Chess-Theory, New Chess Theory (NCT), 'New Chess Theory' Lecture, Chapter VII - 'Control and Domination I', chess: New Theory

NEW CHESS THEORY

NCT VII - CONTROL AND DOMINATION I

We use here the expression «Control and Domination» to signify the following simple idea: to arrive at the checkmate, ultimate goal of a chess game, it is appropriate to dominate his adversary. One can thus consider that the "domination" is, for a chessplayer, a good intermediate objective.
Now, we show here that the quality of the "control", exerted on the chessboard, is a decisive element to succeed in the domination. Remarks and considerations on this subject, constituting the present chapter, have been presented for the first time in 2002 («Courrier des échecs» 522, october 2002, p.289 to 294)

NCT VII-A - Surgery of
the Space Domination

1^o) What exactly means the "Domination"?

The term "domination" has, without any doubt, several meanings. First of all the domination expresses a clear advantage of a camp on the other. This one can take several forms. But, exactly as in the art of warfare, the domination mainly will be expressed by a space advantage.

It is advisable to understand that, like always in this lecture, we try to leave the field of the "qualitative", to arrive to those of the "quantitative", only way in view to progress in our investigation. Also, we are particularly interested by the notion of "space domination", even if we seek to estimate not only its extent, but also its quality!

And, from this point of view, it is precisely a meticulous examination of the control exerted by each camp which will lead us towards the good way.

2^o) Examination of the notion of "Control"

There is several manners of approaching the concept of control and we must thus, for methodological reasons, make a choice. It is rather clear that the total control exerted by a camp is resulting from the control exerted by each piece (pawns and figures) of this one. In this case we will speak about "Total control" or "Global control".

This concept is interesting and we will return there very soon. But we now will explore another way which we will call "Local control" and which relates to only one square.

3^o) Surgery of the "Domination" & "Control"

In fact it is by the study of the "local control", carried out square after square, on all the chessboard, which we will arrive to a true "surgery of the space domination". That will enable us to have a measuring instrument of the domination, and thus, as we wished, to lead to a quantitative formulation of this concept.

But, which is particularly pleasant in our method it is that it leads to a "geometrical representation", not only of the domination, but also of the localization of combats in progress. This representation will be a "cartography of the chessboard", rich of teaching and easy to illustrate, as we will do it, by concrete examples.

NCT VII-B - Various "states" of
squares of the chessboard

1^o) "Occupation" and "Control"

In a first time we consider a position P on the chessboard and a square noted x. In view to simplify, in this study we do not take into account the camp (White or Black) having to play. Then, the square x may be in one or more following "states":

i) x is occupied by a piece (pawn or figure).
ii) x is non occupied (empty square).
iii) x is controlled (by White or Black).
iv) x is controlled by no piece.

By convenience we use the following notations:

x is occupied: (o)

x is occupied by White: (oW)

x is occupied by Black: (oB)

x is occupied by no piece: (no)

And similarily we use the following notations:

x is controlled: (c)

x is controlled by White: (cW)

x is controlled by Black: (cB)

x is controlled by no piece: (nc)

2^o) What means exactly the "Control"?

In a position P, a piece X (pawn or figure) "controls" a square x if, supposed that a piece owning at the same camp occupies this latter, all being identical in addition, this piece would be protected by X. As an example, let us consider the well known beginning:

World Chess Championship Match:
Topalov - Kramnik - Game N^o 4
- Kramnik - Topalov, (D47) semi-slav, 1-0
(Elista, Kalmikia 2006 (RUS), decision match):

1.d4 d5 2.c4 c6 3.Nf3 Nf6 4.Nc3 e6 5.e3 Nbd7 6.Bd3 dxc4 7.Bxc4 b5 8.Be2 Bb7 9.0-0 Be7 10.e4 b4 11.e5 bxc3 12.exf6 Bxf6 13.bxc3 c5

This way, we reach the position

DIAG 1 :

In the DIAG 1 you are able to make some interesting observations related to the control of squares, in particular on the center. Hence, squares c6, d5, e4, f3 are controlled by the Black Bishop b7; squares d4 et e5 are simultaneously controlled by both camps; in particular the d4-square is controlled 3 times by White and 2 times by Black. Notice equally that some square like the e4-square are controlled per none of both sides.

