Chess and Checkers : the Way to Mastership · Chapter 21III
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While in the examples of elementary endings given in the previous chapter, the correct method of play was comparatively easy to find, positions with few men often occur which look very simple but which require considerable thought to be handled in the right way. The knowledge of these positions, of which there are five distinctly different types, is essential for any one who desires to become a fair player and they are, therefore, thoroughly explained in the following five characteristic examples.
It does not make any difference in the method of play whether the Black man is located as shown in Diagram 93 or on 3, 4, 7, 8, 10, 11 16, 20 or 24. The essential point is that he must not be able to march to the King row without being intercepted by White.
The winning maneuver is this: White turns the Black King out of the double corner in the manner shown in the play from the position of Diagram 89 and thereby compels the Black man to advance, finally forcing an exchange which secures the opposition.
32 31 30 +———————————————————-+ | | | | | | | | | 29 |———————————————————-| 28 | ** | | | | | | | | |———————————————————-| | | | | oo | | | | | 21 |———————————————————-| 20 | | | oo | | | | | | |———————————————————-| | | | | | | | | | 13 |———————————————————-| 12 | ** | | | | | | | | |———————————————————-| | | | | | | | | | 5 |———————————————————-| 4 | | | | | | | | | +———————————————————-+ 3 2 1
DIAGRAM 93.—White to Move and Win.
This maneuver, as will be evident from a careful study of the position, is possible only in case White has the move. If Black has the move the ending is a draw.
Black White
(1) … 23-27 (2) 28-32 19-23 (3) 32-28
Black cannot play 12-16, as 27-24 would win a piece.
(3) … 27-32 (4) 28-24
Again 12-16 is not possible on account of 32-27 winning a piece in three moves.
(4) … 23-18
32 31 30 +———————————————————-+ | | oo | | | | | | | 29 |———————————————————-| 28 | | | | | | | | | |———————————————————-| | | ** | | | | | | | 21 |———————————————————-| 20 | | | | | oo | | | | |———————————————————-| | | | | | | | | | 13 |———————————————————-| 12 | * | | | | | | | | |———————————————————-| | | | | | | | | | 5 |———————————————————-| 4 | | | | | | | | | +———————————————————-+ 3 2 1
White played 32-28 Black would exchange by five 24-19 and draw the game.
In the position of the Diagram Black has the choice between 24- 20, 12-16, 24-19 or 24-28, but he loses, no matter what move he makes as demonstrated below.
(A) (5) 24-20 32-27 (6) 20-16 18-15 (7) 16-20 15-18 (8) 12-16 18-15
Now Black cannot play (6) 16-19 because of the exchange 32-27; (6) 16-20 would also lose quickly through 15-18, (7) 24-19, 32- 28, (8) 19-16, 18-23. The best try is (6) 24-28.
Against 15-18 Black would now draw by (7) 16-19, 32-27; (8) 19- 23.
The only way to win is
(6) … 15-11
after which Black can do no better than
(7) 16-19 32-27 (8) 28-32 27-31 (9) 32-28 11-16 (10) 19-24 16-19, etc.
(C) (5) 24-19 32-28 (6) 12-16 28-32 (7) 19-24 18-15
and White continues as shown before.
(D) (5) 24-28 18-15 (6) 28-24 32-28 (7) 24-27 15-18 (8) 12-16 28-32 (9) 27-24 18-15
and wins as before by 15-18 in reply to (10) 16-20 or 15-11 in reply to 24-28.
THE SECOND POSITION (See Diagram 95)
White's advantage is that he can crown his two men while Black remains with only one King and two men. The reason why Black cannot use his two men to advantage is that they are pinned on the side of the board while White's men are located in the center where they have much more mobility. All the same White must have the move in order to win, just as in first position.
