FURTHER PRINCIPLES IN END-GAME PLAY
We shall now go back to the endings in search of a few more principles,
then again to the middle-game, and finally to the openings once more, so
that the advance may not only be gradual but homogeneous. In this way the
foundation on which we expect to build the structure will be firm and
solid.
9. A CARDINAL PRINCIPLE
[Illustration]
In the position shown above, White can draw by playing P - Kt 4 according
to the general rule that governs such cases, i.e. _to advance the Pawn that
is free from opposition_. But suppose that White, either because he does
not know this principle or because he {36} does not, in this case,
sufficiently appreciate the value of its application; suppose, we say, that
he plays 1 P - Q R 4. Then Black can win by playing 1... P - Q R 4,
applying one of the cardinal principles of the high strategy of chess--
_A unit that holds two._
In this case one Pawn would hold two of the opponent's Pawns. The student
cannot lay too much stress on this principle. It can be applied in many
ways, and it constitutes one of the principal weapons in the hands of a
master.
EXAMPLE 22.--The example given should be sufficient proof. We give a few
moves of the main variation:--
1. P - R 4 P - Q R 4
2. K - Kt 2 K - B 5
(Best; see why.)
3. P - Kt 4 P x P
(Best.)
4. P - R 5 P - Kt 6
5. P - R 6 P - Kt 7
6. P - R 7 P - Kt 8 (Q)
7. P - R 8 (Q) Q - K 5 ch
8. Q x Q K x Q
This brings the game to a position which is won by Black, and which
constitutes one of the classical endings of King and Pawns. I shall try to
explain the guiding idea of it to those not familiar with it. {37}
* * * * *
10. A CLASSICAL ENDING
[Illustration]
EXAMPLE 23.--In this position White's best line of defence consists in
keeping his Pawn where it stands at R 2. As soon as the Pawn is advanced it
becomes easier for Black to win. On the other hand, Black's plan to win
(supposing that White does not advance his Pawn) may be divided into three
parts. The first part will be to get his King to K R 6, at the same time
keeping intact the position of his Pawns. (This is all important, since, in
order to win the game, it is essential at the end that Black may be able to
advance his rearmost Pawn one or two squares according to the position of
the White King.)
1. K - Kt 3 K - K 6
2. K - Kt 2
If 2 K - Kt 4, K - B 7; 3 P - R 4, P - Kt 3 will win. {38}
2. ........ K - B 5
3. K - B 2 K - Kt 5
4. K - Kt 2 K - R 5
5. K - Kt 1 K - R 6
The first part has been completed.
[Illustration]
The second part will be short and will consist in advancing the R P up the
K.
6. K - R 1 P - R 4
7. K - Kt 1 P - R 5
This ends the second part.
[Illustration] {39}
The third part will consist in timing the advance of the Kt P so as to play
P - Kt 6 when the White King is at R 1. It now becomes evident how
necessary it is to be able to move the Kt P either one or two squares
according to the position of the White King, as indicated previously.[2] In
this case, as it is White's move, the Pawn will be advanced two squares
since the White King will be in the corner, but if it were now Black's move
the Kt P should only be advanced one square since the White King is at
Kt 1.
8. K - R 1 P - Kt 4
9. K - Kt 1 P - Kt 5
10. K - R 1 P - Kt 6
11. P x P
If K - Kt 1, P - Kt 7.
11. ........ P x P
12. K - Kt 1 P - Kt 7
13. K - B 2 K - R 7
and wins.
It is in this analytical way that the student should try to learn. He will
thus train his mind to follow a logical sequence in reasoning out any
position. This example is excellent training, since it is easy to divide it
into three stages and to explain the main point of each part.
The next subject we shall study is the simple {40} opposition, but before
we devote our time to it I wish to call attention to two things.
* * * * *
11. OBTAINING A PASSED PAWN
When three or more Pawns are opposed to each other in some such position as
the one in Example 24, there is always a chance for one side or the other
of obtaining a passed Pawn.
[Illustration]
EXAMPLE 24.--In the above position the way of obtaining a passed Pawn is to
advance the centre Pawn.
