Even then, this isn't actually what you want. When people say deterministic, at one level they mean "this thing should be a function" (so input x always returns the same output y). Some people also use determinism to mean they want a certain level of "smoothness" so that the function behaves predictably (and they can understand it). That is "make me a sandwich" should not return radically different results to "make me a cucumber sandwich".

As you note, your scheme significantly solves the first problem (which is a pretty weak condition) but fails to solve the second problem.