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Subject: The Basics of Chess Strategy rss

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Moshe Callen
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μῆνιν ἄειδε θεὰ Πηληϊάδεω Ἀχιλῆος/ οὐλομένην, ἣ μυρί᾽ Ἀχαιοῖς ἄλγε᾽ ἔθηκε,/...
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1. Introduction

The recent call for strategy articles made me realize that I have not really written any strategy articles. This fact got me to thinking, and I realized that the game which is most fundamental to strategic thinking to me is undoubtedly Chess. The principles of this game can with appropriate modification be applied literally to any game, but like any genuine principles they must be learned via practical application. Learning to play chess well is a long process. Like Go, the game does take a lifetime to master, but the game has some very basic principles which-- if one does not thoroughly learn and understand them-- no amount of memorizing openings will help. In a sense therefore this discussion is aimed at reasonably novice players, but this statement is true only insofar as more advanced players should know these principles already. Yet even an expert can gain a new perspective on the fundamentals, because I am presenting simply one way of thinking about these elements of the game. At least as many ways of looking at these principles exist as do players of the game.

My perspective on the game is fundamentally geometric, both in defense and offense. The reason for this is that by understanding the geometry of the game, one can better understand what in principle either side could do and so minimize the need to consciously think about what either player actually will do in future moves. Yet geometry needs to be supplemented by understanding relative pieces values, pawn structure and bearing in mind constantly that the object of the game is to check-mate the opponent. The key notions are control and momentum, although another way of thinking of control is as "good shape", to borrow the term from Shogi. Personally, I think the term control more easily understood, but good shape becomes a useful notion when the principles are understood and being applied.

2. The foundations of the geometrical point of view

Quote:
The now defunct site ChessUp.net was originally used in creation of diagrams. The diagrams are being replaced by links to this site on the rules of chess.


The board consists of an 8x8 grid of spaces without any obstructions except the pieces. Each piece moves in a simply geometric pattern, although the knight's move constitutes a topological handle.

The rook, bishop and queen move and capture in straight lines outward, respectively in orthogonal directions, diagonal directions or both.
how a rook in principle attacks
how a bishop in principle attacks
how a queen in principle attacks
One should imagine lines of force extending out from any given piece in all directions as far as that pieces can move, because except for the pawn all pieces capture as they move. For the pawns, the lines of force extend diagonally one space forward on either side. In the diagram below,
Quote:
Original diagram missing
the lines of force are marked by brown x's but the black ones show where a pawn can move-- not the same thing. (N.B.: In the new diagram arrows are used for all possible moves and the lines of force are the diagonal arrows.) One may think of the lines of force as extending over all spaces any given piece is in principle attacking in its next move. A line of force represents a possible attack in the next move by any given piece. That a square is empty currently does not negate the ability of a piece to attack for these purposes. The lines of force end when a piece is encountered, whether as protecting a friendly piece or in principle attacking an enemy piece.

The knight jumps from point to point in an L-shape either outside two spaces and then one space to either side or outward one space and then two spaces to either side.
how a knight attacks

In the geometric view, this constitutes a topological handle. The upshot is that the knight cannot be blocked, and its starting and ending points do not form a line either diagonally or horizontally/vertically. This aspect makes the knight a powerful piece in spite of its limited movement.

The king also exerts lines of force one space in any direction,

but this highlights the modification of lines of force by relative piece value.

3. The basic concept of control

As one may see, lines of force overlap one with another, not merely those from a given player's pieces with his other pieces but also those of his opponent similarly. In principle, at every point of the board, each player has multiple lines of force.(ignoring the kings for now). The player with more lines of force connected to a given space will typically control that space. I say typically because when comparing multiple lines of force, implicit remains the possibility of an exchange of pieces. If one cannot lose a piece (as in the case of the king) then no such exchange is possible and the piece or pieces one is unwilling to lose do not genuinely exert a line of force on the given space. In this way relative value of pieces enters the game.

