase its lead at the center at the next moves and putting its king in security, then attacked Whites' central pawn by moving its pawn to d5.  Whites took it, what led to an exchange of pawn with Blacks' knight having taken next the pawn.  Whites prefered not to have an exchange of knights that would have led to a threat of its rook at a1 by Blacks' queen but attacked instead and further Blacks' bishop.  Blacks retreated  its bishop to b6 and attacked Whites' knight with its pawn moving to f5.  Whites' knight retreated and moved back to c3, but meanwhile has moved its king's bishop to g3 in order to have it also in the battle for the center and to protect its king's rook.  Blacks then decided to put its queen's bishop at the front's line by moving it to e6.   however, at the end of the 10th move by both sides, the game has been deemed level by the computer, with the Whites controling d5, e4, d4 and f4 at the center and the Blacks having in control c5, d4, e4 and f4 which is an equal number of controled cases in this rectangular center of 8 cases.   The record of this opening having ended at the 10th moves is: 1.e4 e5 2.b3 Nf6 3.Nc3 Bb4 4.Bb2 d6 5.Nge2 O-O 6.a3 Bc5 7.g3 d5 8.exd5 Nxd5 9.Ne4 Bb6 10.Bg2 f5 11.N4c3 Be6 *.  Another set of tactical moves would have led to the same result at the end of the 10th moves and can be written: 1.e4 e5 2.b3 Nf6 3.Nc3 Bb4 4.Bb2 d6 5.Nge2 O-O 6.a3 Bc5 7.g3 d5 8.exd5 Ng4 9.d4 exd4 10.Ne4 Bb6 *

This opening seems to be complex.  However, the tactical moves are easy to understand with the intention of controling the center by having the Whites' bishop on the larger diagonals (1) and the knights moving together either to the right or the left parts center and protecting each other (2) , the king free to castle (3) and the queen free and ready to protect and support the smaller pieces on the right or left side of the board (4).

MAY 19, 2007

Yesterday, I was consulting some chess books - The Big Book of Chess of Eric Schiller and the Chess Basics of Nigel Short - at the Barnes & Noble and have reviewed the set of rules, mostly the rules in different situations of draw. There are twelve different situations in my referenced link (reserve a l'auteur). MAY 17, 2007, PREPARING THE NEXT GAMES AT THE CHESS & CHECKERS' HOUSE IN CENTRAL PARK

Chess' databases

One way to learn about chess inferences (see below) and to work it up is to go to the database of world championship's chess games -   yes, it is big - or, at least, to go to its opening's database.  A few years ago, a chess book having this database was in sell at the Barnes & Noble Library.  You can even build your own database that may include your own chess games or openings, after having analysed and corrected your blunders (réservé à l'auteur).

MAY 17, 2007 - AFTERNOON GAMES. In this cold afternoon of May, among the many games I played at the Chess and Checkers' House, I won two, but one of them might have been a draw by perpetual check without mate: 3 consecutive checks are just enough, but I am not very sure.

How can we define an opening?

There can be as many openings as there are players in the world, but to define an opening we do not need to go till the 10th move.  An opening can be defined by just the first two moves as it was for the Caro-Kahn below, the other moves setting its variations.  Therefore, the game I won against this beautiful white working for AT & T was opened with the Queen's gambit, although the gambit, the sacrifice of the pawn, did not really take place.

A game lost by lack of inferences - Setting the variations for an opening

Before analysing this game, let us begin by some ads.  Come to the Chess and Checkers' House in Central Park to play and learn chess.  It is free and it is fun, since you wil get fresh air and plenty of sun in a beautiful and sunny day of summer and perhaps you will meet one of the "masters" who sometimes visit this site and even Max who wants to teach chess as a professional, having really some abilities.
      Inferences are often what are lacking a chess player to become a good player or to overcome the stade of debutants.  The more you can do the better you are.  How can we define inference and how can we get it?  In the American Heritage Dictionary, inference is defined as the "act or process of deriving logical conclusions ...from factual knowledge or evidence".  In chess, it is seing the next moves of your opponent and yours in a tactical context and the farther you can see the better you are.  In fact, seing five moves ahead is really a significant progress for  player to move from the stade of debutants.  How can we get inferences?  As for many things we do, we may have some abilities to make inferences in chess.  It is also linked to our ability to learn. This ability is the greater during childhood and it is the greatest in infancy, afterwards it decreases in geometric progression.  However, this ability to make inferences in chess is also linked to the our knowledge of chess rules and tactics and overall to the size of our brain.  As our brain is not fully developed till we get adulthood, our ability to infere was less when we were a child than we we become an adult.  Therefore, the best chess players are those adults who begin to learn chess when they were child. Inferences are also linked to our knowledge in chess, i.e., to our practice and theory of chess.  For me, I am looking only for the theoretical aspects of inference in chess, since I do not really want to devote too much of my time at playing chess, having many other things to do.  As for the practical aspects, the theoretical aspects of inference can be worked up, but it is the most difficult way to get it.  It begins by knowing the rules (1), understand the geometry of the board (2), understand how the chess pieces move (3).  It progesses by studying the tactical moves made by great chess players and their strategies (4); what can be done by analysing their games through books and softwares.  It ends, if ever it has an end , by putting those learnings in action in the improvised context of a chess game (5).
       As chess obey to Bayesian statistics, learning the openings is perhas the best way to build inferences (reserve a l'auteur).   Learnings some tactical moves at the middle and at the end games come after that.

MAY 16, 2007, PREPARING THE NEXT GAMES AT THE CHESS & CHECKERS' HOUSE IN CENTRAL PARK

Queen's gambit - How Blacks can prevent Whites' gambit? - Ruy Lopez and Whites' reponse

To prevent the gambit offfered by Whites, Blacks choose not to open with Caro-Kahn, but to open instead with the Ruy Lopez ....