1. P - Kt 6 R P x P
If B P x P; P - R 6,
2. P - B 6 P x B P
3. P - R 6
and as in this case the White Pawn is nearer to Queen than any of the Black
Pawns, White will {41} win. Now if it had been Black's move Black could
play
1. ........ P - Kt 3
2. B P x P B P x P
It would not be advisable to try to obtain a passed Pawn because the White
Pawns would be nearer to Queen than the single Black Pawn.
3. P x P P x P
and the game properly played would be a draw. The student should work this
out for himself.
* * * * *
12. HOW TO FIND OUT WHICH PAWN WILL BE FIRST TO QUEEN
When two Pawns are free, or will be free, to advance to Queen, you can find
out, by counting, which Pawn will be the first to succeed.
EXAMPLE 25.--In this position whoever moves first wins.
[Illustration] {42}
The first thing is to find out, by counting, whether the opposing King can
be in time to stop the passed Pawn from Queening. When, as in this case, it
cannot be done, the point is to count which Pawn comes in first. In this
case the time is the same, but the Pawn that reaches the eighth square
first and becomes a Queen is in a position to capture the adversary's Queen
when he makes one. Thus:
1. P - R 4 P - K R 4
2. P - R 5 P - R 5
3. P - Kt 6 P x P
Now comes a little calculation. White can capture the Pawn, but if he does
so, he will not, when Queening, command the square where Black will also
Queen his Pawn. Therefore, instead of taking, he plays:
4. P - R 6 P - R 6
5. P - R 7 P - R 7
6. P - R 8 (Q), and wins.
The student would do well to acquaint himself with various simple endings
of this sort, so as to acquire the habit of counting, and thus be able to
know with ease when he can or cannot get there first. Once again I must
call attention to the fact that a book cannot by itself teach how to play.
It can only serve as a guide, and the rest must be learned by experience,
and if a teacher can be had at the same time, so much the faster will the
student be able to learn. {43}
* * * * *
13. THE OPPOSITION
When Kings have to be moved, and one player can, by force, bring his King
into a position similar to the one shown in the following diagram, so that
his adversary is forced to move and make way for him, the player obtaining
that advantage is said to have _the opposition_.
[Illustration]
EXAMPLE 26.--Suppose in the above position White plays
1. K - Q 4
Now Black has the option of either opposing the passage of the White King
by playing K - Q 3 or, if he prefers, he can _pass_ with his own King by
replying K - B 4. Notice that the Kings are directly opposed to each other,
and the number of intervening squares between them is odd--one in this
case.
The opposition can take the form shown above, {44} which can be called
actual or close frontal opposition; or this form:
[Illustration]
which can be called actual or close diagonal opposition, or, again, this
form:
[Illustration]
which can be called actual or close lateral opposition.
In practice they are all one and the same. The Kings are always on squares
of the same colour, there is only one intervening square between the Kings,
and the player who has moved last "_has the opposition_." {45}
Now, if the student will take the trouble of moving each King backwards as
in a game in the same frontal, diagonal or lateral line respectively shown
in the diagrams, we shall have what may be called _distant_ frontal,
diagonal and lateral opposition respectively.
The matter of the opposition is highly important, and takes at times
somewhat complicated forms, all of which can be solved mathematically; but,
for the present, the student should only consider the most simple forms.
(An examination of some of the examples of King and Pawns endings already
given will show several cases of close opposition.)
In all simple forms of opposition,
_when the Kings are on the same line and the number of intervening squares
between them is even, the player who has the move has the opposition_.
[Illustration]
EXAMPLE 27.--The above position shows to advantage the enormous value of
the opposition. The {46} position is very simple. Very little is left on
the board, and the position, to a beginner, probably looks absolutely even.
It is not the case, however. _Whoever has the move wins._ Notice that the
Kings are directly in front of one another, and that the number of
intervening squares is _even_.
