When it comes to checkers, four basic families of checkers are recognized. The fifth one combines two families. Examples of the families and movement and capturing are included
- Turkish (Turkish, Greek, etc) [Orthogonal and sideways] [No backcapturing]
- International (Interational, Brazillian, Russian, Pool, etc.) [Diagonal] [Backcapturing]
- Spanish (Spanish, Argentinian, Czech, etc.) [Diagonal] [No backcapturing]
- American/British and Italian [Diagonal] [*No backcapturing]
- International+Turkish (Frisian, Armenian, etc.) [Diagonal and orthogonal]
[Backcapturing allowed for Frisian] [No backcapturing for Armenian, the basic variant]
In the checkers variant you have just referred to (International), the orthogonal directions in movement or capturing are not used, therefore, only the diagonal directions for movement and capturing are included.
Now let's go back to your questions again
Your Q:-[on our copy of the game say a king can take in any direction even if there are empty spaces between the king and the piece it will take.]
Answer: - Yes, he can
Explanation :-In all of these checkers families, the king can take in any direction and there must be space between it and the piece. From that space, it can choose to go further in the capturing process if in front of it is a new victim to be captured.
Your Q: - [Also, can a king take a piece then change direction and take another one?]
Answer: - Yes he can change any direction when he captures
In Family (1) Turkish, a king can change the direction when he captures orthogonally for example N to S or sideways E to W. Something to bear in mind is that within a multicapture, turning 180 degrees between two captures is not allowed
Note: - The flying king can choose to slide to any empty area after the captured piece except in Greek checkers where the king is subject to king Halt , that is it must stop directly after the captured pieces
In Family (2)International , a king can change the direction when he captures diagonally for example SE to NE or NW or for example from NE to SE or SW
Note :- The flying king can choose to slide to any empty area after the captured piece
In Family (3) Spanish, a king can change the direction when he captures diagonally for example SE to NE or NW or for example from NE to SE or SW.
Note:- In Argentinian or Thai, the flying king is subject to king halt, that is it must stop directly after the captured pieces. Note that in Thai, a king could immediately reverse direction in a capture
In Family (4) American, a king can change the direction when he captures diagonally for example SE to NE or NW or for example from NE to SE or SW.
Note:- In American or Italian checkers, the king isn’t of the type flying king. It is a short-range king where it directly stops after the captured piece. It can’t slide to any empty area on the board.
In Family (5) Inter+Turk, it depends on the checkers variant in terms of movement. For example, in Armenian, men move like Turkish with an additional privilege, diagonal movement.
In Frisian checkers, men move diagonally in 2 directions(NE,NW) but capture in 8 directions, 4 diagonally (NE,NW,SE,SW) and two orthogonal (S,N) and two sideways (E W). The Frisian king moves in 4 directions and captures in 8 directions as well
Also, the concept of quantity is very important in checkers. Some checkers variants allow maximum capture of pieces as in Turkish or International.
Others dont allow that. They allow you to capture any sequence as long as all possible captures are made as in American or Pool. In both cases Kings abide these rules.
Moreover, whether pieces are removed immediately (during the capture) or after the whole move is very crucial in capturing.