If one considers the following situation,[IMAGE DEFUNCT] In principle, both black and white have three pieces attacking the space d6, but in reality black firmly controls the space.
Quote:
For those not familiar with the standard system, both rows and columns are counted from white's closest left-hand corner. Rows are numbered 1-8 and ranks (i.e., columns) are lettered a-h.
White is attacking space d6 with a rook, queen and knight but back is attacking the space with two pawns and a knight. A knight exchange would be equal, but all other exchanges would be unequal in black's favor. Admittedly, a sacrifice might be warranted for a sufficient tangible benefit such as directly leading to check-mate, but barring such considerations black controls the space. Whenever both players are attacking a space in equal numbers, the player who is more able to afford the exchange or exchanges implicit in taking the space controls that space.

One important thing to remember is that a piece never controls the space that it occupies. [IMAGE DEFUNCT] In the above example, control of space d6 is not strengthened for black by the presence of its pawn on that space. If anything, the control of that space is weakened because if white takes first, black will lose an additional pawn compared to the previous example. The pawn on d6 simply gives black control of c5 and e5.

Especially in the early and middle game, a player wants to control as much of the board as possible. Memorized openings do not negate the need to establish control of the board in the early game; they simply provide a solid base to work from. One must however also know when to depart from the textbook paradigm. That is the danger to new players of memorized openings; too often such players do not know when to do something different and instead merely play by rote.

4. Good shape

Borrowing this term from shogi, I tend to use the term good shape to mean a combination of maximizing control of the board and mutual support of pieces-- which is just another aspect of control as described above. At the start of the game,
each side controls the three rows nearest to the given player. The rooks protect (i.e., control the space of) the pawn in front of each and the knight. The knights protect the pawns in front of the king and queen, as well as attacking the space in front of the rook's and bishop's pawn. The bishop protects the knight's pawn as well as either the king's or queen's pawn. The queen protects the bishop, the three pawns in front of it directly and diagonally and to a lesser extent the king. The king protects the queen and its own bishop as well as the three pawns in front of it directly and diagonally. Each pawn controls the two spaces (apart from edge pawns) diagonally in front of it.

When developing pieces (i.e., moving them out to exert greater control) one wants defensively to keep pieces on spaces one controls, while offensively one wants to control as much of the board as possible. The more of the board one controls, the fewer viable options one's opponent has. By maintaining good shape, meaning simultaneously maximizing control of the board and especially of the space's one's own pieces occupy one largely will eliminate the need to plan moves ahead of time. In so doing, one is covering all the possibilities by the way.

Of course every move of the game changes control. One must always examine how a move-- whether one's own or one's opponent-- changes the control of the board. This means not only what a given piece attacks or does not attack, but also what other pieces may be opened up by the move.

5. Position

If one move clearly maximizes one's control or usually equivalently minimizes the opponent's control, that move will usually be the move one should make. Yet most often more than one move will have a comparable effect on control of the board. In some respects, choosing in such situations remains a judgment call, but even then some basic principles apply.

To borrow a diagram created for Othello, [IMAGE DEFUNCT] the board can be divided into a number of sections. The four center-most squares are the darker blue. The lighter blue spaces are also central spaces.
Quote:
I believe these spaces were those orthogonally adjacent to the four center squares.
The key concept here is the idea of the relative power of spaces on the board. One should imagine a queen on the various spaces of an empty board. The more of the board the queen would control from a given space, the more powerful in principle that space is. The center four squares of the board are most powerful. In the case of a queen, the piece controls 27 of the 64 spaces of the board from the central four squares. [IMAGE DEFUNCT] The same number of squares would be controlled from the four squares diagonally outward from the central four as well, [IMAGE DEFUNCT] but these spaces are in the early game especially either more vulnerable or blocked due to proximity of pawns, respectively one's opponent's or one's own. The central spaces on the third and sixth rows suffer the same problem. The remaining central squares are noticeably weaker than the four central squares. [IMAGE DEFUNCT] A queen on such a space controls only 25 of the 64 spaces of the board, compared to the 27 in the central four squares. The middle edges (marked in yellow) of the board are less powerful than the center of the board, [IMAGE DEFUNCT] but more powerful than the corners. [IMAGE DEFUNCT] The proper corners are by far weakest and so marked above as red. The white regions in the corners are next weakest. Within any region, the more central spaces are more powerful than those closer to the proper edge of the board. Thus for example [IMAGE DEFUNCT] a queen near the edge controls 23 spaces of the 64 but a queen on the edge properly as shown above controls only 21 out of 64 spaces. Clearly not all spaces on the board are created equal.

