Ko-an

Ko-an is a 1994 game by David Welch and Paul Whitehorn, published at Image Games.

Each player has two types of pieces: five squared pieces and six octagonal pieces. The board is composed of a grid of yellow squares and green octagons.

This is the initial setup:

• Pieces only move forwards, not backwards nor sideways, to an empty space. There's a further move restriction: a piece cannot move between squares [in a better designed board, like the one below, it's easy to see why: squares do not touch on a 4.8.8 grid].
• Pieces can also move forwards to a space occupied by an enemy piece, which is then captured (captures are by replacement).
  
• However, captures also depend on piece type: octagonal pieces can only capture pieces on octagons, and squared pieces can only capture pieces on squares.
  
• Capturing is not mandatory.
  
• Wins the player that moves a friendly piece to the last row or stalemates the adversary (which includes capturing all the enemy army).

Here's a board (by r0cka) to play the game:

From a 1994 review by Richard Breese:

[...] Considering its simplicity, the game can develop in a surprising variety of ways. For example, pieces of both players may bunch up on one side of the board, several 'skirmishes' may occur all over the board, or a large stand off may arise across the center of the board. This variety adds to the attractiveness of the play.

Of the two types of playing pieces the octagonal piece is stronger and this factor probably explains why in most games it is a octagonal shaped piece which makes the winning break through. This strength arises from the situation where an octagonal shaped piece confronts a squared shaped piece. As the square spaces do not join each other it is necessary for all pieces to move onto the octagonal shaped spaces - the spaces on which the octagonal shaped pieces can capture. Consequently an octagonal shaped piece is much more likely to be able to capture a square shaped piece than vice versa.

Some pics from the original game package: