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     MODERN CHESS THEORY     

Updated: Feb 2009  

MCT II - VALUE OF PIECES
(by Michel Bruneau CTW)

We may be fair towards Steinitz and Tarrasch by recognizing that they had a rather exact vision of the value of chess pieces. In this particular field more recent contributions certainly did not revolutionize the subject. Nevertheless, this singular question about the value of chess pieces deserves to be going into detail, because it reveals many imbricated facets of the Chess game. It is for this reason that we choose to treat first this motif.

The first reason for which it is useful to compare chess pieces and to attribute a specific value to each of them is to estimate, in a game, after some exchanges, if the «material» balance is preserved or not. This question is at the basis of the judgment that we may express about a position. And then, all the problematic is that if you wish to judge if a position is equal or if a camp (White or Black) has the advantage, you need to take into account not the "theoretical" value of each piece, but its "real" value, according to the position. Here is the true difficulty!


       Modern Chess Theory - MCT II - Menu       

   - MCT II-A - Theoretical value of chess pieces
   - MCT II-B - Chess pieces value and Materiality
   - MCT II-C - Material sacrifices and compensations
   - MCT II-D - Comparative value of chess pieces
   - MCT II-E - Good and Bad Bishops and Knights
   - MCT II-F - Confrontation between figures and pawns
   - MCT II-G - «Dynamical value» (DV) of Chess pieces
   - Game N°125: Carlsen, M - Dominguez, L [D81] 1-0
   - Game N°011: Bachmann - Fiechtl [C67] 1-0
   - Game N°109: Anand, V - Aronian, L [C89] 0-1
   - Game N°059: Kluger, G - Tal, M [A43] 1-0
   - Game: Kasparov, G -Timman, Jan H [E13] ½-½


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   MCT II-A - Theoretical value of chess pieces   


It is usual to confer on each chess piece a value estimated by a number of pawns. In other words, you consider a pawn as the unit of value, awarding to it the value 1.

1o) The theoretical value of chess pieces

The «Theoretical value of chess pieces» (also called: "chess piece relative value system" or "standard valuation of chess pieces") is given by the following table:

     PIECE           VALUE     
Pawn 1
Knight 3
Bishop 3
Rook 5
Queen 9


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   MCT II-B - Chess piece value and Materiality   


The main interest of the "Standard valuation of chess pieces" is to allow to estimate the Material value of both White and Black armies. Materiality, of course, is insufficient to give an accurate overview of a Chess position; nevertheless, it is an useful first step in view to valuate all given position.

1o) Material valuation of original chess position

At the beginning of a chess game each camp owns: 8 pawns, 2 Rooks, 2 Bishops, 2 Knights, a Queen and a Kings. If we do not take into account the King, we find, according to the theoretical valuation of chess pieces:

8 + 10 + 6 + 6 + 9 = 39

Now, let us designate King value by the letter k. It is usual to consider that k is infinite or is a very great number arbitrarily chosen. We will discuss about this question later in this lecture. Anyway, the «Material value» of each army is, at the beggining of the game:

8 + 10 + 6 + 6 + 9 + k = 39 + k

Let us designate by W the material value of the White army and by B the one of the Black army. Then, in the original position:

(1)      W = 39 + k    ,    B = 39 + k

2o) Evolution of the material chess value

In the unfolding of a Chess game, the «Material value» of each camp (W for White and B for Black) is subject to evolution. Let us consider, as an example, the recent game: Carlsen, Magnus (2776) - Dominguez Perez, Lenier (2717) [D81] 1-0, Corus A 2009 Wijk aan Zee NED (10) (Game N°125 in the Chess-Theory Analysed Game Collection):

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  «Carlsen, Magnus (2776) - Dominguez Perez, Leinier (2717)
1-0 [D81], Corus Chess Tournament (NED) (10), 2009»

After the first moves:

1.d4 Nf6 2.c4 g6 3.Nc3 d5 4.Qb3

we reach the position:


