If it tells you what to do, not just depending on what your opponent does, but on what you do, then testing 1-move modifications is sufficient to test optimality.
The statement of sufficiency I made is true for all complexities of opposing strategies.
The statement of insufficiency is not. If the opponent’s strategies are, for instance, linear, then it should be false. But some opposing strategies ARE very complex, so it’s presumably true.
It depends on how big your strategy is.
If it tells you what to do, not just depending on what your opponent does, but on what you do, then testing 1-move modifications is sufficient to test optimality.
If not, then it isn’t.
Doesn’t an optimization question depend as much on the complexity of opposing strategies as it does on the complexity of my strategy?
The statement of sufficiency I made is true for all complexities of opposing strategies.
The statement of insufficiency is not. If the opponent’s strategies are, for instance, linear, then it should be false. But some opposing strategies ARE very complex, so it’s presumably true.