Black White
(1) … 30-26 (2) 9-14 26-23 (3) 14-10 23-18
32 31 30 +———————————————————-+ | | | | | | o | | | 29 |———————————————————-| 28 | | | o | | | | | | |———————————————————-| | | | | | | oo | | * | 21 |———————————————————-| 20 | * | | | | | | | | |———————————————————-| | | | | | | | | | 13 |———————————————————-| 12 | | | | | | | ** | | |———————————————————-| | | | | | | | | | 5 |———————————————————-| 4 | | | | | | | | | +———————————————————-+ 3 2 1
DIAGRAM 95.—White to Move and Win.
(4) 10-6 18-14 (5) 6-1 14-9 (6) 1-5 9-6 (7) 5-9 6-2 (8) 9-5 2-6 (9) 5-1 6-9 (10) 1-5 9-14 (11) 5-1 14-18 (12) 1-6 18-15 (13) 6-9 15-19 (14) 9-14 27-23 (15) 14-10 23-18 (16) 10-6 18-14 (17) 6-1 14-9 (18) 1-5 9-6 (19) 5-9 6-2 (20) 9-5 2-6 (21) 5-1 6-9 (22) 1-5 9-14 (23) 5-1 14-18 (24) 1-6 18-23 (25) 6-10 23-27 (26) 10-14 19-23 (27) 14-10 23-18 (28) 10-6 18-14 (29) 6-1 14-9 (30) 1-5 22-17
At last White has a position in which he can reduce the ending to one of the fundamental cases by exchange.
(31) 5-14 17-10 (32) 21-25
It will be noticed that through the exchange Black gained to move. White regains it by a second exchange.
(32) … 10-15 (33) 25-30 15-19 (34) 30-26 27-32 (35) 26-22 19-24 (36) 20-27 32-23
and wins.
Second position as a rule results from a "Bridge position" like the following: Black men on 20, 21, 23, Black King on 26. White men on 30 and 32, White Kings on 15 and 19. Black to move:
(1) 26-31 19-26 (2) 31-22 32-27
and White wins by "second position."
By the exchanges of men in the foregoing example the move was altered in each case. However, exchanges of pieces often occur which do NOT change the move, and as win or loss in a great number of endings depends upon which player has the move, it is necessary for the beginner to obtain a clear insight into the questions involved. An exchange always alters the move if the capturing piece is recaptured in turn. If a different piece is recaptured, it depends upon the relative position of the captured pieces, whether the move has remained with the same player or gone over to his opponent. For the purpose of calculating the move and its changes it is useful to imagine the Checker board as being composed of two "systems of squares"—the Black system containing the ranks starting with the squares 1, 9, 17 and 25, and the White system containing the other four ranks. If each of the two systems contains an EVEN number of men, the player whose turn to play it is, loses the opposition, that is: his opponent has the move. If the number of men in each system is ODD, the player whose turn to play it is, gains the opposition, that is, he has the move. As the calculation of the move enters only into such positions in which both players have the same number of pieces, it is sufficient to correct the number of men in one of the systems to obtain the desired information. Diagram 96 furnishes an example.
Counting the men of a system, the Black one, for instance, shows their number to be odd. Therefore, the player whose turn it is to play, has the move, which in the present instance
32 31 30 +———————————————————-+ | | | | o | | | | | 29 |———————————————————-| 28 | | | | | | | | | |———————————————————-| | | o | | | | | | | 21 |———————————————————-| 20 | | | o | | | | | | |———————————————————-| | | | | | | | | | 13 |———————————————————-| 12 | * | | | | | | | | |———————————————————-| | | * | | | | | | | 5 |———————————————————-| 4 | | | | | * | | | | +———————————————————-+
3 2 1
secures the win for White and a draw for Black, thus
(A) Black to move
Black White
(1) 8-11
This is apparently Black's best move; if he plays 2-7, White replies 19-15, obtaining a very strong position.
(1) … 31-26 (2) 2-6 26-22 (3) 6-10 22-18 (4) 11-16 18-15 Draw.
(B) White to move
Black White
(1) … 31-26 (2) 2-6 26-22 (3) 8-11 24-20 (4) 6-10 22-19 Block.
