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When I was a child, I was playing a game such as the following:

  • The game is played on a standard chessboard, but only on the black squares.
  • There are two players: the white player has a single white pawn which is the "sheep"; the black player has four pawns which are the "wolves".
  • The players start at opposite sides of the board, and make a single diagonal step each turn.
  • The goal of the wolves is to capture the sheep - surround it such that it cannot move.
  • The goal of the sheep is to escape the wolves and get to the opposite side of the board.

Recently I tried playing it again, but found out that I do not remember the exact rules. Specifically: * Is the sheep allowed to go backward, or only forward? * Are the wolves allowed to go backward, or only forward?

We tried to play this game with all four combinations. In each combination, the game turned out to be too easy for one side and too difficult for the other side.

What are the rules that make this game sufficiently challenging for both sides?

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It sounds like you're describing Fox and Hounds here:

  • The four Hounds can only move forward diagonally.
  • The Fox can move forward or backwards diagonally.

There is no jumping or capturing involved; the Hounds win when the Fox can't make any legal moves, and the Fox wins if it reaches the far rank (where the Hounds started).

This game is inherently unbalanced; with perfect play on both sides, the Fox (aka the Sheep, in your case) cannot win. I find it likely that, as a child, finding the game "sufficiently challenging for both sides" was more due to your inexperience in recognizing the optimal plays than in any house rules that actually balanced the game.

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