NCT VII-C - Factor of
Control and Domination

1^o) Control of a piece (c)

Let us consider a position P on the chessboard and a particular square noted x. In view to simplify, in this study we do not take into account the camp (White or Black) having to play. The control of x by a side is the resultant of the potential control exerted on x by every piece of this side.

In this respect it is wise to clarify the following points:

If two or three heavy pieces of the same camp are in contact (i.e. without any other piece between them, of a camp or the other) on the same rank or the same file, noted L, and if one of them controls the x-square, equally situated on L, then all this pieces control the x-square.

If a Queen and a Bishop of the same camp are in contact (i.e. without any other piece between them, of a camp or the other) on the same diagonal, noted D, and if one of them controls the x-square, equally situated on D, then this two pieces control the x-square.

If a Queen or (and) a Bishop and a pawn of the same camp are in contact (i.e. without any other piece between them, of a camp or the other) on the same diagonal, noted D, and if this pawn controls the x-square, equally situated on D, then the Queen or (and) the Bishop controls (control) equally the x-square.

For example, in the DIAG 1, the White Queen in d1 and the White Bishop in e2 control the f3-square. Hence, the f3-square is controlled three times by White and, this way, the Knight f3 is protected three times.

2^o) Factor of Control (fc)

Let us consider a position P on the chessboard and a particular square noted x. Again we do not take into account the camp (White or Black) having to play. Then, relatively to the position P:

"Factor of Control" of White on x, noted:
fcW (x) is the sum of the number of White figures controlling the x-square and three times the number of White pawns controlling the x-square.

"Factor of Control" of Black on x, noted:
fcB (x) is the sum of the number of Black figures controlling the x-square and three times the number of Black pawns controlling the x-square.

You may judge this notion complicated and rather "artificial". But, by this choice we integrate the difference of value and role between figures and pawns.

Our schematisation will not always, admittedly, represent the exact reality, even more complicated, but will be always an excellent approximation, largely sufficient from our point of view.

3^o) White Domination (Wd) and Black Domination (Bd)

The concept of "local domination" in x result of the comparison bedtween "factor of control" of both camps (White & Black).

x is "Dominated" by White, noted:

Wd (x) means: fcW (x) > fcB (x)

x is "Dominated" by Black, noted:

Bd (x) means: fcW (x) < fcB (x)

4^o) "Contested" (cWB) and "Free" (f) squares

Concepts of "Contested" and "Free square" result equally from the study of the "factor of control" of both camps (White & Black).

x is "Contested" (by White & Black), noted:

cWB (x) means: fcW (x) = fcB (x) > 0

x is "Free" (not controlled), noted:

f (x) means: fcW (x) = fcB (x) = 0

NCT VII-D - Cartography
of the full Chessboard

1^o) Factor of Control and Partition

Let us consider a position P; again we do not take into account the camp (White or Black) having to play. By commodity we denote BOARD the full chessboard, constituted by all the 64 squares. Then we have to our disposal the two fonctions defined without ambiguity:

White "Factor of Control":

fcW : x in BOARD ---> fcW (x)

Black "Factor of Control":

fcB : x in BOARD ---> fcB (x)

By using this two functions we are able to clearly define a "Partition" (i.e. sharing) of the board in four zones.

2^o) Partition of the chessboard

Let us consider a position P; again this time we do not take into account the camp (White or Black) having to play. Relatively to P we define the following four zones W, B, R, Y of the chessboard constituting a partition of BOARD:

BOARD = W + B + R + Y

"White zone" (W):
   A "White square" is a square occupied or dominated by White, but not contested or dominated by Black; all the White squares of the board constitute the "White zone".
"Black zone" (B):
   A "Black square" is a square occupied or dominated by Black, but not contested or dominated by White; all the Black squares of the board constitute the "Black zone".
"Red zone" (R):
   A "Red square" is a contested square; all the Red squares of the board constitute the "Red zone" or "Contested zone".
"Yellow zone" (Y):
   A "Yellow square" is a free square not occupied; all the Yellow squares of the board constitute the "Yellow zone" or "Not occupied free zone".