32 31 30 +———————————————————-+ | | o | | | | | | o | 29 |———————————————————-| 28 | * | | o | | | | | | |———————————————————-| | | | | | | | | | 21 |———————————————————-| 20 | | | | | | | | | |———————————————————-| | | | | | | | | | 13 |———————————————————-| 12 | | | | | | | | | |———————————————————-| | | | | | | | | * | 5 |———————————————————-| 4 | * | | | | | | | | +———————————————————-+ 3 2 1
From the above explanation it is evident that in the case of an exchange the move remains unaltered if the captured pieces were located in the same system, and that the move changes if the captured pieces belonged to different systems.
Exceptions to the rule sometimes occur due to a piece having no mobility, as for instance in the position of Diagram 97 where Black, on the move, loses because his man on 28 is blocked.
32 31 30 +———————————————————-+ | | | | | | | | | 29 |———————————————————-| 28 | o | | | | | | | | |———————————————————-| | | | | | | | | | 21 |———————————————————-| 20 | oo | | ** | | | | | | |———————————————————-| | | | | | | | | | 13 |———————————————————-| 12 | oo | | ** | | | | | | |———————————————————-| | | | | | | | | | 5 |———————————————————-| 4 | | | | | | | | | +———————————————————-+
3 2 1
DIAGRAM 98.—White to Move and Win.
White being a man ahead appears to have an easy win; but owing to the difficulty of getting the man crowned he has a hard task before him.
If the Kings on 11 and 12 were removed White would not be able to win at all, as the Black King would go back and forth between 19 and 23. It is, therefore, clear that in forcing a win from the position of the diagram the King on 12 must cooperate.
Another point to be borne in mind is that the following position would be a draw with White to move.
32 31 30 +———————————————————-+ | | | | | | | | | 29 |———————————————————-| 28 | | | | | | | | | |———————————————————-| | | | | | | | | | 21 |———————————————————-| 20 | o | | oo | | oo | | | | |———————————————————-| | | | | | | | | | 13 |———————————————————-| 12 | | | ** | | | | | | |———————————————————-| | | | | | | | | | 5 |———————————————————-| 4 | | | ** | | | | | | +———————————————————-+ 3 2 1
White is unable to make any headway because he cannot threaten an exchange. The method in which White threatens the exchange of the King on 19 in the example of third position given in Diagram 98 is the following:
Black White (1) … 20-24 (2) 11-15 24-27
12-8 would be of no use as 19-23 would force 8-12 again.
(3) 15-11
If 15-18 White wins by 27-31
(3) … 27-32
27-31 would admit of a draw by (4) 19-23, 28-24; (5) 23-27, 24- 20; (6) 27-23, 12-16; (7) 11-15, etc.
(4) 11-15 12-8 (5) 15-18 32-27 (6) 18-15 27-31 (7) 15-18 8-11 (8) 18-23 11-7 (9) 19-15
This is better than allowing the Kings to get together.
(9) … 28-24 (10) 23-27 24-20 (11) 27-23 7-2 (12) 15-11 2-6 (13) 23-19 6-10
If he moved the other King, Black would draw by 19-16.
(14) 19-23 10-14 (15) 23-19
Black would lose easily if he allowed the man to advance
(15) … 14-18
Threatening to exchange
(16) 19-24
The only move to avoid the exchange.
(16) … 18-23 (17) 24-28 23-19 (18) 28-32 31-26 (19) 32-28 26-23 (20) 28-32 23-18 (21) 32-28 19-15 (22) 11-8 20-16
and White cannot be prevented from getting another King.
An earlier setting of third position is shown in Diagram 100.