Now as to the procedure to win such a position. The proper way to begin is
to move straight up. Thus:
1. K - K 2 K - K 2
2. K - K 3 K - K 3
3. K - K 4 K - B 3
Now White can exercise the option of either playing K - Q 5 and thus
passing with his King, or of playing K - B 4 and prevent the Black King
from passing, thereby keeping the opposition. Mere counting will show that
the former course will only lead to a draw, therefore White takes the
latter course and plays:
4. K - B 4 K - Kt 3
If 4...K - K 3; 5 K - Kt 5 will win.
5. K - K 5 K - Kt 2
Now by counting it will be seen that White wins by capturing Black's Knight
Pawn.
The process has been comparatively simple in the variation given above, but
Black has other lines of {47} defence more difficult to overcome. Let us
begin anew.
1. K - K 2 K - Q 1
Now if 2 K - Q 3, K - Q 2, or if 2 K - K 3, K - K 2, and Black obtains the
opposition in both cases. (When the Kings are directly in front of one
another, and the number of intervening squares between the Kings is _odd_,
the player who has moved last has the opposition.)
Now in order to win, the White King must advance. There is only one other
square where he can go, B 3, and that is the right place. Therefore it is
seen that in such cases when the opponent makes a so-called waiting move,
you must advance, leaving a rank or file free between the Kings. Therefore
we have--
2. K - B 3 K - K 2
Now, it would be bad to advance, because then Black, by bringing up his
King in front of your King, would obtain the opposition. It is White's turn
to play a similar move to Black's first move, viz.:
3. K - K 3
which brings the position back to the first variation shown. The student
would do well to familiarise himself with the handling of the King in all
examples of opposition. It often means the winning or losing of a game.
{48} EXAMPLE 28.--The following position is an excellent proof of the value
of the opposition as a means of defence.
[Illustration]
White is a Pawn behind and apparently lost, yet he can manage to draw as
follows:
1. K - R 1 !
The position of the Pawns does not permit White to draw by means of the
actual or close opposition, hence he takes the distant opposition: in
effect if 1 K - B 1 (actual or close opposition), K - Q 7; 2 K - B 2,
K - Q 6 and White cannot continue to keep the lateral opposition essential
to his safety, because of his own Pawn at B 3. On the other hand, after the
text move, if
1. ........ K - Q 7
2. K - R 2 K - Q 6
3. K - R 3 ! K - K 7
{49}
4. K - Kt 2 K - K 6
5. K - Kt 3 K - Q 5
6. K - Kt 4
attacking the Pawn and forcing Black to play 6... K - K 6 when he can go
back to Kt 3 as already shown, and always keep the opposition.
Going back to the original position, if
1. K - R 1 P - Kt 5
White does not play P x P, because P - K 5 will win, but plays:
2. K - Kt 2 K - Q 7
If 2...P x P ch; 3 K x P, followed by K - K 4, will draw.
3. P x P P - K 5
and mere counting will show that both sides Queen, drawing the game.
If the student will now take the trouble to go back to the examples of King
and Pawns which I have given in this book,[3] he will realise that in all
of them the matter of the opposition is of paramount importance; as, in
fact, it is in nearly all endings of King and Pawns, except in such cases
where the Pawn-position in itself ensures the win.
{50}
* * * * *
14. THE RELATIVE VALUE OF KNIGHT AND BISHOP
Before turning our attention to this matter it is well to state now that
_two Knights alone cannot mate_, but, under certain conditions of course,
they can do so if the opponent has one or more Pawns.
[Illustration]
EXAMPLE 29.--In the above position White cannot win, although the Black
King is cornered, but in the following position, in which Black has a Pawn,
[Illustration]
White wins with or without the move. Thus:
1. Kt - Kt 6 P - R 5
{51} White cannot take the Pawn because the game will be drawn, as
explained before.
2. Kt - K 5 P - R 6
3. Kt - B 6 P - R 7
4. Kt - Kt 5 P - R 8 (Q)
5. Kt - B 7 mate
The reason for this peculiarity in chess is evident.
_White with the two Knights can only stalemate the King, unless Black has a
Pawn which can be moved._
EXAMPLE 30.--Although he is a Bishop and a Pawn ahead the following
position cannot be won by White.
