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

Diagram 96.

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
|---------------------------------------|