Opening with the Queen's gambit or the Caro-Kahn

The Queen's gambit opens the game to an aggressive strategy, perhaps the most of all where the player dedicates himself to an early and sustained offensive. Played with the Whites its first five moves are: 1.e4, 2.c4, 3.d4, 4.Nc3, 5.Bg5.  The first three moves gives this opening its identity. The opening is completed after the eleventh move as it shown here: 6.Be2, 7.Be3, 8.Qc2, 9.O-O-O, 10.Kb1, 11.Qb3. The pawn is offered as a sacrifice at the third move; it is an intuitive sacrifice (as stated below). First, e4 is played to free the Queen, the king's Bishop and somewhat the king's Knight and allows them a range of 13 dominated cases (huge for a first move!).  Second, c4 is played to free somewhat the queen's Knight and to increase to 3 the range of cases dominated by the Queen.  Third, d4 is played to free the queen's Bishop and to increase to 2 the range of cases dominated by the Queen and to 1 that of the queen's Knight.  After those three moves, the number of cases dominated by the white pieces withouth taking in account the two lateral cases dominated by the knights are given by this addition: 13 + 3 + 2 = 18 cases.  Comparatively, the number of cases dominated by the black pieces are 8, barely the half of those of the Whites. 
      Nevertheles, Blacks have begun with the Caro-Kahn which opens for a strategy based on a strong defense: 1.e4 c6, 2.c4 d5, 3.d4 dxe4, 4.Nc3 Nf6, 5.Bg5 Nbd7.  "In this opening, Black challenges the centre in an unusual way and pays less attention to piece development.  Black's plan is to establish a strong defence with a solid pawn structure before beginning to attack. Black's first two moves give this opening its identity." (Norwood D.; The Usborne Guide to Advanced Chess, p.20; Usborne Publishing Lt.; 1990)

MAY 15, 2007, AFTERNOON GAMES

Center and Center

Considering the geometry of the board in the game of chess, the center is only the 4 cases that stand at the middle of the board (d5, e5, d4 and e4).  In terms of tactical and strategical maneuvers and strenghts, the geometry of the center shall extend to the 8 cases of the middle of the chess' board (the rectangle that goes from the c to the f line and from the 4th to 5th column).

Computer's Evaluation vs. Master's Evaluation

In the simulated game analysed below, under the title "A retouched queen's gambit", computer's evaluation gave a large account to numerical advantage, putting therefore the Whites having opened with the Queen gambit at a disadvantage, at the beginning, and considered the game to be level only after the 26th move.  In my analysis of the battle of the center, I saw that the Whites have had since the Gambit "the hands high on" the game and have constantly threatened the Blacks, having been more often in their territory than their enemies were in theirs.  So, in terms of strategical and tactical maneuvers and positions, the game might well have been unbalanced since the beginning.

An instructive end of game

In this end game that I have watched between a master, named Max, and his pupil and chessmate, the master explained that he made a mistake by attacking his pupil's queen with two rooks on the 7th line while they were also facing two contiguous passed pawns respectively on the 5th and 6th lines.  All the pupil would have to do was to take a rook with the queen and, while the other rook would have moved to take the queen, the protecting pawn would have advanced on the same line with the pawn that was protected.  His only rook would then have been unable to stop at least one of them of being promoted, all the other part of the set having been far away of this final confrontation.   Nevertheless, his pupil did not know what to do, but the master ended the game in resigning.

A "retouched" queen gambit!!

In this Tuesday and warm afternoon of May 2007, of the four games I played in Central Park, I won two, having applied for one of them the art of retreating, and lost two.  In the two games I lost, I thought I was playing a retouched Queen's gambit in order to prevent my opponent of taking an opening pawn.  However, I came to understand that I did not know what is really a gambit.  In the American Heritage Dictionary, a gambit is described as an "opening in chess in which a minor piece, or pieces, usually a pawn, is offered in exchange for a favorable position," what means the sacrifice of a pawn at the opening.   So, why should I have been afraid to have my pawn taken?  It was probably silly of me.  Computer simulation of the opening showed me that was only till the 26th move that I would have regained the adavantage lost at the beginning of the game and the game would have become a level or balanced game; a thing that would have been very difficult for me to realise.  So, I did not play really the Queen's gambit and I was liying to myself all the afternoon in having thought I was playing the Queen's gambit. You can really be silly in chess if you try to apply things withouth having fully understood them. 
     This is how the game would have looked like after the 43rd moves in playing the computer against itself: 1.e4 c6 2.c4 d5 3.d4 dxe4 4.Nc3 Nf6 5.Bg5 Nbd7 6.Be2 h6 7.Be3 Nb6 8.Qc2 Bf5 9.O-O-O e6 10.Kb1 Bb4 11.Qb3 a5 12.Ka1 O-O 13.h4 Qe7 14.d5 Nbd7 15.d6 Bxd6 16.Qxb7 c5 17.Nh3 Rfb8 18.Qc6 Be5 19.Na4 Ra7 20.Rd2 Rab7 21.h5 Kh8 22.Nf4 Bxf4 23.Bxf4 e5 24.Be3 Ne8 25.g4 Rc7 26.Qa6 Be6 27.Qxa5 Rc6 28.Rhd1 Nc7 29.Qc3 Na6 30.b3 Rc7 31.Qa5 Ra8 32.Qb5 Rca7 33.Qc6 f5 34.Qd6 Qxd6 35.Rxd6 Re8 36.g5 f4 37.gxh6 gxh6 38.Bd2 f3 39.Bf1 Kg7 40.Kb2 Re7 41.Bc3 Nc7 42.a3 Bf5 43.Bd2 Ne6 *.  Two moves after the 26th, I would have gained a small or possible advantage, 10 moves after, the advantage would have increased to clear and 15 moves after, it would have been sizable with me having had a better pawn structure and tow bishops facing two knights of my opponent.   In this simulated game, the gambit would have thus allowed me to win the battle of the center, at the opening, by having had a range of control of 22 cases against 15 for my opponent, after the 6th move.   My superiority at the center would have been the control of 7 cases against 5 for my opponent (c5, d5, e5, f4, e4, d4 et c4, for Whites against c5, d5, e5, f4 et e4, for Blacks, having considered a large rectangular center of 8 cases instead of the small square center of 4 cases which would have put them equal).
     