What this means is that if one has a choice between moving a piece to the center or to the edge or corner of the board, control of the board being equal after both moves, usually the move toward the center is to be preferred. Similarly the edge is preferred over the corner. Some players will even prefer the more central move even at a minimal sacrifice of control, but I would generally only recommend a sacrifice of either a piece or of control if a definite tangible object of making the sacrifice actually exists.

6. Sacrifices and exchanges

Yet not only are not all spaces on the board equal in power, not all pieces are as previously mentioned. One should not be afraid of losing a powerful piece so long as in doing so one makes a reasonable exchange. In some circumstances, sacrifice of a stronger piece will be compensated by sufficiently superior gain in control of the board to make the sacrifice worthwhile, but I would discourage beginners from making avoidable sacrifices. Even more experienced players are wise to do so only when the benefit is tangible such as either soon recovering the equality of pieces in play or a very strong gain in control. How much control one should gain to justify the sacrifice of a given piece is a bit of a judgment call.

My recommendation is that one only make a sacrifice (if possible) if one in so doing both maintains the momentum (discussed below) and makes a significant gain in control of the board. The most common scenario is when by making a sacrifice, one initiates a series of moves each of which places the opponent in check while keeping one's own king safe. Often in such circumstances when one can no longer continue checking (assuming one does not achieve mate) one can recoup the loss of the sacrifice if not doing so in the process of checking itself.

Checks are useful for forcing the opponent to make unwarranted sacrifices, but one should not necessarily grab a "free piece", meaning an enemy piece which is not protected. The opponent may be offering up the piece as bait in a form of sacrifice himself. A piece should only be taken at any point in the game if one both gains a material advantage after any resulting exchanges and gains or maintains control of the board, again after any resulting exchanges.

This axiom does not mean to discourage aggressive play, but rather one should not pointlessly play aggressively. (See the discussion below of momentum.) The trap to be avoided is rendering one's self vulnerable, i.e., undermining one's control of the board, by captures that leave one's own pieces open to capture later because of the opponent's gains in control.

A sacrifice is defined as the loss of a piece without immediately taking at least equivalent material from the opponent. To understand what this means, one needs to understand what the actual values of pieces are. Although the king is relatively weak, the piece is invaluable. If one loses the king, one loses the game. Next most valuable is the queen which combines the power of a rook and a bishop. This means that a queen is as valuable as a rook and a bishop, and vice-versa. The queen is not all-powerful, and one should not be afraid to lose the queen as long as the exchange is worthwhile. The rook is next most valuable because it can move across the board in a single move and can attack any space on the board. A bishop has properties similar to the rook, but the piece cannot move to any space of a different color because it moves diagonally. This makes it less valuable than a rook. Generally the knight is regarded as equivalent in power to a bishop, although some argue it is more powerful and some that it is less powerful. I find that the relative power of a bishop and knight depends on one's style of play, except that a knight is not confined to a single color of spaces on the board. In spite of its more limited movement, I am inclined to the opinion that the knight is more powerful than the bishop in most cases because a piece cannot make itself invulnerable to attack by a knight simply by moving to a space of another color. The pawns are the least valuable piece, albeit the rule of thumb is that three pawns are worth one bishop or knight. Also a pawn past the fourth row gains in value increasingly with each space toward the other end of the board because at that point in principle a pawn will be exchanged for either a queen or in rare cases a knight.

When considering whether or not to make an equal exchange, apart from the relative value of pieces and effects to control of the board, one should consider effect on momentum (again see below) and material on the board. If both players have equal material on the board, an exchange is justified by gaining or maintaining momentum or control of the board. If a player has a material advantage, exchanges are almost always in that player's favor. An unequal exchange is a sacrifice and should be justified as such.

