Add to a chess pawn's movement the ability to move backward: one step backward into an empty square or a diagonally backwards capture. Somewhat similar to the wazir-ferz hybrid, except it can't move sideways.
A possible interesting restriction: Consider the triangle formed by pawn and the two diagonals southwest and southeast emanating from a white pawn. A pawn may only move backwards if there is an enemy piece somewhere in that triangular area, the pawn's cone of backward vision. A pawn can "advance" toward the enemy. A far advanced pawn has a larger backwards cone, so is more powerful because it can move backwards more frequently.
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