How have I applied the art of retreating in one of the last game I won?  After having gained a small numerical advantage at the opening, I have tried to conserve it during the middle of the game by retreating my attacking pieces before I could set a new and planned attack.  My opponent launched then a general attack, advancing his set all over the board, but for any threat I faced I was able to find an answer, my pieces having retreated and not scattered through the board.  Finally, I made a breakthrough and my opponent line of defense crumbled.

MAY 15, 2007

Does it exist a technic for the overture?  Can the opening be technical?

My answer is yes.  However before we come to that, let me tell you why I came to write about that.  There are many openings but most of them are senseless to me; I do not understand them.  That should not be.
     The opening is part of the strategy which ultimate goal is to checkmate the other king.  So, since the opening I can look for that goal and the easier and faster it can be, the best it will be for me.  However, precipitation does not pay and a short opening - less than 5 planned moves, for example - may result in catastrophe.  The best way also to understand the opening is to try to explain each move in terms of the overall strategy of the game. If you succeed it is the path to chesss master. If your plans at the opening are often broken, do not be discouraged, but work harder. Think it also: a long opening is not necessarily the best because it can be too slow and lead also to catastrophic results: 5 to 10 moves shall be the normal lenght. However, there are no strict rules in regard to the lenght as well in regard to the tactical moves. With an easy opponent you can shorten your opening and with a strong one you can make it longer. There have been many openings in the history of international chess championship. You can learn some good ones that may fit your goal, but the best will be to come with your own and hopefully it can be the best for you. In fact, the opening is completed when all the major and minor pieces are ready for actions and are not trapped in their original positions. Then comes the middle of the game.
     Let us examine this opening called the Queen Gambit.  Played by the Whites it is as follows: 1.e4, 2.c4, 3.Nc3 in the following game: 1.e4 d6 2.c4 Nf6 3.Nc3 g6 *.  The white Queen prepares herself to checkmate the black King in d7 with her king's Bishop and/or with her Queen's Knight.  There are 7 to 8 crucial cases for this purpose: d7, for sure, a4, b5, f3, h5, f7, b3 and c4.  How many moves will it be needed for that if the black King does not move and if no black piece or pawn has moved?  I will tell you it promptly: 3 for the Knight, 1 or 2 for the Queen and 1 for the Bishop. However, I did not take in account the presence of the black knight in f6 and those of the pawns in g6 and f7. To get rid of them will require more tactical moves and a bitter fight of the rest of the board.  Computerized simulation show that the next best move for the Whites is d4 to free the queen's Bishop so that it can threatens the Knight. In this opening also, the white Queen has much freedom and can move easily in one direction or the opposite to sustain her attacking pieces; that makes her moves difficult to predict. We have not finished yet withe Queen's gambit, but let us resume the tactical laws of the opening:

1. avoid precipitationdo not be too slowsee "where you are going"be plastic (think to "The Fox of the Desert")
2. free your pieces

 

MAY 13, 2007

In the many games I played in Central Park this Sunday, I won four of which one was by forfeit when my opponent broke the rules, lost one and have one draw. Let me begin by the loss.

Loss by failure of having castled

The game I lost was played against a young player from Bengladesh or India.  I came to test a new opening and had in mind or on paper some tactical moves.  They were to open with d6, Nf6, g6, Bg7 while playing blacks...  However, at a point I did not knew what to do and could noyt play Qb6.  The opening game was like that: 1. g3 d6; 2. c4 Nf6; 3. d3 g6; 4. Bd2 Bg7; 5. Bc3 c6; 6. Bh3. By analysing the game with my computer, the best move would have been to castle in the King side and to play: d6, Nf6, g6, Bg7, c6, 0-0, b5, b4, h6, Bg4, Nbd7 (i.e., pion devant reine d'une case; cavalier roi vers centre; pion cavalier roi d'une case, fou roi d'une case, pion fou reine d'une case, petit roque, pion cavalier reine de deux cases, puis d'une case;) .  During the whole game I was in difficulty and finally lost all chances when I isolated my knight by having tried a vain breakthrough.  I resigned. (Computer simulation of a level game using this opening game: 1.e4 d6 2.Nc3 Nf6 3.Bc4 g6 4.Nf3 Bg7 5.O-O c6 6.Ng5 O-O 7.d4 b5 8.Bd3 b4 9.Ne2 h6 10.Nf3 Bg4 11.Nh4 Nbd7...)

A faulty tactical opening in a game played with the white set

In this tactical move I moved my bishop protected by my queen on the first column to attack my opponent's knight, but did not see that my bishop can be aggressed by an incoming and protected pawn that will have put me in a difficult position and has to retreat resulting in a loss of time and the advance of my opponent's line of attack. Computer simulation showed how, with no further error, the party would have ended in a draw asked by the white king in difficulty in e3 after three consecutive checks in d4 by the same black rook after the 47 moves.  Two times in the simulated game done after a real opening , a white bishop has been beaten in retreat causing a considerable lost of time by the whites: 1.e4 c5 2.d4 cxd4 3.Qxd4 Nc6 4.Qa4 g6 5.c3 Bg7 6.Nf3 Nf6 7.Bb5 a6 8.O-O Qb6 9.Be2 O-O 10.b3 d5 11.Be3 Qc7 12.Ng5 Bg4 13.f3 Bh5 14.g4 b5 15.Qa3 b4 16.Qc1 Bxg4 17.fxg4 Nxe4 18.Nxe4 dxe4 19.a4 bxc3 20.Nxc3 Nd4 21.Bd1 Nxb3 22.Bxb3 Bxc3 23.Rb1 Rad8 24.Rf2 e6 25.Bh6 Rfe8 26.Bf4 Qc6 27.Bg5 Rd3 28.Qc2 Qc5 29.Bh4 Bd4 30.Qxc5 Bxc5 31.Bc2 Bxf2+ 32.Bxf2 Ra3 33.Be1 Rc8 34.Bb4 Re3 35.Bd1 Kg7 36.Kf2 Rh3 37.Bd6 Rd3 38.Be5+ f6 39.Rb7+ Kh6 40.Bxf6 Rxd1 41.h4 Rc2+ 42.Ke3 Re1+ 43.Kd4 Rd1+ 44.Ke3 Re1+ 45.Kd4 Rd1+ 46.Ke3 Re1+ 47.Kd4 drawHowever, the real game was won by the whites by forfeit. The faulty tactical opening was for the whites: 1.e4, 2.d4, 3.Qxd4, 4.Qa4, 5.c3, 6.Nf3, 7.Bb5, 8.O-O, 9.Be2, 10.b3