DIAG 1: Game N°125: 4.Qb3 :


W and B are always given by (1) (i.e. Material values are unchanged). But after the first exchange:

4... dxc4 5.Qxc4

the new material values are:

(2)      W = 38 + k    ,    B = 38 + k

This time many moves are played without any exchanges and, until 13.Nf3, Material values are always given by (2):

5... Bg7 6.e4 0-0 7.Be2 Nfd7!? 8.Be3 Nb6 9.Qd3! f5 10.Rd1 f4 11.Bc1 e5!? 12.d5! c6! 13.Nf3 cxd5 14.Nxd5 Nxd5 15.Qb3!N

after Magnus' novelty, the new material values are:

(3)      W = 34 + k    ,    B = 37 + k


DIAG 2: Game N°125: 15.Qb3!N :


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   MCT II-C - Material sacrifices and compensations   


In the DIAG 2 Black has a material advantage, with a Knight extra. But, the d5-Knight is pinned and its "Real" value is 0 and not 3! In other words White has a strict compensation for the Knight lost and we may speak of a "Dynamical compensation". Notice that in the present case the d5-Knight may be win back by White easily; it is only a pseudo-sacrifice. But very often, when a camp sacrifies one or several pieces, he obtains some interesting positional compensations, which deserve to be analyzed.

1o) Material and Dynamical chess value

In view to clarify our argument we use the expression of «Dynamical value of a chess piece» for naming the value of this one in a concrete position. Material value (i.e. Standard or Theoretical value) will be noted MV and Dynamical value DV; of course, it will be possible to attribute an accurate value to DV only in some particular cases.

2o) Study of a short game with trap!

We are studying here the short game with Queen sacrifice: Bachmann - Fiechtl [C67] 1-0, Regensburg (Germany), 1887 (Game N°011 in the Chess-Theory Analysed Game Collection):

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  «Bachmann - Fiechtl [C67] 1-0, Regensburg (Germany), 1887»

This game is a Ruy Lopez beging like this:

1.e4 e5 2.Nf3 Nc6 3.Bb5 Nf6 4.0-0 Nxe4 5.Re1 Nd6 6.Nxe5 Nxe5?! 7.Rxe5+ Be7 8.Nc3

We reach the position:


DIAG 3: Game N°011: 8.Nc3 :


After the exchange of a pawn and a minor piece, material value of both camps W and B are equal and given by:

(3)      W = 35 + k    ,    B = 35 + k

The game continues by:

8... Nxb5 9.Nd5

and then White has a material deficit compensated by an attack against the opponent's King:

(4)      W = 32 + k    ,    B = 35 + k

The game proceeds as follows:

9... d6 10.Rxe7+ Kf8 11.Qf3?! f6??

and we reach the following position:


DIAG 4: Game N°011: 11... f6?? :


Then are played the moves:

12.d3!? c6?? 13.Qxf6+!! gxf6

leading to the position:


DIAG 5: Game N°011: 13... gxf6 :


After the Bachmann's Queen Sacrifice, Black owns a significant material advantage:

(4)      W = 23 + k    ,    B = 31 + k

but is mate in two moves:

14.Bh6+ Kg8 15.Nxf6#

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   MCT II-D - Comparative value of chess pieces   


According to the practice of Chess Masters since many centuries, experimental rules of comparison have been established:

  • 1) The Queen is not as strong as two Rooks.
  • 2) The Queen is not as strong as three Minor pieces.
  • 3) A Rook has the same value that a Minor piece and two pawns.
  • 4) A Bishop and a Knight have the same value.
  • 5) The pair of Bishops is stronger than two Knights.
  • 6) A Minor piece is a bit stronger than three pawns.
    •

    This rules are useful in a first time but must be considered simply as landmarks and starting points of a close reflection. But it is recommended to "relativise" them at the maximum in front of all concrete situation. We invite you to have a look to paragraphs B & C of the Chapter IV, in the Classical Chess Theory Lecture, where this question is studied with the help of many examples.

