CAPÍTULO 2. GENERACIÓN DE FORMAS
7. TURBULENCIA
7.2. Modelización de la turbulencia
7.2.1. Modelos RANS
What chess book would be complete without the age-old comparison of the two minor pieces? There is not really anything I can say that has not already been said before. Which of the two is the better depends on the position, although in general it is fair to say that bishops are held in higher esteem in the endgame.
Weaker players tend to favour knights, not so much because they can jump but because they can oper
ate on both light and dark squares.
Of course this is a valuable asset, but as the king is always around to per
form the same function, perhaps the long-range power of the bishop is a more important factor.
With special reference to ' flat' po
sitions with pawns on both sides, it has long been thought that the bishop is superior. The following old game is one such example of the bishop's power on a relatively open board.
Even with Black to play, many players would assume that a draw should be the fair result. Watch and learn !
1 . . . �g8-f8
As usual the first step for both sides is to centralise the king. It
B
Stoltz -Kashdan The Hague 1928
should be observed even at this stage that although the white knight occu
pies a nice central square, its possi
ble entry points are covered by the bishop.
2 �gt-n 3 �fl-e2 4 �e2-d3
'iitf8-e7 rj;e7-d6
�d6-d5 The black king has been able to go one rank further in the centre, but as the white pawns can advance to dark squares, it will eventually be re
quired elsewhere to attack them.
Black's next aim is to force the white king to give way, and another of the bishop's attributes - its ability to gain (or lose) a tempo - will con
tribute to this phase. The fact that the knight cannot 'pass ' prompts White
104 All the King 's Men
into having to bide time with pawn moves.
5 h3-h4 i.d7-c8 Black's intention is to make the white king commit itself so that his own king can invade in the opposite direction. If both players then create passed pawns the bishop is capable of both aiding his own pawns while keeping an eye on the opponent's.
The knight, on the other hand, takes longer to get from one side of the board to the other.
6 tbd4-f3 7 'it>d3-c3
i.c8-a6+
h7-h6 White seems to have decided to put his king on the queenside, so Black will now focus his attention on a kingside invasion. First he must keep the knight at bay.
8 tbf3-d4 g7-g6 9 tbd4-c2 �d5-e4 10 tbc2-e3
White attempts to erect a barrier.
Black's pawns are on hand to facili
tate the decisive breakthrough.
10 t7-f5
11 ""c3-d2 f5-f4 12 tbe3-g4 h6-h5 13 tbg4-f6+ 'it>e4-f5 Black is happy to retreat his king from the centre because he has his eye on the h4-pawn. White now re
lies on his knight to provide a counter-attack on Black's g-pawn, as g2-g3 merely creates another weak
ness which cannot be defended.
14 tbf6-d7 i.a6-c8 Forcing the knight to make a deci
sion.
15 tbd7-f8
An unattractive choice which aims to distract Black's king. After 1 6 tbd7-c5 'iPf5-g4 1 7 tbc5-d3, in
stead of the immediate 1 7 .. . �g4xh4 (allowing 1 8 tbd3xf4) Black has 1 7 ... i.c8-f5 .
15 • . . g6-g5
Although this allows White to trade off the pawn that he feared los
ing for nothing, Black now has big
ger fish to fry. 16 h4xg5 'iPf5xg5 will result in the black king going back to attack the trapped knight.
16 g2-g3 g5xh4 17 g3xh4 'iPf5-g4 (D)
18 tbf8-g6 .i.c8-f5 19 tbg6-e7 i.f5-e6 Now the b3-pawn is under attack.
Also possible is 1 9 .. . i.f5-e4. In or
der to demonstrate the major princi
ple in question, here is an illustrative sample variation: ( 1 9 .. . i.f5-e4) 20 tbe7-c8 �g4xh4 2 1 tbc8xa7 r.Ph4-h3 followed by 22 .. . �r.Ph4-h3-g2, when there is no stopping the h-pawn (the bishop has the b-pawn under control).
20 b3-b4
Efficient. Now 25 lbc6-e5+ meets with 25 . . . �g4-f4. And Black soon won.
It is in blocked positions that knights are better than bishops. In such endgames the knight demon
strates its superiority with an ability to manoeuvre to all the good squares.
A lot depends on just how obstructed by pawns the bishop is. Below is an example of 'good' knight vs ' bad' bishop.
w
Averbakh - Panov Moscow 1950
White has a dream position. His knight is exceptionally well placed, combining with the kingside pawns
All the King 's Men 105
to produce an impenetrable barrier.
Consequently the black king is un
able to j oin in the game (the same is not true of White's king, which is ready to infiltrate the opponent's po
sition). Black has a supported passed pawn on e5, but like the other centre pawns it is on the same colour square as the bishop. Therefore the terms ' good' knight and 'bad' bishop -White has an attacking minor piece and Black a passive one. Note that the bishop cannot attack the white pawns.
1 g4-g5
Making way for a king invasion on f5 . Black is powerless to prevent this.
1 �g8-g7
2 �f2-f3 �g7-r7 3 �f3-g4 i.f8-e7 4 �g4-f5 i.e7 -f8 The bishop must continue to pro
tect the d6-pawn, and Black is deter
mined to keep the enemy king out of the e6-square.
