Well, it's at least as complex as a Turing machine. That's a statement of complexity. Maybe you are asking whether it is possible for the winning strategy of a

Well, it's at least as complex as a Turing machine. That's a statement of complexity. Maybe you are asking whether it is possible for the winning strategy of a very simple deterministic game to be non-computable. In other words, maybe there's a possible way of defining computability which is orthogonal to complexity. The CS definitions of both terms are closely connected to Turing machines, though. Can you imagine a simple deterministic game that couldn't be "solved" by an algorithm?