       «Classical Chess Theory - CCT IV - Value of pieces»


    1o) The Queen against two Rooks

    We will study the evolution of «Dynamic value of chess pieces» in a further paragraph. But it is useful to specify right now that at the beginning of a Chess game, during practically all the Opening and a good part of the middle game, a Queen is clearly stronger than both Rooks of the adversary because her mobility. But in the endgame it is true that two Rooks may be stronger than a Queen if they are on the same line (rank or file) and defending each other. The main reason is that two Rooks in battery may attack or defend a piece twice times, and the Queen only one time. Nevertheless in the ending, with white to play:


    DIAG 6: Queen vs Two Rooks: :


    the force of both Rooks is compensated by the mobility of the Queen and the game is probably a draw.

    2o) The Queen against three Minor pieces

    Again this comparaison is not of great interest in the Opening and is difficult to justify, in all generality, in the Middle game. During the Endgame, it is usually admit that three Minor pieces are stronger that a Queen, in particular if they are well coordinated and protecting each other. The following diagram give an example:


    DIAG 7: Queen vs three Minor pieces: :


    Of course Black has a significant advantage, but the ending might be difficult to conduct until the win.

    3o) A Rook against a Minor Piece and two pawns

    In the confrontation between a Rook and a Minor piece with one or two extra pawns it is not easy to state a general rule and all is function of the position. A clear example is given by the game: Anand, Vishy (2799) - Aronian, Levon (2739) [C89] 0-1, Morelia/Linares XXV SuperGM MEX/ESP (2), 2008 (Game N°109 in the Chess-Theory Analysed Game Collection).

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       «Anand Vishy (2799) - Aronian, Levon (2739) [C89]   
    0-1, Morelia/Linares XXV SuperGM MEX/ESP (2), 2008»

    In this game, after the exchange:

    31.fxe3 Qxf3

    we get the position:


    DIAG 8: Game N°109: 13... Qxf3 :


    where White owns a Rook and two pawns vs a Black Bishop, what represents a material advantage of 4 (pawns), in spite of which Black wins easily: White is mate in five moves!

    4o) The Bishop against the Knight

    It is classic to confront Bishops and Knights. This two kind of pieces have the same "Material value" but they are so different that all comparison is questionable. Nevertheless it is interesting to indicate that J.R. Capablanca expresses in his writings, at this subject, some sharp judgments:

  • 1) The Bishop is very often superior to the Knight.
  • 2) The Bishop is more efficient than the Knight in view to struggle against pawns.
  • 3) Associated with pawns, the Bishop is stronger than the Knight against a Rook.
  • 4) Rook and Bishop are stronger than Rook and Knight.
  • 5) It happens that Queen and Knight are stronger than Queen and Bishop.
  • 6) Two Bishops and a Knight are stronger than two Knights and a Bishop.
  • 7) Two Knights and a Bishop are stronger than two Rooks.
    •

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       MCT II-E - Good and Bad Bishops and Knights   


    Before a more accurate study of the DV (Dynamical value) of a Chess piece, we wish study and discuss the connected notion of «Good» and «Bad» pieces. This concept is classically put into practice about the Bishop. But it may be interesting to extend it to other pieces (chessmen and pawns).

    1o) Classical concept of "Good" and "Bad" Bishops

    A Bishop is referred to as "Good" if friendly pawns are mainly on squares of the color where the Bishop cannot move to (i.e. on dark squares for a light square Bishop and reciprocally). At the contrary, a Bishop which is impeded by friendly pawns is said to be "Bad".