[Illustration]
It is the greatest weakness of the Bishop, that when the Rook's Pawn Queens
on a square of opposite colour and the opposing King is in front of the
Pawn, the Bishop is absolutely worthless. All that Black has to do is to
keep moving his King close to the corner square. {52}
[Illustration]
EXAMPLE 31.--In the above position White with or without the move can win.
Take the most difficult variation.
1. ........ K - R 7
2. Kt - Kt 4 ch K - R 8
3. K - B 1 P - Kt 4
4. K - B 2 P - R 7
5. Kt - K 3 P - Kt 5
6. Kt - B 1 P - Kt 6 ch
7. Kt x P mate
Now that we have seen these exceptional cases, we can analyse the different
merits and the relative value of the Knight and the Bishop.
It is generally thought by amateurs that the Knight is the more valuable
piece of the two, the chief reason being that, unlike the Bishop, the
Knight can command both Black and White squares. However, the fact is
generally overlooked that the Knight, at any one time, {53} has the choice
of one colour only. It takes much longer to bring a Knight from one wing to
the other. Also, as shown in the following Example, a Bishop can stalemate
a Knight; a compliment which the Knight is unable to return.
EXAMPLE 32.
[Illustration]
The weaker the player the more terrible the Knight is to him, but as a
player increases in strength the value of the Bishop becomes more evident
to him, and of course there is, or should be, a corresponding decrease in
his estimation of the value of the Knight as compared to the Bishop. In
this respect, as in many others, the masters of to-day are far ahead of the
masters of former generations. While not so long ago some of the very best
amongst them, like Pillsbury and Tchigorin, preferred Knights to Bishops,
there is hardly a master of to-day who would not completely agree with the
statements made above. {54}
EXAMPLE 33.--This is about the only case when the Knight is more valuable
than the Bishop.
[Illustration]
It is what is called a "_block position_," and all the Pawns are on one
side of the board. (If there were Pawns on both sides of the board there
would be no advantage in having a Knight.) In such a position Black has
excellent chances of winning. Of course, there is an extra source of
weakness for White in having his Pawns on the same colour-squares as his
Bishop. This is a mistake often made by players. The proper way, generally,
in an ending, is to have your Pawns on squares of opposite colour to that
of your own Bishop. When you have your Pawns on squares of the same colour
the action of your own Bishop is limited by them, and consequently the
value of the Bishop is diminished, since the value of a piece can often be
measured by the number of squares it commands. While on this subject, I
shall also call attention to the {55} fact that it is generally preferable
to keep your Pawns on squares of the same colour as that of the opposing
Bishop, particularly if they are passed Pawns supported by the King. The
principles might be stated thus:
_When the opponent has a Bishop, keep your Pawns on squares of the same
colour as your opponent's Bishop._
_Whenever you have a Bishop, whether the opponent has also one or not, keep
your Pawns on squares of the opposite colour to that of your own Bishop._
Naturally, these principles have sometimes to be modified to suit the
exigencies of the position.
EXAMPLE 34.--In the following position the Pawns are on one side of the
board, and there is no advantage in having either a Knight or a Bishop. The
game should surely end in a draw.
[Illustration] {56}
EXAMPLE 35.--Now let us add three Pawns on each side to the above position,
so that there are Pawns on both sides of the board.
[Illustration]
It is now preferable to have the Bishop, though the position, if properly
played out, should end in a draw. The advantage of having the Bishop lies
as much in its ability to command, at long range, both sides of the board
from a central position as in its ability to move quickly from one side of
the board to the other.
[Illustration] {57}
EXAMPLE 36.--In the above position it is unquestionably an advantage to
have the Bishop, because, although each player has the same number of
Pawns, they are not balanced on each side of the board. Thus, on the King's
side, White has three to two, while on the Queen's side it is Black that
has three to two. Still, with proper play, the game should end in a draw,
though White has somewhat better chances.
