Copyright (c) 1992 Bill Taylor

The game starts at an empty nxn rhombus board, say 10x10,  with the following setup (Green player starts):

GOAL CELL - The board obtuse corners are the goal cells (one for each player).
MOVE - A player, at each turn, moves the white stone into an empty adjacent cell. After the move, the player also drops a black stone into the cell where the white stone was. 
However, it is illegal to go to a cell from which it becomes impossible to reach any home cell. (It is valid if only one can be reached.).
GOAL - That player wins whose goal cell is entered (regardless of who moves it). If the  White stone becomes impossible to move in a non-goal cell, it is a tie.
An example

If it is Red to move, he can play at g11 and Green has no good move to answer. If g10 then h11, h10, i11, ... and if h11 then i12

If it is Green to move, and if he plays g11, then the same move sequence is not longer good for Red.

Here is a sample game for a smaller board.

A game of Slime Trail

Green starts (marked stone) 

Moves: e nw e nw ne nw ne! nw w sw se w sw e se w t se w sw e sw e se e

Red resigns 1-0. Green wins.

The board shows the final position. 

Slime trail can also played on a square grid. Here is a game played on a 8x8 chess board.

A game of Square Slime Trail

Green starts (marked stone) 

Moves: sw e sw e e ne e n nw w s e sw se sw se w w n w nw nw n nw ne nw s ne e s e sw! [any other move would be a win for the Green!]  

Green resigns 0-1, Red wins

The board shows the final position. 

One variant is Slime-Moku. After each move, the slime leaves alternating color stones. A player wins if he makes a 5 in-a-row with his stones (if no player are able to do that, after the board is full, the game is a tie). Also, if before the board is full, the Slime cannot move (all adjacent cells are occupied), the next player may move the Slime to any other empty cell.

Another variant for 3 players is called Snake Pit is played on the next hexagonal board. Each player has 4 stones (snakes) that can move. On each turn, each player moves 3 of the 4 snakes to an empty adjacent cell (PIE rule: in the 1st and 2nd move, the players only move 1 and 2 snakes). A player loses when he can no longer make his legal move, i.e. when he has TWO snakes totally blocked.