7. Pawn-structure

Perhaps ironically pawns gain in power due to being the least powerful piece on the board. No exchange with a pawn is equal except with another pawn. One should note that an exchange of pawns may be unequal. If for example a pawn captures en passant but is then itself immediately captured, this exchange is not equal. As stated just above, a pawn past the middle of the board gains in value by its increasing probability of becoming a more powerful piece.

The term pawn structure refers to how well pawns mutually protect one another and how easily an opponent can get a piece behind the pawns to attack either them or more valuable pieces. A pawn vulnerable to attack from behind is said to be overextended. Precisely because a pawn is one's most expendable piece, pawn's generally will bear the brunt of attack. This does not mean that one should needlessly waste or endanger pawns, but chess is inherently a wargame in its essence however much it may have become abstracted in its current form.

Pawns will generally be in the front ranks of the combat in the early game, and even later in the game when one has developed one's pieces-- meaning essentially that the pieces have moved past one's pawns-- pawns will be the vanguard of defense. For this reason, pawn structure is key to the game. A well structured set of pawns will keep one's king from being put in check in the first place. Undermining an opponent's pawn structure is usually worth even a small sacrifice.

8. Momentum

I have referred a few times to momentum, a concept that describes who is making the moves which the other player is responding to. What this means is that a player on the offense has momentum generally, and a player on the defense does not. If one can keep one's opponent on the defensive long enough, one will almost certainly eventually win. Namely, to win, one must attack.

White as the first player begins the game with the momentum, although that momentum is not strong in the sense that white cannot attack on the first move. White does get to choose between playing an open or a closed game. Because of its power, one wants in the early game to seize and control the center of the board. Doing so will give one a decided advantage in control of the board. This is why one sees experienced players either advancing the king's pawn two space (the open game) or the queen's pawn two spaces (the closed game). Open and closed refers to whether the king is either opened up or closed in on its own rank. Opened and closed games do not differ in viability, meaning one's chances of winning, but it is well to note that more players are comfortable with the open game than the closed when choosing an opening.

Black needs therefore to gain the momentum. Here is where aggressiveness comes into play. When playing chess, one is first and foremost playing one's opponent. In that respect one needs one gauge an opponent's reaction, just like playing Poker. The most common way to gain momentum is to attack one's opponent, but one needs to make a stronger attack than the opponent is making. The idea is to make an attack one's opponent cannot ignore.

Sometimes though one will not want to make one's attack obvious. Revealed attacks, namely an attack opened up by moving another piece, can be powerful especially if one manages to get the opponent overly focused on what the piece moved is doing. Just because a player moves a given piece does not mean that the piece moved is the piece primarily attacking. Always examine the board thoroughly. Yet at the same time, one should maintain the proverbial poker-face and look like one knows what one is doing even if one has no clue. Unless one is playing a computer, intimidation often works, even if subconsciously. By the same token, one should keep one's eyes away from any spots on the board which offer one opportunities lest the opponent be alerted to those opportunities, but one can always give false hints. Momentum is in the mind as much as on the board. Yes, a player making a stronger attack than the other player has momentum in principle, but a player who intimidates his opponent so that the opponent plays defensively effectively has the momentum-- even if not actually. In such cases, effective momentum will usually shortly becomes actual momentum.

9. Strong and weak checks

All this must be borne in mind in the context that above all else the object of the game is to check-mate one's opponent's king. One's own king should be amidst one's most well controlled part of the board at all times. Novice players therefore often think they should check whenever possible, but that is decidedly not the case.

A check, i.e., a move that attacks an opponent's king, is considered strong if it leads to check-mate, another check while forcing the king into a more exposed (i.e., less protected) position or a forced sacrifice by the opponent. Other checks are called weak and should be avoided because they will most often just allow the opponent to strengthen his position while exposing the attacking piece to risk of capture. Not all strong checks will lead to check-mate or even a material sacrifice, but they must at least reduce an opponent's control of the board or the check or checks are not strong.