[Illustration]
EXAMPLE 37.--Here is a position in which to have the Bishop is a decided
advantage, since not only are there Pawns on both sides of the board, but
there is a passed Pawn (K R P for White, Q R P for Black). Black should
have extreme difficulty in drawing this position, if he can do it at all.
{58}
EXAMPLE 38.--Again Black would have great difficulty in drawing this
position.
[Illustration]
The student should carefully consider these positions. I hope that the many
examples will help him to understand, in their true value, the relative
merits of the Knight and Bishop. As to the general method of procedure, a
teacher, or practical experience, will be best. I might say generally,
however, that the proper course in these endings, as in all similar
endings, is: Advance of the King to the centre of the board or towards the
passed Pawns, or Pawns that are susceptible of being attacked, and rapid
advance of the passed Pawn or Pawns as far as is consistent with their
safety.
To give a fixed line of play would be folly. Each ending is different, and
requires different handling, according to what the adversary proposes to
do. Calculation by visualising the future positions is what will count.
{59}
* * * * *
15. HOW TO MATE WITH A KNIGHT AND A BISHOP
Now, before going back again to the middle-game and the openings, let us
see how to mate with Knight and Bishop, and, then, how to win with a Queen
against a Rook.
With a Knight and a Bishop _the mate can only be given in the corners of
the same colour as the Bishop_.
[Illustration]
EXAMPLE 39.--In this example we must mate either at Q R 1 or K R 8. The
ending can be divided into two parts. Part one consists in driving the
Black King to the last line. We might begin, as is generally done in all
such cases, by advancing the King to the centre of the board:
1. K - K 2 K - Q 2
Black, in order to make it more difficult, goes towards the white-squared
corner:
2. K - Q 3 K - B 3
3. B - B 4 K - Q 4
{60}
4. Kt - K 2 K - B 4
5. Kt - B 3 K - Kt 5
6. K - Q 4 K - R 4
7. K - B 5 K - R 3
8. K - B 6 K - R 2
9. Kt - Q 5 K - R 1
The first part is now over; the Black King is in the white-squared corner.
[Illustration]
The second and last part will consist in driving the Black King now from
Q R 8 to Q R 1 or K R 8 in order to mate him. Q R 1 will be the quickest in
this position.
10. Kt - Kt 6 ch K - R 2
11. B - B 7 K - R 3
12. B - Kt 8 K - R 4
13. Kt - Q 5 K - R 5
Black tries to make for K R 1 with his King. White has two ways to prevent
that, one by 14 B - K 5, {61} K - Kt 6; 15 Kt - K 3, and the other which I
give as the text, and which I consider better for the student to learn,
because it is more methodical and more in accord with the spirit of all
these endings, _by using the King as much as possible_.
14. K - B 5 ! K - Kt 6
15. Kt - Kt 4 K - B 6
16. B - B 4 K - Kt 6
17. B - K 5 K - R 5
18. K - B 4 K - R 4
19. B - B 7 ch K - R 5
20. Kt - Q 3 K - R 6
21. B - Kt 6 K - R 5
22. Kt - Kt 2 ch K - R 6
23. K - B 3 K - R 7
24. K - B 2 K - R 6
25. B - B 5 ch K - R 7
26. Kt - Q 3 K - R 8
27. B - Kt 4 K - R 7
28. Kt - B 1 ch K - R 8
29. B - B 3 mate
It will be seen that the ending is rather laborious. There are two
outstanding features: the close following by the King, and the controlling
of the squares of opposite colour to the Bishop by the combined action of
the Knight and King. The student would do well to exercise himself
methodically in this ending, as it gives a very good idea of the actual
power of the pieces, and it requires foresight in order to accomplish the
{62} mate within the fifty moves which are granted by the rules.
* * * * *
16. QUEEN AGAINST ROOK
This is one of the most difficult endings without Pawns. The resources of
the defence are many, and when used skilfully only a very good player will
prevail within the limit of fifty moves allowed by the rules. (The rule is
that at any moment you may demand that your opponent mate you within fifty
moves. However, every time a piece is exchanged or a Pawn advanced the
counting must begin afresh.)
