Clearly it’s rather trivially meaningful in the sense that if a game has calculating that specific output as the win state, then obviously that algorithm will be a winning strategy. But somehow in my head there was a much more nebulous idea I can’t put into words which had something to do with all mathematical objects themselves being moves in such games, corresponding to the way they might be used in algorithms.
I even had a vague sense that any objects, such as sets, numbers, algebras, etc, could in some manner be interpreted as players of games in their own right, with certain defined patterns of behavior (AI?) which are somehow equivalent or isomorphic to the definition and structure of the object itself – that is, from knowing an object’s structure, you could determine how it would behave in any given game, and pitting it against other objects and determining which is more likely to win would have implications for their relationship in general.
I was too sleepy to go much further with this idea but it keeps returning to my mind even though I don’t know what to make of it or how to use it or even how to express it with any degree of rigor. If anyone else can think of a way to use this “insight”, or something to relate it to which might be used to expand upon it, I’d love to have your input. 🙂