Faulting by underestimation: a passed pawn.  How to deal with it?

The best tactic in this case is prevention.  Try always to prevent your opponent's pawns of becoming passing pawns.  If they did, try to get rid of it as soon as possible, even at the loss of another pawn if the later is not to give passage to another pawn or result in incredible losses.

A motif of distraction

Chess is the supreme game of the mind.  It requires full attention and powerful concentration. Lest us not playing chess with music in our ears or cigarettes in our hands.

Breakthrough and getting behind the lines: how good are your tactics?

In this game I won, I was in a difficult position when I succeeded at making a breakthrough inside my opponent's line of defense, but took care before that to move my king in a safer position.  I was behind his line of defense with a rook and my queen. My opponent counterattacks with his rook on the last column and last row  and tried to checkmate me.  However, it was too late.  I gave my rook in sacrifice in order to prevent him to move his too fast, then put him in check and threatened at the same time its imprudent rook that was taken at my next move.  His king was in check.  He came back with his queen that left the attack to come at the ressource of his defense.  We exchange queens and it was over.  I had too much a numerical advantage.  What a surprise to him!  I played the end of the game boldly, was never afraid of making sacrifices and won.  It is good to play bold, but avoid imprudence. Then came the ugliness.  My opponent, unhappy with this loss, asked me with insistence (like mugging me) to have my chess game sold to him for $20.00.  No chess player should ever do that after a game and for whatever the price is.  There are stores where chess games are sold.  I could have only given their addresses to him:
Chess Forum: 219 Thompson St.; New York, NY; Tel.: (212)475-2369; take the C from the West side in Manhattan; get out at Fourth Street Station (Worth Station) on the Avenue of the Americas, walk three blocks - Mc Donald, Sullivan and then Thomsom St., turn right; the store is at the middle of the block.

 

MAY 12, 2007

Combinations and surprises, not precipitation

To begin, let me tell you how its has been in the park yesterday.  In the four games I played against different opponents of which two were with the same mate, I won two.  I won my first game by putting in application a new startegy that consist at attaking my king's opponent as soon as possible in order to force it to move and thus prevent hin to castle.  It is done by putting it in check successively and it implies sacrifices.  Yesterday it was big sacrifices not only one the knight but also of a bishop and even a rook.  My opponent was stunned in surprise and soon it fell.  Unfortunately I did not take any note and I cannot remember all the moves I did in this beautiful party.  However, in the last three games it was more precipitations than good combinations or tactical moves.  I was about to loose also the last game and had a numerical disadvantage when my opponent gave the opportunity to retake the initiative, correct the numerical advantage and threaten his queen.  Soon it was done and my opponent resigned. My other strategies are the domination of the center and trapping my opponent's king in its corner after that he has castled, by attacking him with as much pieces as possible and realising a relative numerical advantage in that part of the board.

The law in any exchange of multiple pieces protecting each other

The law in any exchange of multiple pieces facing each other is that when there are an equal number of pieces of the same value, the attacker has the advantage, unless there is a pawn interposing itself between. 

 

MAY 10, 2007

Does chess fit to Bayesian statistics?

In some of the games I played recently against Alberto, I saw that by having allowed my chessmate to exchange his pieces with me (and nothing than that), I had my plans broken and the end of the game came to obey more to chance than to (previous) strategical or to tactical moves.  On the board we came to have almost an equal probability to win or loose the game.  It was then only chance like when we play the lottery. 
     Chess, by difference with the games of cards, does not allow much chance to play; therefore, it is more a cerebral sport than a saloon game. In chess, chance has a minute role at the beginning of the game but, as the game progresses, this probability (chance) dwindles till it came to be nil at the end of the game and the opposite probability (the one which depends on tactics and strategies) grows till to be equal to 1.  It is conditional probability where the probability of wining or loosing the game is conditioned by the anterior and linked probabilities of wining or loosing at each move.

More about sacrifices

These lines which follow are to comment a game I played against my Korean chessmate today.  In classic chess literature, there two kinds of sacrifice: calculative sacrifice and intuitive sacrifice.  "In a calculative sacrifice a piece is given up for immediate benefit - to win a piece of greater value ... or to give" immediate "checkmate."  In an intutive sacrifiice, the "benefit is not immediately apparent," since intuition is "the act or faculty of knowing or sensing without the use of rational processes" (American Heritage Dictionary).  It may be done, "for instance, for a long term attack opportunity or an improvement in the position and mobility of your pieces." (Norwood D.; The Usborne Guide to Advanced Chess, p.46; Usborne Publishing Lt.; 1990). For me, there are different kinds of sacrifice that I will divide in three to four types, but all of them are done in order to gain the control of a crucial case:

1. Obligatory Accepted sacrifice or Obligatory sacrifice that you should do in order to avoid the mate and that your opponent cannot avoid to take, being either in check or otherwise threatened; Non Obligatory sacrifice that your opponent sould avoid to take, even if it is tempting and even after having lost a pawn or a piece; absolute sacrifice where a pawn or a piece has been taken in exchange of a higher or more valuable piece. It is more like the calculative sacrifice. In fact, both the obligatory and the non obligatory sacrifices can fell in this category.
2. Relative sacrifice where no pawn or piece has been taken for the piece that is offered and that is, sometimes, more a trick than a sacrifice, but that can be done also in order to occupy temporarily a case that allows you to move to a crucial one in the next move. It is more like the intuitive sacrifice.

