This is correct, but I think we all understand a valid way to a solution (apart from practicality of resources) is to use heuristics (eg Stockfish evaluations based on incomplete analysis) to arrive a strategy.
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Not true, I don't.
I've just posted a king and rook v king position where SF15 gives four bum attempts at a move. I don't understand that that approach will eventually converge to a solution.
I think the heuristics that van den Herik was talking about were the kind of heuristics that Allis included in his connect4 solution which were perfectly valid and proven techniques that could be used in particular situations. Distinct in kind from: Stockfish (or even @tygxc) thinks so.
A strategy is an algorithm that determines what move to play in every position that is reached.
Not precisely. We can say that we use a strategy of using an algorithm to determine moves. We can't say that the algorithm is the strategy.
Yes, we can. I did.
As an analogy, a function in a computer program is some code that takes inputs with specified properties and outputs something. This implements the static mathematical notion of a function, which relates each member of the domain to a unique thing.
If you want it formalised, I can do so, but I see no room for misunderstanding.