    As the pawn skeleton is relatively stable, this characteristic perpetuates a long time during the game, usually from the middle game to the ending. Nevertheless this notion must be relativized for many reasons:

  • 1) It is extremely rare that the integrality of pawns of a side are on squares of the same color.
  • 2) The pawn structure change progressively during a chess game.
  • 3) Independently of pawns, a Bishop may be durably hampered by friendly figures as Knights, Rooks and the King.
  • 4) If a "Bad" Bishop controle one or two Open diagonals it is "relatively Good".
    •


    DIAG 9: Relatively Good Bishop :


    2o) New concept of "Good" Chess pieces

    Without deny the legitimacy of the classical concept, it is well advised to introduce a more flexible notion. We say that a Chess piece is «Good» if it is active and able to take part in the struggle. Conditions required are adapted at the specificity of each piece:

  • 1) A Bishop is "Good" if it has one or two Open diagonals, where it is able to attack opponent's pieces or pawns. The power of a Bishop is increased if it is in battery with the friendly Queen.
  • 2) A Knight is "Good" if it is entered into the enemy territory (or is on the verge of it) and is able to coordinate its action with those of friendly pieces. The best case is when the Knight occupies a Hole (Strong square) in the 5th or 6th rank (possibly the 4th rank).
  • 3) A Rook is "Good" if it is posted on an Open file and is able to penetrate into the 7th or 8th ranks. A Rook reaches a maximal efficiency if it is in battery with the other Rook and the Queen. The action of the Rook on the Rank where it is posted is another favourable aspect. It must be added that a particularly valuable action for a Rook is to support the advance of a passed pawn.
  • 4) A Queen is "Good" if she is developped and active. Her role is to take part in the battle and to coordinate this one. She may equally play a significant role by increasing the Rook(s) pressure on an Open file.
    •

    A chess piece is referred to as "Bad" in the opposing case.

    3o) A typical example about "Good" & "Bad" pieces

    We are now interested by the game Kluger, Gyula - Tal, Mihail [A43] 1-0, Kislovodsk, 1964 (Game N°059 in the Chess-Theory Analysed Game Collection)

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       «Kluger, Gyula - Tal, Mihail   
    [A43] 1-0, Kislovodsk, 1964»

    After 34... Rd7 + - we observe that White piece are well coordinated and actives, while Black's troups are disorganised and rather in a defensive posture. In particular Black has "Bad" Minor pieces!


    DIAG 10: Game N°059: 34... Rd7 :


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       MCT II-F - Confrontation between figures and pawns   


    The comparison between Pieces and pawns is another exciting reflection theme. It is usually considered that a Bishop has a DV (Dynamical value) a few upper than three pawns, but J.R. Capablanca affirms that a Knight may be inferior to 3 pawns. Again, we think that all uniform rule on such a subject is doubtful and that the only rigorous approach is to consider a concrete position! Also we invite you to have a regard to the game:

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    Garry Kasparov (2700) - Jan H Timman (2640) ½-½ [E13] Nimzo-Indian Hybrid, Hilversum KRO (4) 19.12.1985 ("Garry Kasparov's Greatest Chess Games" Vol. 1 by Igor Stohl)

    1.d4 Nf6 2.c4 e6 3.Nf3 b6 4.Nc3 Bb4 5.Bg5 Bb7 6.e3 h6 7.Bh4 g5 8.Bg3 Ne4 9.Qc2 Bxc3+ 10.bxc3 d6 11.Bd3 f5?! 12.d5! Nc5 13.h4 g4! 14.Nd4 Qf6 15.0-0

    We get the position:


    DIAG 11: Game Kasparov-Timman: 15.0-0 :


    Igor Stohl remarks that is out of the question: 15.dxe6? Bxg2 16.Rg1 Be4 -/+ and risky: 15.Nxe6?! Nxe6 16.dxe6 Bxg2 17.Rg1 Bf3 =/+

    15... Nba6 16.Nxe6 Nxe6 17.Bxf5 Ng7 18.Bg6+ Kd7 19.f3 Raf8 20.fxg4 Qe7 21.e4

    In the present position White owns a Bishop and three pawns against two Knights for Black. The game is quite balanced, but it is interesting to observe what concretely happens in this event.