In the last game I played against my Korean chessmate it was clearly of the last kind.  My king which had not yet castled was threatened to be checkmated, having been attacked by my opponent's queen, knight, bishop and/or even rook and some of his pawns were in a very advanced position, one of them to be soon promoted to queen.  My king moved intelligently behind my defense line, away from its attackers, having had much place to move, but was still in very great danger.  I offered my knight in sacrifice to my opponent's very advanced pawn in order to have it moved from a column controled by one his rook.  It was happy to take it.  If he had not done also his queen would have been be menaced in the next move and could have even been taken or, otherwise, would have to abandon the attack.  I moved then my queen to check my opponent after having taken his pawn. His king who had castled on the king's side was left alone but had not been behind his defense line, having been moved from its hiding but too tight or narrow place by my advancing pawn which was protected by my rook, on the last column.  It was then checkmated after having taken an "obligatory" tempo in a series of checks he delivered to my king and having massacred much of my defense line.  In fact, I had this mate in mind since my opponent had castled on the king side and I had moved hastily my pawn on the last column. And for him it was a great surprise that he took some time to realise (probably 5 sec.)!

Know how to retreat

In some of the games I lost recently I won the opening with my early domination of the center and got an early numerical advantage, having sometimes even taken my opponent's queen, but, after that, my attack lingered and my advantage dwindled.  My "posthumous" and final analysis of these games showed me that when my opponent began to develop his pieces mine (my ones) more scattered than his become vulnerable.  Retreating after haven taken a good numerical advantage would have helped probably.  Retreating allows you to put more emphasis on defense and when you have a clear numerical advantage that can help.

Bishop for self-defense: the art of retreating

I red about the Battle of Waterloo.  The author explained that one of the major mistake of this military genius who was Napoleon Bonaparte was, in his last battle, the failure to have planned a honourable retreat when his attacking plans were thwarted and to have tempted a vain breakthrough in the ranks of his adversaries. By the contrary, the opposing armies played well this strategy of attacks and retreats and eluded him in lingered attacks till they got him surrounded. It was also the art of guerilla warfare (that, maybe, no good general, not even Julius Cesar, knew how to win). I already knew the role of the bishop in defending an advancing pawn where both can support each other in self-defense and, today, I played well on it in a game won over my chess companion Alberto.   However, what I knew is only the tip of the iceberg since the bishop has a more intense and active role in the defense, being able to be used in long range as well in short range defense. Today two chess companions showed it to me.  Indeed, in two of the games I lost today I failed to understand how importnat is the role of the bishop in self-defense and did not give the correct response to the attack of my opponent.  In one of the game played against my Korean chessmate, a young Afro-American spectator who could have also taught chess to kids showed it to me.  While I had a tactical advantage at the end of the game but not a numerical one, by having had a bishop and two rooks while my opponent had more pawns and also two rooks, I came to be in a difficult position when all my three pieces were aligned on a single column and were attacked by the two rooks of my opponent.  Having thought in error that I would have left this tactical confrontation in inferiority I moved away one my rook to capture a non crucial pawn.  My Afro-American companion explained to me my error by showing to me the right move.  First, I should have moved and left my rooks on the same column but on a row where my retreating bishop (to another row) could have protected them while facing my opponent's rook. In the other game, my chessmate, a young Mexican guy showed how my bishop could have helped trapping his queen which has ventured in a lonely and not well planned attack.

The advantage of castling on the Queen's side

Today, my victory against my opponent, an old but athletic Korean man with no definite strategy or no more one than the exchange of pieces was due to me having not castled on the king side while my opponent did.  Soon, he found himself trapped on this side with my adavancing pawn on the last column protected by the king's rook.  While after having dominated the center at the opening, I lost terribly by my mistakes this battle at the middle game and almost lost the game if it was not because my king had more place to move than the king of my opponent and was defended.  Finally with sacrifices to win crucial positions, I won the game and checkmated my opponent with the help of my king's rook, a pawn in an advanced position on the last column and my queen while he was only one move away (late) to win the game.

A win at the opening that could not concretize in victory

Finally what caused me to loose most of my games these days while I won the opening is a battle of the center that could not concretize in victory. Putting also too mamy pieces in the attack make them more vulnerable and more difficult to control.

The art of the opening: checkmate in four to seven moves with or withouth sacrifices

In three of the games I played against different opponents, two with Alberto and one with the Korean athlete, I succeeded at mating my opponent in 4 to 6 moves.  It was an application of my strategy "wining as fast as possible" with quick and combined moves of knights, bishops and queen.

A general withouth its army

In tow ganes I won against two different opponents, they made or were forced to make the mistake of moving their king in front of their defense.

 

MAY 8, 2007

Sacrifices, always sacrify

Wining with an opening often implies that you have to sacrify pieces or pawns to gain very fast some crucial position or cases.  You know probably about sacrifices of pieces or pawns , but sacrifices go even beyond that and can be that of the pawn structure by allowing your opponent to excange some pawns with you.  It has workd rather well for me in two of my last games with Alberto.

MAY 1, 2007

"The Old Man and the Park"

We have often heard about the legend of The Old Man and the Sea.  Today, you will hear about a new legend.  Years before I knew that they were playing chess in Central Park in New York, I used to come and jog in the park, mostly along the shortest path, around the reservoir, a huge one.  It is there I met a man who has been called and named the mayor of the park.  It was an honour that the City granted to Mr. Alberto Arroyo, of Puerto Rican descent, who was probably the first or one of the first joggers around the reservoir.   Alberto was also a boxer at this time and no one would have ever challenged or mugged him along this mostly desert path, at this time.  If Central Park has become safer we may also thank Mr.  Arroyo.   Alberto is also a good example for any one who wants to exercise and keep himself healthy.  At ninety years old, Alberto is in excellent physical and mental health.  I meet Alberto on January the first of each year and we will continue to do so as long we are both alive.