5 lbe4-f6 h7-h6 6 g5xh6
6 g5-g6+ looks attractive, but White is aware that he must win an enemy pawn eventually. He knows that he will never be able to capture the d6-pawn while it is protected by the bishop because this leaves the e
pawn free to make a sprint for pro
motion. With this in mind he needs to create a distraction.
6 i.f8xh6
7 lDf6-e4 i.h6-f8 8 h5-h6 i.f8xh6
106 All the King 's Men
Black must capture this pawn sooner or later, e.g. 8 . . . 'it>f7-g8 9 'iPf5-f6 <Ji>g 8-h7 IO r.Pf6-f7 i.f8xh6 1 1 �e4xd6.
9 �e4xd6+ <j;f7-e7 10 �d6-e4
The knight wisely returns to its dominant post. Instead IO �f5xe5??
i.h6-g7+ is suicidal, resulting in a similar situation to that discussed in section 9, in which the bishop is used to control squares and gain tempi so that White can't defend the c4-pawn.
10 i.h6-e3
11 d5-d6+ 'i;e7-d7 12 'it>f5xe5 1-0
White intends 1 3 c.Pe5-d5 to take the c5-pawn. Let us see how the game may have ended had Black in
sisted on forcing his opponent to demonstrate his excellent endgame technique:
12 • . . 'ot>d7-c6
13 'it>e5-e6 ( D)
With his king up in support White wants to go it alone with the d-pawn.
Black will therefore need his bishop to cover the d8-square, but to say that this is not easy is an understatement.
Q. Can you find a safe route for the bishop to cover the queening square of White's d-pawn?
A. No? Good, because neither can I! The central knight is so powerful it controls every relevant square - even on a fairly open board. With 1 3 d6-d7 c.Pc6-c7 14 �e6-e7 coming next, it is no surprise that Black resigned earlier.
If a bishop is accompanied by a rook then the presence of a pawn or two fixed on the same colour square as the bishop is usually less of an in
convenience because the activity of the rook should compensate. It is this sort of logic that has led several grandmasters to occasionally say that 'there is no such thing as a bad bishop' . I do not think that this should be taken literally, but the in
ference is there. Players often under
estimate the impact a bishop can have on the assessment of an end
game.
There is certainly no denying the power of the two bishops. When you have two strong bishops, particularly in an endgame where your opponent has another combination of two mi
nor pieces, the bishops generally prove to be a dangerous team. The range of squares within your grasp is vast, and the logic is that if you have one ' bad' bishop, then the other should be brilliant (I once managed to get two bad bishops, but we will not go into that!).
The position below is more like opening theory.
w
Polugaevsky - Ostojic Belgrade 1969
For years this position was de
bated with many claiming that Black is comfortable. He has no obvious weaknesses and we could be forgiven for believing that a trade of dark
squared bishops results in 'good' knight vs 'bad' bishop endgame.
In fact White's excellent handling of the game is one of the reasons why none of today's top players is willing to take Black in this position.
15 :ctxc8+!
This appears to be the most accu
rate treatment. White concedes the c
file but he has every intention of winning it back.
15 . . . l:.a8xc8
16 g2-g3!
Black's queenside pawns are weak. Although the immediate 1 6 .te3xa7 runs into 1 6 .. . l:tc8-a8 Black still must keep a careful watch over
All the King 's Men 107
his queenside, and . . . a7-a6 creates a hole on b6.
The text threatens simply to chase Black's rook off the c-file.
16 lDf6-d7
17 .tfi-h3 :cS-c7 (D)
18 :ht-cl!
Were it not for the fact that his b
pawn is en prise White may have considered 18 .th3xd7 followed tak
ing control of the c-file. As it is, he is happy to retain the advantage of the two bishops.
18
19 rJi>d2xcl 20 'ifi?cl-c2
:c7xcl tDd7-b6
�g8-f8 White can now win a pawn with 21 .te3xb6? ! a7xb6 22 .th3-c8, but this leads to an opposite-coloured bishop endgame which Black has ex
cellent chances to draw. As you will discover later, these endings tend to be drawish.
21 b2-b3 'ifi?f8-e8 22 a4! (D)
The black queenside is suddenly looking rather delicate.
108 All the King 's Men
22 23 a4-a5 24 .i.h3xc8
�e8-d8 lDb6-c8
Only now is White prepared to break up his bishop duo, for this time he is about to emerge a clear pawn up in a same-coloured bishop ending. As we know, with sufficient pawns remaining on the board this usually means a winning advantage.
Indeed after 24 .. . �d8xc8 25 i.e3xa7 White went on to win comfortably.
I hope that this section has helped you weigh up the pros and cons a lit
tle. Obviously much depends on the specific position. Bishops are excel
lent in that they can rest on one side of the board and still have a consid
erable influence on the other. Having said that, it is also true that while a bishop controls more squares than a knight, some of these squares are often irrelevant. The knight is slow, but if there is sufficient time it can reach any square, whereas a bishop is permanently denied access to half of the board.
Generally the prospects of win
ning the game are excellent with either minor piece if you are a pawn up, although if there are pawns on both sides of the board a bishop is preferable, while a knight is stronger the closer the pawns become.