3^o) Cartography of the chessboard

Relatively to a position P, we name Cartography of the board the concrete representation of the board where each square is strictly vilualized with its own color. Like this the cartography of the DIAG 1 is the following:

In this "Cartography of the DIAG 1" it is instructive to note some examples:

f3 is White: fcW(f3) = 5 > fcB(f3) = 0

d4 is White: fcW(d4) = 5 > fcB(d4) = 4

a6 is Red: fcW(a6) = 1 = fcB(a6) = 1

b6 is Black: fcW(b6) = 0 < fcB(b6) = 5

c5 is White: fcW(c5) = 3 > fcB(c5) = 1

d6 is Yellow: fcW(d6) = 0 = fcB(d6) = 0

NCT VII-E - Radiation
(Influence) and Domination

1^o) The "Radiation Rate"

Let us consider a position P; the "cartography of P" give a visual estimation of the domination or influence of each camp. But it is pleasant to have also a numerical estimation of this one. Such is the object of the rate of radiation. By convenience, let us lay down:

| W | = Number of White squares

| B | = Number of Black squares

| R | = Number of Red squares

| Y | = Number of Yellow squares

Then, the "White Radiation Rate", noted WRR , is the percentage (proportion by 100) between the number of White squares and the number of all squares occupied or controlled by one or the other of both camps, but not contested:

WRR = 100 W / (64 - R - Y) %
= 100 W / (W + B) %

In clear, WRR is a percentage equal to hundred times the number of White squares divided by the number of squares of the board occupied or dominated.

Similarily, the "Black Radiation Rate", noted BRR , is the percentage (proportion by 100) between the number of Black squares and the number of all squares occupied or dominated by one or the other of both camps, but not contested:

BRR = 100 B / (64 - R - Y) %
= 100 W / (W + B) %

In clear, BRR is a percentage equal to hundred times the number of Black squares divided by the number of squares of the board occupied or dominated.

2^o) Various forms of the space domination

In a given position P, there is domination of a camp if the RR (Radiation rate) of this camp is maintained rather durably on a raised level, for example higher or equal to 53 %. This domination can take one or simultaneously several of the following forms:

i) A general advance of the front.
ii) The occupation or the domination of the center.
iii) The penetration (of the adverse camp) on the Queenside or on the Kingside.
iv) The penetration (of the adverse camp) on the Center.
v) The penetration in the 7^th or 8^th rank for White (2^th or 1^th rank for Black).

NCT VII-F - Some
Illustrations and Commentaries

1^o) About the initial position

In the inital position, each camp occupies 16 squares (the 1^th rank and the 2^th rank for White ; the 7^th rank and the 8^th rank for Black). Moreover White dominates the 3^th rank and Black dominates the 6^th rank. Finally the Free zone is consisted of the two central rank (4^th and 5^th ranks).

The cartography of the initial position is thus the following one:

In this case we have the numerical values:

| W | = 24

| B | = 24

| Y | = 16

| R | = 0

Of this values we immediately deduce the "radiation coefficients":

WRR = 100 x 24 / (64 - 16) % = 50 %
BRR = 100 x 24 / (64 - 16) % = 50 %

2^o) Examples of "Factors of control"

Like concepts of "protection" and "control", putting here in obviousness, are complex, most clearly is their illustration by example. Always in the initial position, the square a3 is controlled by the Knight b1, the pawn b2 and the Bishop c1; hence:

fcW (a3) = fcW (h3) = 5

It is curious to note that all the other squares of the 3^th rank have the same factor of control, excepted f3 and g3. Precisely:

fcW (x3) = 7 for x = b, c, d, e, ; fcW (f3) = 8 ; fcW (g3) = 6

3^o) Influence of the first move 1.e4

Let us see the influence of 1.e4. If one considers the situation from the point of view of White, certain squares see their state modified as follows:

Dominated and not occupied: e2

Occupied and not controlled: e4

Controlled and not dominated: a6

Dominated: b5, c4, d5, f5, g4, h5

Contested: none

In this conditions we have the numerical values:

| W | = 31

| B | = 24

| Y | = 9

| R | = 0

Of this values we immediately deduce the "radiation rates":

WRR = 100 x 31 / (64 - 9) % = 56 %
BRR = 100 x 24 / (64 - 9) % = 44 %

4^o) Additional commentaries

The "Space domination", presented here, is a structural data. In other words it appears on the long term and, so it is relatively insensitive with the fact of knowing which of both players must play in first (except just at the beginning of a game).

The "Space domination" is effectively a significant aspect allowing to judge the quality of a position. But it is not the only criterion and we will utilize some others thereafter. It is indeed useful to specify that the domination space can prove to be insufficient and even misleading.

Thus one can affirm that the concept of "Dynamic spectrum", introduced in the chapter IX, will be a more relevant criterion of a real quality of a position.

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«NCT VIII - CONTROL AND DOMINATION II»

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