Copyright (c) 1982 Berlekamp, Conway & Guy

Presented on volume I of Winning Ways, this game is played on a NxM board (say 10x10), with a number of white and black stones facing each other on each board edge. Let's assume here the following setup:

JUMPERS - Red (Black) jumpers move any number of cells to the right (left). They can also jump over an enemy piece directly below them (also above?), landing on the immediate adjacent cell (this is only valid if that cell is empty). 
If that jumped piece is a Jumper, it is demoted to a slipper.
When a piece moves off the board, it is removed.
SLIPPERS - Behave like the Jumpers, but cannot jump.
GOAL - Wins the player that made the last move.

An example

The Jumper at f9 can jump below to the empty f7 cell, demoting the f8 Jumper to a Slipper.