32 31 30 +———————————————————-+ | | o | | | | o | | | 29 |———————————————————-| 28 | | | * | | * | | | | |———————————————————-| | | | | * | | | | | 21 |———————————————————-| 20 | | | oo | | | | | | |———————————————————-| | | | | | | | | | 13 |———————————————————-| 12 | | | | | | | | | |———————————————————-| | | | | | | | | | 5 |———————————————————-| 4 | | | | | | | | | +———————————————————-+ 3 2 1
White wins by
(1) … 19-24 (2) 27-31 32-28 (3) 23-27 30-23 (4) 27-32 23-18 (5) 32-27 24-20 (6) 27-23 19-15, etc.
Although White is a piece ahead he has great difficulties in winning on account of the weak position of the man on 12. Black's man on 3 holds
32 31 30 +———————————————————-+ | | | | | | | | | 29 |———————————————————-| 28 | | | | | | | | | |———————————————————-| | | | | | | | | | 21 |———————————————————-| 20 | | | | | | | | | |———————————————————-| | | | | | | oo | | | 13 |———————————————————-| 12 | o | | oo | | oo | | | | |———————————————————-| | | | | | | | | | 5 |———————————————————-| 4 | | | * | | ** | | ** | | +———————————————————-+ 3 2 1
DIAGRAM 101.—White to Move and Win.
him in check without being impaired in his effectiveness towards the center of the board. If Black had the move, White could not win at all, as he would be unable to dislodge Black's Kings. As it is, he wins by means of a sacrifice which often occurs in endings with 4 Kings against 3.
Black White
(1) … 14-9 (2) 1-5 9-13 (3) 5-1 11-15 (4) 2-6 10-14 (5) 1-5 15-18 (6) 5-1
32 31 30 +———————————————————-+ | | | | | | | | | 29 |———————————————————-| 28 | | | | | | | | | |———————————————————-| | | | | | | | | | 21 |———————————————————-| 20 | | | | | oo | | | | |———————————————————-| | | | | | | oo | | oo | 13 |———————————————————-| 12 | o | | | | | | | | |———————————————————-| | | | | | | ** | | | 5 |———————————————————-| 4 | | | * | | | | ** | | +———————————————————-+ 3 2 1
It would not help Black to play 6-2 on account of 13-9; (7) 5-1, 9-5; (8) 2-6, 14-17; (9) 6-2, 17-13; (10) 2-6, 18-15; (11) 6-2, 15-10, etc.
(6) … 14-9 (7) 6-2 9-5 (8) 2-6 18-15 (9) 6-2 15-10
This is the important move, which forces the win.
(10) 2-6
If 2-7, White exchanges by 13-9
(10) … 10-7
Only with this pretty sacrifice can White win the game. After (11) 3-10 White plays 5-9 and should Black answer (12) 6-2, White would get "two for one" by 9-6. Therefore, Black can do no better than play (12) 10-15, 9-2; (13) 15-19, etc., and get a King in each double corner. White then wins as explained in the chapter on elementary endings.
Fourth position results in a draw only when the man is held on 12 or 21, according to whether the weaker side is Black or White. In third position it is useless to hold the man on the above squares, but sometimes a draw is obtained by holding him on 20 or 13.
In defending a game with two Kings against two Kings and a man, the weaker side must have the move in the system in which the man is pinned. The following position for instance is drawn with White on the move.
32 31 30 +———————————————————-+ | | | | | | | | | 29 |———————————————————-| 28 | | | | | | | oo | | |———————————————————-| | | | | | | oo | | | 21 |———————————————————-| 20 | | | | | | | | | |———————————————————-| | | | | | | ** | | * | 13 |———————————————————-| 12 | | | | | | | | | |———————————————————-| | | | | | | | | | 5 |———————————————————-| 4 | | | | | ** | | | | +———————————————————-+ 3 2 1
Black, on the move, would win by (1) 13-17, 22-13; (2) 14-9.
