I'm thinking about sequential, rules-based games where both players have perfect information about each other and what moves they'll be able to make (such as Chess, Connect 4, tic-tack-toe, Nim, etc.).
In such games, it is typical that either one player has a winning strategy (or a strategy to draw). This leads to a position in the game being declared "winnable" or "unwinnable".
I've been reading about the solutions to such games. Connect 4 is an example of a solved game, whereas Chess and Go are not solved yet.
The problem is that, while for the player in the winnable position some strategies can be said to be strictly better than others, for the player who isn't in the winning position, this makes no sense. The definition cannot be used for that player since there are no good moves that they can make.
It is common in this subject to hear things like: "if both players play with their optimal strategy, here is how the game will end up". Like in Numberphile's YouTube video about Connect 4 for example (I suggest you watch it, but anyways), how can they compare strategies for losing player? From a strict perspective their moves don't matter, but it if you're playing Connect 4 against a fellow human than A) you typically don't know which player has the advantage and B) it's idiotic to resign on move 1 just because you are the second player - if your playing against a human you could still win. The concept of winning strategy becomes totally irrelevant in games where you don't know if you're winning or not; if you're probably losing, then perhaps you should make moves to throw off you're opponent, or to survive as long as possible. But the point is that to play "optimally" in such games you must know whether you're winning or losing (which again as humans neither us nor our opponents tend not to know), because they have possibly separate objectives. It would be better imo if the best moves in any position (winning or losing) could fall under the same definition too, but that's a bonus I suppose.
What are these objectives? What are some of the ways in which optimal strategies are defined for losing players?