    DIAG 12: Game Kasparov-Timman: 21.e4 :


    21... Rc8 22.Qd2 Kb8 23.Rxf8+?! Rxf8 24.Qxh6 Bc8 25.Re1?!

    According to Igor Stohl is stronger: 25.g5 Nc6 26.Rf1

    25... Bxg4 26.c5 Qf6 27.cxd6 Bh5 28.e5


    DIAG 13: Game Kasparov-Timman: 28.e5 :


    Igor Stohl judge as a sharp idea: 28.d7! Qxg6 29.Qxg6 Bxg6 30.Be5 +/=

    28... Qxg6 29.Qxg6 Bxg6 30.e6 Nc5! 31.d7


    DIAG 14: Game Kasparov-Timman: 31.d7 :


    31... Nxd7! 32.exd7 Rd8 33.Re6!

    And not: 33.Re7? Nf5 34.Re6 Nxg3 -/+


    DIAG 15: Game Kasparov-Timman: 33.Re6! :


    Presumably the acceptance to the Quality sacrifice leads to the draw: 33... Nxe6!? 34.dxe6 Be8 (forced) 35.h5 Bxd7 (the best) 36.Bh4! Bxe6 37.Bxd8 Bxa2 +/=

    33... Bh5 34.Be5 Rxd7 35.Rh6 Bf7?! 36.Bxg7 Bxd5 37.Be5 Bxa2 +/=


    DIAG 16: Game Kasparov-Timman: 37... Bxa2 :


    After these echanges both camps have identical material. Nevertheless the game is still very rich and complicated. The draw was concluded at the 62th move.

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       MCT II-G - The «Dynamical value» (DV) of Chess pieces   


    If you understand how is constructed the «Four Lever Chess Lecture», you will not be surprised by a kind of conceptual unity in its development, in spite of the integration of main parts of the historical Chess heritage, with for consequence the overlapping of some ideas. Anyway, it does not matter if you find, from time to time, a flashback, a repeating, a digression or an anticipation. We believe that such interweavings reflect adequately a living thought and are favourable to the progression of the reasoning until ultimate conclusions.

    The DV notion that we try to specify here is possibly one of the many footbridges between MCT and further (experimental) NCT. Well!

    1o) «Dynamical value» (DV) of Chess pieces

    The «Dynamical value» (DV) of a Chess piece named P represent the actual value of P, during the unfolding of a Chess game, in a given position; in other words after a given number of moves. In clear after n moves and White to play the DV of P may be noted: DV[P,n] and after n noves and Black to play the DV of P may be noted: DV[P,n½].

    At the beginning of a game the DV of all figures excepted the Knight is null (DV = 0), because they are unable to play. At the contrary, a Knight or a pawn own a not null DV, but this one is weak because they threaten nothing in one move. In the Opening, the true objective of each side is to increase, as quickly and effectively as possible, the DV of each piece. As Chess is an experimental field, we carry forward a more accurate study of this question and examine right now the evolution of both Timman's Black Knights in the game Kasparov - Timman studied above.

    2o) DV of both Timman's Black Knights

    In the game: Garry Kasparov (2700) - Jan H Timman (2640) ½-½ [E13] Nimzo-Indian Hybrid, Hilversum KRO (4) 19.12.1985 ("Garry Kasparov's Greatest Chess Games" Vol. 1 by Igor Stohl), during the 15 first moves the b8-Knight remains at home, while the g8-Knight is rather active:

    1... Nf6,   8... Ne4,   12... Nc5    (see: DIAG 11)

    We may also compare the path of both Timman's Knights:

    g8 - f6 - e4 - c5 - e6 - g7   (17... Ng7)
    b8 - a6 - c5 - d7   (17... Nxd7!)

    Both Timman's Knights have occupied the c5-square, which is a Strong square (a Hole) for Black. This is the best square that each one has occupied during its travel and where its DV has reached the highest value.

    ***

    MODERN CHESS THEORY :

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