It's possible, although it seems unlikely, that white is in zugzwang [1] on the starting position, in which case black would have a win with perfect play.

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-...

> 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?

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.

It isn't known theoretically whether perfect play is enough for black to force a draw. It is also an infinitesimal probability that white starts off in zugzwang (i.e. all possible moves are bad).

However the consensus guess is that perfect play yields a draw.

Why is that the consensus guess? I could imagine that a perfect play completely contradicts common chess theory.

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.

Because when great players realize they have a position that they connect win are still able to figure out how to force a draw so they don't lose.

> 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.

That's an interesting point.

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.

Unless I missed something recent, it is not known whether any player has a winning strategy (or a drawing strategy, for that matter). It would be quite the discovery as well.

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.

It's not a solved problem but our best players and best computers perform better with white. The edge isn't tiny either.

They don't anymore, at least not the computers. When you let them start from normal starting position and provide decent hardware and some time it's always a draw and has been for a few years now.

> always

Not always. Almost always.

No one is going to waste the CPU time running Stockfish (or GPU with Leela) against each other at classical time controls long enough to see a decisive game which might never happen anyway so we will likely never know. I think current Stockfish on a modern ThreadRipper with classical time control will never be beaten. I am not 100% sure I am right but I don't expect (but would love to!) to be proven wrong.

Stockfish won't solve it. We need a full game tree. Stockfish is not designed to build a full game tree.

Generating a full game tree would be a truly daunting undertaking, and I can't even fathom how much memory would it take.

Due to alpha-beta cutoffs, you don't need a full game tree. But if you did build a tree with all legal chess positions, it would have approximately 4.8x10^44 of them [1].

[1] https://github.com/tromp/ChessPositionRanking

I am not saying Stockfish is going to solve it. I am saying it will not lose from the initial position. In other words my hypothesis is that we already have a soft solution to chess available. I can't prove it but I can proceed accordingly in practice (in opening preparation or correspondence games for example) and no one will prove me wrong or exploit it.

Stockfish lost a handful of games against Leela from starting positions that were a couple of moves into mainstream openings. I don't think it's at at all unlikely that there's a route that beats it.

Can you provide an example of such a game? I am following computer chess pretty closely and it's just all draws if we start from mainstream openings. By mainstream I mean things that are considered solid by today top players and engines. Some of the traditional mainstream openings turned out to be problematic (King's Indian for example). I am talking about recent Stockfish (the one with NNs) as the traditional version had pretty serious problems in certain positions and needed an extensive opening book to steer it out of trouble.

When have you last seen a decisive game from the starting position by two modern engines on normal hardware? I haven't seen one for many years.

There is a small chance that deep into the tree the first to play gets into zugzwang first, meaning position with no good moves. Is there any other scenario where playing black would give you theoretical edge?

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.

Zugzwang is the only way for white to lose. Without Zugzwang and a winning strategy for black for chess with Zugzwang, white could skip the first move and now has the winning strategy.

What do you mean skip the first move? Like play a neutral move? Why would such a move exist?

Skip your turn. Don't move anything at all.

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 know what zugzwang is. I was just asking what he meant by 'skipping turns' because skipping turns by simply refusing to make a move is illegal, so i was not sure what point was Gehinnn trying to make.

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.

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.

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.

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.

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.

You can play e.g.

1. e3 e5 2. e4 whatever

And you effectively have a king's pawn opening with colours reversed

Can black refuse this 'color switch'? It seems like he can, for a while, by mimicking moves. 1. e3 e6 for example.

Does this strategy necessarily leads to provably losing position?

Provably there's little that can be said about chess at large when it comes from opening to endgame. Heuristically speaking though matching moves against even a beginner is a very bad strategy for play, as a recent speedrun being done by GM Aman Hambleton on youtube has been showing.

[1] https://www.youtube.com/watch?v=uUfF6l4A6Ks

Having that happen in one place deep in the tree wouldn't mean much: black would need to be able to get such a zugzwang (or other win) against anything white does.

Many think that perfect play from both sides will result in a draw but there is no prove for that yet. So I'm reality we do not know.

Still an open problem.

Unlike tic-tac-toe we're not certain if it is a win or a draw for perfect players.

To give an example from a game more complicated than tic-tac-toe, it is known that the player who goes first in Connect 4 can always win with perfect play if (and only if) they play in the middle column on their first turn.

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...

AFAIK it's not a solved game so we cannot say with certainty.