In theory, wouldn't the player who takes the first move have a tiny tiny edge? Or is the second mover always able to guarantee a draw if they play perfectly?
Chess is only solved for positions with 7 pieces or less (and some configurations of 8 pieces [2]), so we're far from knowing best play from the 32-piece starting position.
[1] https://en.wikipedia.org/wiki/Zugzwang
[2] https://www.chess.com/blog/Rocky64/eight-piece-tablebases-a-...
White cannot have a tiny tiny edge against perfect play.
Either it is possible to force a win against perfect play, or it's not. So white is either winning or the game is a draw (or black is able to force a win against white's perfect play, but that's a whole different level of unlikely).
When talking about perfect play, terms like "tiny edge" lose their meaning.
However the consensus guess is that perfect play yields a draw.
Just like we can efficiently find approximate solutions for the traveling salesman problem (that are at most 50% longer than the optimal solution), these heuristics have not much to do with the optimal solution.
> I could imagine that a perfect play completely contradicts common chess theory.
So can anyone. Nobody knows what perfect chess play is. Our best guess though is that whatever your opponent plays you can always force a draw before they can win.
Unfortunately it leaves us in the position of not having much to go by, if expert experience doesn't help analyze the game.
I wonder how different a chess engine and optimal play look for the reduced sized boards.
https://en.wikipedia.org/wiki/Connect_Four#Mathematical_solu...
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.
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.
Not always. Almost always.
Generating a full game tree would be a truly daunting undertaking, and I can't even fathom how much memory would it take.
So until proven otherwise it's still possible that its theoretical win for white, theoretical draw or theoretical win for black as i understand it.
1. e3 e5 2. e4 whatever
And you effectively have a king's pawn opening with colours reversed
Does this strategy necessarily leads to provably losing position?
Zugzwang means that you would be better off not moving any piece on your turn letting your opponent make two moves in a row. There are a number of endgames that depend on getting your opponent into a position where he has only one legal move and by making it you can then play the winning move. If your opponent could instead skip his turn you have no ability to win the game.
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.
> 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.
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.
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.
Unlike tic-tac-toe we're not certain if it is a win or a draw for perfect players.
The chess analogue to this would be that there is a single opening move for white that a perfect player can guarantee a win from, or maybe a limited set of opening moves.
In fact, there is a variant of chess where this the case, namely "pawns-only chess", where 1.b4, 1.c4, 1.f4, and 1.g4 are winning for white, whereas all other first moves are a win for black with perfect play.
https://chess.stackexchange.com/questions/8755/is-the-result...