In Diagram 104 the drawing move is 27-31. The game ought to run like this:
(2) 20-24 23-27 (3) 24-28 27-32 (4) 30-26 31-27 (5) 22-18 27-24
32 31 30 +———————————————————-+ | | | | | | ** | | | 29 |———————————————————-| 28 | | | oo | | | | | | |———————————————————-| | | | | oo | | ** | | | 21 |———————————————————-| 20 | * | | | | | | | | |———————————————————-| | | | | | | | | | 13 |———————————————————-| 12 | | | | | | | | | |———————————————————-| | | | | | | | | | 5 |———————————————————-| 4 | | | | | | | | | +———————————————————-+ 3 2 1
(6) 26-23 24-20
and White moves back and forth between 24 and 20. In the position of Diagram 105 White draws by:
(1) … 23-19 (2) 28-32 19-24 (3) 7-2 24-19 (4) 2-6 19-24 (5) 6-9 24-19 (6) 9-14 19-24 (7) 14-17 15-19
32 31 30 +———————————————————-+ | | | | | | | | | 29 |———————————————————-| 28 | ** | | | | | | | | |———————————————————-| | | | | oo | | | | | 21 |———————————————————-| 20 | | | | | | | | | |———————————————————-| | | | | oo | | | | | 13 |———————————————————-| 12 | * | | | | | | | | |———————————————————-| | | | | ** | | | | | 5 |———————————————————-| 4 | | | | | | | | | +———————————————————-+ 3 2 1
Changing the guard
(8) 17-22 19-23
and Black can make no progress.
White is on the move, and it is evident that he loses if he moves the man on 27 permitting black to reply 11-15. The only way to save the game is to sacrifice the man on 20 by 20-16. The following play would ensue.
32 31 30 +———————————————————-+ | | | | | | | | | 29 |———————————————————-| 28 | | | o | | | | | | |———————————————————-| | | | | | | o | | o | 21 |———————————————————-| 20 | o | | o | | | | | | |———————————————————-| | | | | | | * | | * | 13 |———————————————————-| 12 | * | | * | | * | | | | |———————————————————-| | | | | | | | | | 5 |———————————————————-| 4 | | | | | | | | | +———————————————————-+ 3 2 1
(2) 11-2O 27-23 (3) 20-24 22-18 (4) 24-27 18-9 (5) 10-14
Preventing 23-18
(5) … 9-6 (6) 27-31 6-2K (7) 31-27 2-6
White cannot save the piece and so he runs his opponent.
(8) 27-18 6-9 (9) 13-17 19-15 (10) 18-11 9-18 (11) 17-22 18-25 (12) 11-15 25-22
Drawn. White would lose by 21-17, as after (13) 15-18, 17-13; (14) 18-14, 25-22; (15) 12-16 he cannot gain the double corner.
The following has been suggested as a suitable problem to be called SIXTH POSITION.
32 31 30 +———————————————————-+ | | | | | | | | | 29 |———————————————————-| 28 | | | | | | | | | |———————————————————-| | | oo | | | | | | | 21 |———————————————————-| 20 | | | | | | | | | |———————————————————-| | | o | | ** | | | | | 13 |———————————————————-| 12 | o | | | | | | | | |———————————————————-| | | | | ** | | | | | 5 |———————————————————-| 4 | | | * | | | | | | +———————————————————-+ 3 2 1
Black plays
(1) 7-2
threatening (2) 3-7 and (3) 15-11. White can prevent this only by
(1) … 24-20
Now 3-7 would only draw on account of 16-11.
(2) 2-6 20-24 (3) 6-10 24-20
Again 3-7 had to be prevented.
(4) 10-14 20-24 (5) 14-17 24-27
This time 24-20 would have lost, as Black would have replied (6) 17-13, 20-24; (7) 3-7, 12-8; (8) 15-11.
(6) 17-13 27-32
Avoiding 27-24 which would lose by (7) 3-7
(7) 13-9 32-27 (8) 9-14 27-24 (9) 14-18 24-27
Drawn. White has to watch 3-7 and to take care to play 24-20 at the right time so as to exchange 16-11 if 3-7 is played. At the same time he must beware of playing 24-20 when the Black Kings are on squares 15 and 5 or 15 and 13, as otherwise Black would reply 5-9, 20-24; 3-7, 12-8; 15-11.