Checkers - The Five Fundamental Positions (Part I)

THE FIVE FUNDAMENTAL POSITIONS

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.

THE FIRST POSITION

It does not make any difference in the method of play whether the Black man is located as shown in Diagram 1 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 1 and thereby compels the Black man to advance, finally forcing an exchange which secures the opposition.

DIAGRAM 1.--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

DIAGRAM 2.

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

(B) (5) 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 3)

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.

DIAGRAM 3.--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."

THE CHANGE OF THE MOVE

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 4 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

DIAGRAM 4.

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.

DIAGRAM 5.

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 5 where Black, on the move, loses because his man on 28 is blocked.