Ranking and rating in chess

Rating is a "measure of a player's skill, calculated as a number using a generally accepted formula by an official organization."  Ranking is comparative rating and is a way for the chess federations to evaluate a chess player and make the tournaments more interesting by putting in competition the players who are of almost the same strenght.   «In a ranking system, items in a hierarchy (most frequently people) rise or fall based upon specific, objective, and well-known rules. This is the heart of most multiplayer competitive systems.» «The ELO System is an example of a ranking system used for two-player games, and is used by the U.S. Chess Federation. Days of Wonder uses a multiplayer variant of the ELO system for their online games. Each system builds a simple distribution of player ratings around a norm (typically 1500 points), then awards or deducts points based upon wins and losses.» «The following analysis of the January 2006 FIDE (Federation Internationale des Echecs Amateurs) (World Chess Federation for Amateurs) rating list gives a rough impression of what a given FIDE rating means:

• 19743 players have a rating above 2200, and are usually associated with the Candidate Master title. 1868 players have a rating between 2400 and 2499, most of whom have either the IM (masters) or the GM (grand masters) title. 563 players have a rating between 2500 and 2599, most of whom have the GM title 123 players have a rating between 2600 and 2699, all of whom have the GM title 18 players have a rating between 2700 and 2799 Only Garry Kasparov of Russia, Vladimir Kramnik of Russia, Veselin Topalov of Bulgaria, and Viswanathan Anand of India have ever had a rating of 2800 or above.. The highest ever FIDE rating was 2851, which Garry Kasparov had on the July 1999 and January 2000 lists
• In the whole history of FIDE rating system, only 39 players (to April 2006), sometimes called "Super-grandmasters", have achieved a peak rating of 2700 or more.»
  

Ref.: Wikpedia Encyclopedia and Chess Glossary

More on tactics

Last week and at the beginning of this one I have played against Mr. Alberto whose strenght is probably far lesser than mine.  However, I lost unexpectedly some games.  In reviewing the games I came to realize that my opponent has tried to exchange pieces with me in the games he won.  By allowing him to do so, I was unable to apply one of my fruitful strategy which has consisted at attacking and trapping my opponent's king with more pieces than he can allow himself to put in defense of his king, in his corner, after he has castled (mostly on the king side).  Finally, I came with a "new" tactics bound at preventing him to do so and it worked well.  When you are playing chess pay well attention to your opponent moves and presumed tactical intentions and do your best to prevent him putting them in practice, by blocking his access to some cases with your pawns if possible, even letting his own pieces or pawns be an handicap to him and by not being hasty at removing them in their stuck or locked position. (I have applied mostly this tactic to prevent my opponent at moving his bishop too close to mine in order to exchange them, at the beginning of the game, but it worked also rather well for the knight although it might have been more dangerous.)

Winning as fast as possible and loosing as strong as possible: the art of the openings

When you are used at playing opponents of different strenght you may adopt a strategy that may not work well with opponents of different styles and may linger in your attack in a game with an easy opponent and even loose or draw the game or be easily defeated by a stronger opponent.  One thing you will have to keep in mind is try to keep an opening that will alllow to win fast against an easy opponent and that will allow you at the same time to not be routed by a stronger one.

Pawns against rooks, yes it is possible

This week I saw Mr. Durand loosing a game against Mr. Rob, but the point was he has lost confidence in himself at the end game.  Rob has two rooks amd a Queen and Durand has his Queen and a stronger pawn structure with at least 5 to 6 pawns in support of each other and in an advanced attacking position (at the middle of the board).  The way I saw that Durand should have played was that he should have kept mining the pawn structure of Rob which was already very feeble and was not yet ready to conduct a strong attack on the pawn structure of Durand (he would have needed three to four moves, at least while Durand would have needed only one or two moves to have the pawn structure of Rob opposing his completely destroyed).  In a similar game I played against an opponent I won the game while I had at the end of the game only two pawns in support of each other and in company of their king and my opponent had a rook and his king but did not know how to make them play together.

APRIL 25, 2007

Improper conditions:

Today, at the Chess and Checkers' House in Central Park, we have discussed about the improper condtions in this chess' place.  For many of the players, the chairs are too low and the level of the tables is at the middle of their chest while it should be at their navel to allow them a better view of the board.  However, we all enjoy this natural and improvised place to play chess; we got fresh air and plenty of sun to keep us healthy while playing chess.

A hasty drop:

In one of the games I played today, I saw the trap, but in a moment of distraction I droped hastly my piece, so I lost the game. However, my opponent allowed me to take it back in this friendly game and I won consecutively the game. Distraction is always possible, so try to not drop hastly your pieces while moving them.

A lingering attack:

My opponent of Jewish descent has moved his pawns boldly in an offensive position during the opening and I was worried that soon my defense would crumble, but miraculously for me, he lingered in this attack and allowed me the time to strenghten my defense and move more pieces in the positional confrontation.

A fruiteless sacrifice - An insufficently planned attack:

In the usual strategy I have adopted to play my game, sacrifices are desired and often helpful, but they have to be well planned.  Today, in attacking my opponent's king that has castled on the king side, I sacrificed my white bishop in exchange of the pawn of my opponent defending his king on the last column;  that allows me, then after, to check my opponent with my queen, then to take one of his knight in a central but crucial position and to be able to move her freely to check again my opponent's king on the last line, but I was unable to check-mate it and, to avoid to be check-mated myself, have to check-mate it consecutively and accept the draw.  This could have been avoided if my king's rook had taken a proper position before that, such as the second or third line in order to move it easily on the first column again

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The law in exchanging pieces in a defensive position:

Today, in one of the games I played, I avoid the check-mate by applying the rule of defense where there are exchanging of pieces and your king is in danger of being check-mated.  The rule is to have one piece more than your opponent in the positional confrontation where the pieces are protecting each other and when the opponent has the initiative or, better, to have one pawn protecting an equal number of pieces.

