Sliding rooks and representation

Rooks slide under fixed rules and the last legal move wins. The path to a strategy is to find a representation that exposes the structure: often the position is equivalent to a pile-and-move game you already understand, and once you see the mapping the winning play is inherited.

This is a recurring move in mathematics: solve a hard problem by translating it into a solved one. When two games have the same positions and the same moves, they have the same winning strategy, so recognising the disguise is most of the work.