Fox and Hounds, Fox and Geese, Fox and Dogs, Wolf and Sheep, Hounds and Hare or Devil and Tailors. There might be even more alternate names. In Dutch it is called Kat en Muizen.

Fox and Hounds is played on a chess board or checkers board sized 8x8. 4 similar colored pawns or checkers as hounds and a single pawn or checker in other color as a fox.

Hounds are placed onto fields b8, d8, f8, and h8. Fox starts set onto e1. Fox moves first.

8 H H H H
7. . . .
6 . . . .
5. . . .
4 . . . .
3. . . .
2 . . . .
1. . F .
 abcdefgh

Hounds hunting the fox. The fox moves diagonally one field range forward or backward onto an empty adjacent square per turn. Hounds can only move diagonally one field forward (towards row 1) onto an empty adjacent square.

Since only diagonal moves are allowed the game is played on the 32 dark fields of the chess board only.

There is no capturing by jumping and no stacking of checkers. Neither by jumping the opponent as in Checkers nor by moving onto its field replacing the opponent.

Fox wins by reaching the other side of the board (8th row where hounds started their hunt).
Hounds win by blocking the fox such that it cannot move anymore (when fox has no legal move left).

If moving perfect then hounds will win.

Due to simplicity of the material it is sometimes part of family game collections where a Checkers or Chess set is already included.

See this thread for more information: Same name but played 4:1 on chessboard