APRIL 24, 2007

Stick to your strategy

In the two games I won over Sir Elton, an elegant chess player in the Central Park, I have been sticking to my strategy wich is to attack my opponent with as much power (pieces) as possible.  However, in the second party which was replayed when I accepted that Elton took back his piece after a bad move and conceded the victory, I lost, in a consecutive error, my bishop; it was nevertheless not enough for me to lose the game afterwards.  What then happened?  In my postgame analysis, I saw that I have not stuck to my strategy and that I have scattered my pieces through the board for any solid reason (or attack) while I should have concentrated them on the side of the board where the initial attack on my opponent's king has begun.  My pieces were therefore less able to play in support of each other and that probably caused me to loose the replayed party, because it would have required more attention and caution to play with scattered pieces; what can be diffcult for a casual chess player. APRIL 21, 2007 - A forgotten and ill understood "en passant"

I won the first game I played today after having trapped my opponent's king in a corner, but I lost the second game, probably after having lost an advantage with a forgotten "en passant".  My opponent had just moved his pawn from two cases and placed it next to one of mine on the same row but has not passed me.  I could have taken his pawn with an "en passant", but I was not sure if it could be done. It is only now that I realized it was possible, because if if he has moved only from one case I could have also taken it in view of the definition that follows.   En passant is described as a move in chess in which a pawn that has just completed an initial advance to the 4th rank for Whites or the 5th rank for Blacks is captured by the opposing bypassed pawn as if it had only moved respectively to the 3rd rank or the 6th rank. 

Silly exchanges

I described as silly exchanges those exchanges that are not necessary because they are not done in order to have an advantage or prevent a disadvantage and can be avoided

JANUARY 27, 2007 - My game with Mr. Hawk:  testing a new opening, learned recently in reading a book either from a friend or at the Branes &Noble This text will be also in honour of my chessmate and my guess on this day whose name is Mr. Hawk.  He has studied mathematics, has earned a high degree in this matter and has teached maths for  a while   before having become a homeless man, very probably due to illness.  Mr. Hawk has written about a theory of forms, but this is nothing new.  Plato has also written a theory of form which was mostly metaphysical and inappropriate in scientific language. The well famed German physicist and mathematician Carl Friedrich Gauss, a pioneer in modern maths, the founder* of non-Euclidean geometry,  has also written about forms, after having himself also been "born and brought up in an austere childhood in a poor and uneducated family and having suffered from political turmoil and financial insecurity".  Briefly, I will say how I barely understood it: a mathematical form is a way of presenting the relations between variables or any mathematical structure or set; there are canonical form, quadratic form, logical form, etc.;  a theory of forms belongs to logical algebra and to groups' algebra. Here how Mr. Hawk described his interest in it:  " A theory of forms allows both a new view of mathematical theorem proving and points the way to understanding subtle facts already known." (What's Who in The Frontier of Science & Technology, 1981). 
        I do not know what depth Mr. Hawk has  reached in his theory of forms.  However, even Gauss has admitted that mathematical solutions are "often found after many fruitless investigations and with the aid of deep analysis and lucky combinations", i.e, both chance and hard work; Gauss always had also "more ideas than he had time to develop them ". I appreciate the efforts of Mr. Hawk and I will not discourage him, even if I may disagree with him, but he definitely knows more than me in maths.
        Mr. Hawk lost the chess game by checkmate after that I have isolated his king since the beginning and moved to win the game even with an inferior number of pieces.  The new opening, I never lost a game with a friend since I have adopted it, is to begin the domination of the center with the bishops instead of the knights.  The bishops can dominate from a farther distance withouth a precocious engagement in the battle of the center.
        This day, I met also an Afro-American lady who played extremely well, beating every man in the hall.  I will have to speak about that next time, but I did not play with her.*Gauss made also significant contributions to electricity (magnetic induction), algebra (quadratic equations), differential geometry, probability theory (the Gaussian or normal curve), and number theory. OCTOBER 2, 2006

It is time to define what is tactics and what is strategy in chess

It has now been more than a week since that I haven't played a chess game or access a chess board. However, I will keep up to my strategy for my next games. In the last two games I played, for example, I combined two strategies, one was the domination of the center that should begin early in the game, the other, also a simple one, was the advantage of the number that is linked to this domination. How can this be realized? But, first, let us define what are tactics and what is strategy. In the American Heritage Dictionary, strategy is defined as "the science and art of military command as applied to the overall planning and conduct of large-scale combat operations," and tactics is the "science that deals with securing objectives set by strategy." Strategy is overall planning, planning on a large scale and tactics are the parts of strategy.
   To begin my early domination of the center, I began, as I said it below, by moving my knights, my "cavalry" or my "aviation" to open my game; then, I moved my pawns, my "infantry", in order to have my knights protected and have a coordinated advance in the opened front with them (that are tactical moves) . With the domination of the center (strategy), I could move easily on either side (tactics) and attack my opponent with more pieces (strategy, the second one) while we have had well the same number on the board, at this time of the game, but I have had the advantage of the number on this part of the board. Sometimes, my opponent did not even finish its opening and some of his big pieces, his "artillery" or his "navy", did not take part in his attack or counterattack or even in the game. Most of the time, castling folllowed by a quick move of the pawn moving like a "rocket", in front of that rook, in order to have them early in the attack, allowed me to do that (tactics). If, in addition, my opponent has castled on the same side than me, my task was more easy, his king having been more vulnerable to my numerous pieces attacking him. It was only if he had survived my attack than he could have won and, for this, he had to count on my mistakes not on his strategy.
   In my last game, for example, my opponent has taken a numerous advantage on me by having attacked me at the opposite corner of my attack, having taken one my pawns and having menaced of taking more crucial pawns. I had to defend them but, at the same time, I kept the pressure on his king. In fact, his move was a mistake since he moved his queen away of his defense. Soon, his defense crumbled before my advancing pawn supported by my rook and he resigned.
   With strategy, I can afford me not to play many games while, at the same time, trying to elaborate more serious or complex strategies and invent new tactics. It is chess, a game of invention and the supreme game of the mind. SEPTEMBER 22, 2006 - A difficult and tasty victory My victory today was mostly du to a combined strategy, a first one that I have adopted to open the game and a second one to begin the middle of the game (after having ended the opening with me castling). My opening has been as what has now become usual for me moving, first, either knight; my second move is to move the other knight or, as in this case, a pawn in order to protect the first knight against an advancing and opposing pawn; this is to have an early control of the center. Having been careless, my opponent lost early and inexpectantly a pawn. After having castled, I brought out the pawn that stands before my king's rook of two cases, in order to give the later more space and to attack my opponent with more pieces, his having unfortunately castled on the king side. Akthough I played horribly the middle of the game, I was able to keep the control of the center, having avoided exchanging unduly pawns and thus blocking the distant challenge of the center by my opponent's pieces, his pawns having served as a shield for me. Finally, I was able to check mate the king of my opponent with my queen, a rook and a knight while having been myself under attack by his rook and his queen that were kept in check by two pawns protecting my king. However, before that, I have carefully avoided to exchange my queen for my opponent's one, since it would have given to him a clear advantage for the end of the game, with me losing immediately a crucial pawn.

