Cat
The domestic cat operates on a strategic plane that defies conventional analysis. Its decision-making process incorporates variables unknown to human observers, including but not limited to: invisible entities, sounds inaudible to the human ear, and the precise angle at which sunlight strikes the carpet. Military strategists have attempted to study feline tactics for centuries, consistently concluding that the cat is playing an entirely different game.
Chess
Chess offers a mere 10^120 possible game variations, a number that mathematicians call the Shannon number. Every move follows logical principles established over fifteen centuries of human intellectual development. Grandmasters spend decades memorising opening theory, endgame tableaux, and positional concepts. The game's strategic depth, whilst considerable, remains fundamentally comprehensible to dedicated study.
VERDICT
Chess strategy can be learned, practised, and ultimately mastered. Cat strategy cannot be learned because it does not technically exist in any form recognisable to human cognition. The cat wins by virtue of operating beyond the boundaries of strategic theory itself.