Well, Zermelo's Theorem (what is usually called that name, anyways) uses backward induction in its proof. Backward induction is a method of solving the game backward from the last move. In games with an infinite number of periods, not all possible paths of play have a last move. An infinite number of moves in a finite period game would not prevent the application of backward induction, so infinity matters more in the time/move dimension. If the infinite game is shown to be meaningfully isomorphic to a finite period game after removing some redundancies, then we can use backward induction to show the existence of solution. shapenaji might be suggesting one of those cases. This is not a generic property of infinite games though.

I just wish everyone would remember that when we talk amongst ourselves about having a "winning strategy" or finding an "optimal line of play", that means one thing, and when game theorists talk about those things, it means something else entirely.

You're making me remember why I don't like words...they have too many meanings.

For Go, how would we establish the final position from which the 'proof' proceeds?

_________________
Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21

It's in the premises of the proof. If [i] the game must end and [ii] one of the players must win (at the end of each branch), then there exists at least one final board state that can be reached by legal play where one of the players has won. That's all you need to know about it, for the purposes of the proof. The position on the board doesn't matter at all, just that someone won.

(Now, technically Go is not apt for the strong version of the Zermelo theorem, because even with komi you can still get a triple ko. But if the technical meaning of "optimal play" doesn't deter the would-be game theorists, surely this wrinkle won't either...)

Like most proofs of this ilk, you don't have to establish anything specific.

There are a finite number of board positions (legal or illegal). All paths of play start from an empty board and move from one position to another. With a superko rule that says that any repetition of position results in a draw, the possible length of every path of play is bounded above by #Positions+1 (This is a very loose upper bound). This says that a final position will be reached in less than #Positions+1 turns, no matter what. We don't have to show what that final position might be.

For practical purposes, an optimal strategy for go, although it exists, is not something we can figure out. I do have some confidence that A1 is not a good first move for black.

Can somebody maybe give a brief summary of what "dictionary of basic fuseki" says about niresenei and sanrensei in general? I don't know this series, so if there's a content preview with some sample site feel free to post the link here too.