SEPTEMBER 11, 2006 - Timing in chessThe time for playing chess in most international tournaments is as follows:

1. 40 moves for the first two hours20 moves for the next hour
2. Half an hour for the rest of the game

If one both players (or the other player) cannot complete their game and win by chess mate in the requested times, the game may be adjourned. If one player cannot complete the moves in this requested times, he lost by "sudden class="style1" death." When the game is adjourned, the player who has to move seals his next move in an envelope to keep it secret. The sealed move is then opened when the game resumes at a designated later time. Those are the international rules for classical and competitive over-the-board chess game, the game we play at the Chess and Checkers’ House in Central Park. The rules are different for internet chess games. The time is also different for speed chess.
SEPTEMBER 10, 2006A pinned piece What is pinned piece. In the American Heritage Dictionary, the word pin is defined as "A short, straight, stiff piece of wire with a blunt head and a sharp point, used especially for fastening." Therfore, a pinned piece is a piece that cannot move, having been like fastened in a defensive position to avoid the mate of the king, the removal of a major piece and/or the taking of a strategic position by the opponent. Two weeeks ago, I was watching a game played by a chess comrad, Durand, against a stronger opponent. A rook of Durand was pinned to his king in order to avod a mate. However, Durand, a player of intermediate strenght in the park, did not realize it and moved its other rook to face a menacing rook rook of his opponent. This was a strategic mistake as explained by Andy since the first rook of Durand was pinned to its king who has been menaced of being mated by the opponent's queen, roook and some other chess piece I did not remember. After having its first rook taken, Durand could not not move the second and pinned rook, since its king would have been in check by his opponent's queen. Whenever a piece is pinned, the rule is to let him been taken first, while, at the same time, protecting the strategic case by another piece that can replace it and fill the then empty case; this other piece should not menace any piece of the opponent in order to avoid it of been taken.JUNE 11, 2006 Wining in Chess is the general goal of the game. When I speak of Bayesian statistics, I mean strategy. If I move a piece, this should be for a specific goal such as mating the king in a specific position or after a number of moves or in a specific way or all together. To realize this goal, each move shall be linked to another move and this shall be such since the opening. The first time I met this opponent, at the Chess and Checkers' House in Central Park, he lost after having made a mistake at the end of the game. The second time we met in a three games encounter, my opponent won the first two games, but he lost the last game. Before this lost, he explained to me that by exchanging my King's bishop with his Queen's knight, early in the game, in order to have him doubled a pawn after my having castled on the King's side, I put me in a vulnerable position for his attacking pieces (a combination of a knight and a bishop), at the beginning of the middle of the game. However, I told him, before we begin the last game, that I will try to remove his pieces in their threatening positions, and I did. My reason was that I did not want to change my opening which has been developed and worked by me with the goal of putting in work the Bayesian statistics, i.e., the linked probabilities. To do so, I began to move the pieces cautiously in order to have them in support of each other. The strategic mistake my opponent might have done was having exchanged his attacking pieces with my defending ones, while he could not benefit of these exchanges, at this time of the game; he lost his bid. To make more comments on this game, I will say that it has been harsh with a lot of exchanges of pieces, early in the game, and, even, an offer of a bishop in sacrifice, in order to have a pawn promoted. The issue of the game did not become clear till we enter the end of the game.
   I began to move my king, boldly and early at the end of the game, in support of my advancing pawns. These were scattered through the board while my opponent's ones were occupying mostly the center. Both of us have one bishop left and they were opposing each other on the diagonals of the same color. My bishop was trying to protect my advancing pawns while my opponent's bishop was trying to impede them for doing so. My opponent pushed back the attack of my king with two pawns attacking and supporting each other and backed by his king. Suddenly he removed the support of his king for these pawns and stopped this attack to take care of one of my side pawn who was advancing. Then I offer my bishop in sacrifice to his in order to promote an advancing pawn on the opposite side of the board, but My opponent refused to take the bishop and moved back his bishop in a very retired and defensive position. Then, I move another pawn on the other side of my opponent's bishop and been protected also by my bishop. Now, seen that his bishop was overwhelmed by the task and that his king was out the battle, having been too far away of this scene held on the opposite side of the board, my opponent gave up. As a tactical mistake, I saw that my opponent was slow at moving his king in support of his pawns.

Finally, I shall thank opponent to have called to my attention that I have to take a better care of my opening. He has been and is such a nice guy.