At the same time, whether or not a check is strong may not always be obvious. The general rule therefore is to check if in doubt so long as one can follow-up with more checks. If one can maintain a series of checks long enough, one will most often check-mate one's opponent. In such cases, a sacrifice of control of the board is often warranted if one can use it to keep checking the king without pause. If one pauses, the opponent will almost always strike back with a check if at all possible, if only out of desperation. Yet even desperate attacks can succeed. Controlling all the board except the area about one's king will almost certainly lose one the game. Of course, one wants to get one's opponent into precisely such a position for exactly this reason.

10. Conclusions

The best teacher of this game is experience. If one wants to play well, one needs to play. Doing so will give one needed experience in making judgment calls. Nevertheless bearing these principles in mind will help one play better both in the absence of experience and in making best use of one's experience. Until and unless one masters these basics, I would not recommend memorizing openings as many beginning players wishing to become good players do. That is not to say that memorizing openings is a bad thing. Decidedly it is not. Anecdotally, I have beaten players who taught chess for a living, but most often players who both know these basics and know standard openings (which I do not) will beat me. The point is to learn things in proper order. These principles really are the basics, and as such one needs to learn them first to use standard openings and to consciously use experience to full advantage.
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Sven Teuber
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Thank you for this comprehensible, interesting guide. Well done!
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Warren Davis
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I've been playing Chess since I was three (I'm uncomfortably close to forty), so I can appreciate this review. Alas, if only I could've played more and better players in my life maybe my game would be better and I would beat my computer more often (the rare times I play it).

Great job!
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Peter Mumford
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I've found that theoretical discussion of chess is not nearly as helpful for improving my game as studying chess tactics, or chess problems. A great beginning book of chess problems is Winning Chess Tactics for Juniors. This book is not so simple actually.. many of the problems are still stumpers to me. But even having to look up the solution to a problem is very instructive. Then I make the problem with an X. The next time I am at that problem I see if I can remember the solution.
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It also should be noted that the following squares are the weakest at game start:

c2, f2, c7, and f7.

Nearly all successful attacks in chess are coordinated on a color complex, meaning that you "attack from/the black or white squares". After all, it makes sense: If you are lacking a dark-squared bishop, your dark squares are inherently weaker assuming you still have the light-squared bishop, and you have less forces with which to attack/defnd with on the dark squares, and visa versa.

Another thing that is paramount to successful chess is the study of minor piece imbalances. This means learning how to play for/against positions where the minor pieces are such:

2N vs 2B
1N, 1B vs 2B
1N, 1B vs 2N

Once you achieve a certain level of respect, this knowledge will take you just a bit further and will dictate your previously agonzing decisions of whether to trade a Bishop for a Knight, visa versa, etc.

Chess is cool.cool
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Daniel
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Great write-up. Makes me want to play right now!
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Moshe Callen
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ἄνδρα μοι ἔννεπε, μοῦσα, πολύτροπον, ὃς μάλα πολλὰ/ πλάγχθη, ἐπεὶ Τροίης ἱερὸν πτολίεθρον ἔπερσεν./...
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μῆνιν ἄειδε θεὰ Πηληϊάδεω Ἀχιλῆος/ οὐλομένην, ἣ μυρί᾽ Ἀχαιοῖς ἄλγε᾽ ἔθηκε,/...
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dandechino wrote:
Makes me want to play right now!

Good! Do it.
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Moshe Callen
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ἄνδρα μοι ἔννεπε, μοῦσα, πολύτροπον, ὃς μάλα πολλὰ/ πλάγχθη, ἐπεὶ Τροίης ἱερὸν πτολίεθρον ἔπερσεν./...
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μῆνιν ἄειδε θεὰ Πηληϊάδεω Ἀχιλῆος/ οὐλομένην, ἣ μυρί᾽ Ἀχαιοῖς ἄλγε᾽ ἔθηκε,/...
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Revisited my old article and all the diagrams are gone. I've restored those I easily could but many are still missing.
 
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Trevor James
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[The point is to learn things in proper order.]
If you already know the moves the best published course of training is Yusupov's 9 book course divided into 3 sections: Build your chess, Boost your chess and chess evolution. The 3 sections will take you through from beginner to advanced player in accessible stages.
 
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