It would be wild if it turned out that some of the 20 first moves led into a tree that included a perfect winning path for black while others were draw on perfection: "take it, if you can, I bet you can't"

With connect-4 it's like that: playing in the middle on the 1st move means the first player wins, playing adjacent to the middle means the game will be drawn, and starting further to the side means the second player wins (all assuming otherwise perfect play).

https://en.wikipedia.org/wiki/Connect_Four#Mathematical_solu...

Plenty of forced moves in that game, where there is only one option to not lose immediately. I basically sacrificed the last years of school math to a 10x8 variation of that game, it was almost as if there were two competitions in parallel, who would win and who could call a game decided first. Declaring the other guy winner before he even knew was almost better than winning (but certainly not as good as declaring victory and then explaining why)

Having a winning strategy for black seems impossible though; the discussion is whether white have it or is it a forced draw.

Why would that seem impossible? One could argue that white has to open up his defenses first, allowing black to pick the best response to that.

In general, there’s no guarantee of first mover’s advantage. For example, Hexapawn (https://en.wikipedia.org/wiki/Hexapawn) is a win for black on some boards (https://web.archive.org/web/20050330222720/http://www.chessv...). Versions that are more complex than chess and are a win for black may exist.

White could start with a knight move. Unlike Hexapawn, in chess, white moving first provides an increase in optionality for white, and the board positions are not forcing white on some losing track, because white is free to "burn" a move with many pieces by taking 2 moves to get to the same place they could with 1 move. White can use two bishop moves, or a pawn push to the 3rd rank followed by the 4th rank, to turn around the initiative early in the game.

That would give black two moves in a row, which is a different scenario, and might still be optimal for black.

Black doesn't know it's getting two moves in a row when it makes the first move. And on the second move, it can only take advantage if white's first move reduces white's optionality in a specific manner, e.g. by blocking another piece essential for response to a certain tactic, which by construction, would mean it wasn't really an opportunity to transpose the game to hand over the initiative.

Not sure I follow.

The scenario we're positing is that perhaps, in fully-solved chess, white is actually in zugzwang, where every initial move is actually bad for them.

If there were some way for white to hand the first move to black, then clearly this would be the best solution.

But all the take-back solutions (e.g. move the knight forward and back again) actually give black two moves, which is a different situation.

And the stutter-step solution of white moving a pawn only one space instead of two doesn't work because that's simply refuting the premise that white is in zugzwang.