8 ms·

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?

philipswood 4y ago
Still an open problem. Unlike tic-tac-toe we're not certain if it is a win or a draw for perfect players.
- dane-pgp 4y ago
  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-in-mini-chess-known-with-perfect-play https://chess.stackexchange.com/questions/8755/is-the-result...
Synaesthesia 4y ago
AFAIK it's not a solved game so we cannot say with certainty.
deleted 4y ago
[deleted]
pred_ 4y ago
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.
- usrusr 4y ago
  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"
  - Scarblac 4y ago
    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_solution https://en.wikipedia.org/wiki/Connect_Four#Mathematical_solu...
    - usrusr 4y ago
      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)
- KptMarchewa 4y ago
  Having a winning strategy for black seems impossible though; the discussion is whether white have it or is it a forced draw.
  - Someone 4y ago
    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 https://en.wikipedia.org/wiki/Hexapawn) is a win for black on some boards (https://web.archive.org/web/20050330222720/http://www.chessvariants.org/small.dir/hexapawn.html https://web.archive.org/web/20050330222720/http://www.chessv...). Versions that are more complex than chess and are a win for black may exist.
fileeditview 4y ago
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.
Tenoke 4y ago
It's not a solved problem but our best players and best computers perform better with white. The edge isn't tiny either.
- bluecalm 4y ago
  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.
  - sgjohnson 4y ago
    > always Not always. Almost always.
    - Scarblac 4y ago
      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.
    - bluecalm 4y ago
      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.
      - sgjohnson 4y ago
        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.
        4y ago
FartyMcFarter 4y ago
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 https://en.wikipedia.org/wiki/Zugzwang [2] https://www.chess.com/blog/Rocky64/eight-piece-tablebases-a-progress-update-and-some-results https://www.chess.com/blog/Rocky64/eight-piece-tablebases-a-...
franknstein 4y ago
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.
- Gehinnn 4y ago
  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.
  - franknstein 4y ago
    What do you mean skip the first move? Like play a neutral move? Why would such a move exist?
    - YawningAngel 4y ago
      You can play e.g. 1. e3 e5 2. e4 whatever And you effectively have a king's pawn opening with colours reversed
      - franknstein 4y ago
        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?
        SargeZT 4y ago
        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 https://www.youtube.com/watch?v=uUfF6l4A6Ks
rocqua 4y ago
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.
- Gehinnn 4y ago
  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.
  - bluGill 4y ago
    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.
  - bee_rider 4y ago
    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.
Scarblac 4y ago
> 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.

philipswood 4y ago

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

dane-pgp 4y ago
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-in-mini-chess-known-with-perfect-play https://chess.stackexchange.com/questions/8755/is-the-result...

Synaesthesia 4y ago

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

deleted 4y ago

[deleted]

pred_ 4y ago

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.

usrusr 4y ago
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"
- Scarblac 4y ago
  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_solution https://en.wikipedia.org/wiki/Connect_Four#Mathematical_solu...
  - usrusr 4y ago
    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)
KptMarchewa 4y ago
Having a winning strategy for black seems impossible though; the discussion is whether white have it or is it a forced draw.
- Someone 4y ago
  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 https://en.wikipedia.org/wiki/Hexapawn) is a win for black on some boards (https://web.archive.org/web/20050330222720/http://www.chessvariants.org/small.dir/hexapawn.html https://web.archive.org/web/20050330222720/http://www.chessv...). Versions that are more complex than chess and are a win for black may exist.

fileeditview 4y ago

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.

Tenoke 4y ago

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

bluecalm 4y ago
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.
- sgjohnson 4y ago
  > always Not always. Almost always.
  - Scarblac 4y ago
    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.
  - bluecalm 4y ago
    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.
    - sgjohnson 4y ago
      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.
      - 4y ago

FartyMcFarter 4y ago

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 https://en.wikipedia.org/wiki/Zugzwang [2] https://www.chess.com/blog/Rocky64/eight-piece-tablebases-a-progress-update-and-some-results https://www.chess.com/blog/Rocky64/eight-piece-tablebases-a-...

franknstein 4y ago

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.

Gehinnn 4y ago
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.
- franknstein 4y ago
  What do you mean skip the first move? Like play a neutral move? Why would such a move exist?
  - YawningAngel 4y ago
    You can play e.g. 1. e3 e5 2. e4 whatever And you effectively have a king's pawn opening with colours reversed
    - franknstein 4y ago
      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?
      - SargeZT 4y ago
        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 https://www.youtube.com/watch?v=uUfF6l4A6Ks

rocqua 4y ago

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.

Gehinnn 4y ago
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.
- bluGill 4y ago
  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.
- bee_rider 4y ago
  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.

Scarblac 4y ago

> 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.