Checkers - The Five Fundamental Positions (Part II)

THE THIRD POSITION

DIAGRAM 1.--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.

DIAGRAM 2.
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 1 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 3.

DIAGRAM 3.

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.

THE FOURTH POSITION
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

DIAGRAM 4.--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

DIAGRAM 5.

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.

DIAGRAM 6.

Black, on the move, would win by (1) 13-17, 22-13; (2) 14-9.

In Diagram 7 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

DIAGRAM 7.--WHITE TO MOVE.
(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

DIAGRAM 8.--WHITE TO MOVE.

Changing the guard
(8) 17-22 19-23

and Black can make no progress.

THE FIFTH POSITION

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.

DIAGRAM 9.
(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.

DIAGRAM 10.--BLACK TO MOVE AND WHITE TO DRAW .

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