[Gehinnn]

The question was if there is any other scenario where black could force a win other than by forcing a zugzwang.

I would say no by contradiction. Let's assume black could win without zugzwang. Then white would win (and in particular not lose) by skipping the very first move and then playing blacks strategy (because now black has to make the first move and by white skipping the first move, the colors swapped).

If white would not skip the very first move and play an arbitrary move instead, white loses and black wins.

But this is the very definition of zugzwang! Thus, black can only win because of white's initial zugzwang, which contradicts our assumption.

[asdf_snar]

I think I may share confusion with the other poster. I don't understand the following step:

> Then white would win (and in particular not lose) by skipping the very first move and then playing blacks strategy

I understand the other comment, that there do exist setups in which colors can be effectively switched by e.g. 1. e3 e5 2. e4, but that requires cooperation on black's part. How does white "skip" the first move? Thanks in advance.

Edit: it may be that the statement "without Zugzwang" implicitly (or perhaps by definition) means you are allowed to skip moves? If so, that clarifies my confusion.

[Gehinnn]

Well, applying "zugzwang" means you only win because the opponent has to do a move and cannot skip their turn.

When black has a winning strategy, black already applies "zugzwang" for white's very first move: Black only wins because white has to make a move. If white could skip, black would not win.

> Edit: it may be that the statement "without Zugzwang" implicitly (or perhaps by definition) means you are allowed to skip moves?

Yes. It's not well defined, but I'd say a non-zugzwang win is a win (or rather a winning position) where you would also win when your opponent can skip their turn. A zugzwang win is a win that is not a non-zugzwang win.

[franknstein]

Ahh okay I think I get it now, you are saying if chess is win for black, that immediately implies zugzwang for white from starting position. In the same way, chess being a win for white implies zugzwang for black starting position.

So chess being a win for one side is equivalent to starting position being zugzwang for the other side.

It's obvious now, but so interesting to me, I never thought about it that way! Thanks for taking time for explaining yourself.

[Gehinnn]

White could win without zugzwang! Because white starts. After the first move, the position is no longer symmetric, so it doesn't help black to skip to switch sides.