[Illustration]
EXAMPLE 40.--This is one of the standard positions which Black can often
bring about. Now, it is White's move. If it were Black's move it would be
simple, as he would have to move his Rook away from the King (find out
why), and then the Rook would be {63} comparatively easy to win. We deduce
from the above that the main object is to force the Black Rook away from
the defending King, and that, in order to compel Black to do so, we must
bring about the position in the diagram with _Black_ to move. Once we know
what is required, the way to proceed becomes easier to find. Thus:
1. Q - K 5 ch
Not 1 Q - R 6, because R - B 2 ch; 2 K - Kt 6, R - B 3 ch; 3 K x R.
Stalemate. (The beginner will invariably fall into this trap.)
1. ........ K to R 1 or to R 2
2. Q - R 1 ch K - Kt 1
3. Q - R 5
In a few moves we have accomplished our object. The first part is
concluded. Now we come to the second part. The Rook can only go to a White
square, otherwise the first check with the Queen will win it. Therefore
3. ........ R - Kt 6
4. Q - K 5 ch K - R 1 best
5. Q - R 8 ch K - R 2
6. Q - Kt 7 ch K - R 1
7. Q - Kt 8 ch R - Kt 1
8. Q - R 2 mate
(The student should find out by himself how to win when 3...R - Kt 8;
4 Q - K 5 ch, K - R 2.) {64}
[Illustration]
EXAMPLE 41.--The procedure here is very similar. The things to bear in mind
are that the Rook must be prevented from interposing at Kt 1 because of an
immediate mate, and in the same way the King must be prevented from going
either to R 3 or B 1.
EXAMPLE 42.--We shall now examine a more difficult position.
[Illustration] {65}
Many players would be deceived by this position. The most likely looking
move is not the best. Thus suppose we begin
1. Q - K 5 ch K - B 1
2. K - Kt 6 R - Q 2
The only defence, but, unfortunately, a very effective one, which makes it
very difficult for White, since he cannot play 3 Q - K 6 because of
3...R - Kt 2 ch; 4 K - B 6, R - Kt 3 ch draws. Nor can he win quickly by
3 Q - Q B 5 ch because 3...K - K 1, 4 K - B 6, R - Q 3 ch ! driving back
the White King.
Now that we have seen the difficulties of the situation let us go back. The
best move is
1. Q - Kt 5 ch ! K - R 1
If K - R 2; 2 Q - Kt 6 ch, K - R 1; 3 K - R 6 !
2. Q - K 5 ch ! K - R 2 best
3. K - Kt 5 R - R 2 ! best
If 3...R - Kt 2 ch; 4 K - B 6 leads to a position similar to those in
Examples 40 and 41.
4. Q - K 4 ch K - Kt 1
5. Q - B 4 ch K - R 2
6. K - B 6 R - K Kt 2
7. Q - R 4 ch K - Kt 1
8. Q - R 5
{66} and we have the position of Example 40 with Black to move.
Let us go back again.
1. Q - Kt 5 ch K - B 1
2. Q - Q 8 ch K - Kt 2
3. K - Kt 5 R - B 6
The best place for the Rook away from the King. 3...K - R 2; 4 Q - Q 4,
R - Kt 2 ch; 5 K - B 6 would lead to positions similar to those already
seen.
4. Q - Q 4 ch K - B 1
5. K - Kt 6
5 Q - Q 6 ch, K - Kt 2; 6 Q - K 5 ch, K - B 1; 7 K - Kt 6 would also win
the Rook. The text move, however, is given to show the finesse of such
endings. White now threatens mate at Q 8.
5. ........ R - Kt 6 ch
6. K - B 6 R - B 6 ch
7. K - K 6 R - K R 6
White threatened mate at K R 8.
8. Q - B 4 ch
and the Rook is lost.
Note, in these examples, that the checks at long range along the diagonals
have often been the key to all the winning manoeuvres. Also that the Queen
and {67} King are often kept on different lines. The student should
carefully go over these positions and consider all the possibilities not
given in the text.
He should once more go through everything already written before proceeding
further with the book.
* * * * *
{68}