4 ms·

> there are many states in chess where there is not one superior move, but only a probable optimal move I don't think this statement is true given [0], but may

by hiq 6y ago

> there are many states in chess where there is not one superior move, but only a probable optimal move I don't think this statement is true given [0], but maybe I understood you wrong. [0]: https://en.wikipedia.org/wiki/Zermelo%27s_theorem_(game_theory) https://en.wikipedia.org/wiki/Zermelo%27s_theorem_(game_theo...

magicalhippo 6y ago
I think you misunderstood, and that the point was that in chess, especially during the mid-game phase, there's very often not a single clearly superior move but rather several moves that apparently improves your position by roughly the same amount. The uncertainty is due to the inability to scan the entire sub-tree for each move. The theorem you linked to would only be applicable in certain endgame situations.
- benlivengood 6y ago
  > The uncertainty is due to the inability to scan the entire sub-tree for each move. That uncertainty is specifically why chess is unsolved.
  - magicalhippo 6y ago
    Indeed, I was just being a bit pedantic by pointing it out. edit: so to make it crystal clear, I didn't try to argue chess was solved, just to point out why I think that theorem doesn't really apply to most of chess.
- hiq 6y ago
  > there's very often not a single clearly superior move Maybe it's not clear to human players or current engines, but that does not mean it doesn't exist, and indeed the theorem mentioned above states that at least one player has an optimal strategy (either forcing a draw or winning). Obviously, that does not necessarily mean that we'll ever be able to design an engine that can compute this strategy in a reasonable time. I just think that OP meant something other than the usual definition of "solved", maybe they meant that engines are plateauing, but as others have pointed out, there is also little evidence for that for now.
  - magicalhippo 6y ago
    I think I got a big hung up on the following from Wikipedia: It says that if the game cannot end in a draw, then one of the two players must have a winning strategy (i.e. force a win). It made me think it didn't apply in situations where the other player could force a draw. Reading the linked article[1] though made it more clear what it's about, and I agree with what you said. [1]: http://www.math.harvard.edu/~elkies/FS23j.03/zermelo.pdf http://www.math.harvard.edu/~elkies/FS23j.03/zermelo.pdf
- V-2 6y ago
  The same could be argued for tic-tac-toe (which is obviously and trivially solved). There are many positions in which there's more than one move that is perfectly playable.

by hiq 6y ago

magicalhippo 6y ago

I think you misunderstood, and that the point was that in chess, especially during the mid-game phase, there's very often not a single clearly superior move but rather several moves that apparently improves your position by roughly the same amount. The uncertainty is due to the inability to scan the entire sub-tree for each move. The theorem you linked to would only be applicable in certain endgame situations.

benlivengood 6y ago
> The uncertainty is due to the inability to scan the entire sub-tree for each move. That uncertainty is specifically why chess is unsolved.
- magicalhippo 6y ago
  Indeed, I was just being a bit pedantic by pointing it out. edit: so to make it crystal clear, I didn't try to argue chess was solved, just to point out why I think that theorem doesn't really apply to most of chess.
hiq 6y ago
> there's very often not a single clearly superior move Maybe it's not clear to human players or current engines, but that does not mean it doesn't exist, and indeed the theorem mentioned above states that at least one player has an optimal strategy (either forcing a draw or winning). Obviously, that does not necessarily mean that we'll ever be able to design an engine that can compute this strategy in a reasonable time. I just think that OP meant something other than the usual definition of "solved", maybe they meant that engines are plateauing, but as others have pointed out, there is also little evidence for that for now.
- magicalhippo 6y ago
  I think I got a big hung up on the following from Wikipedia: It says that if the game cannot end in a draw, then one of the two players must have a winning strategy (i.e. force a win). It made me think it didn't apply in situations where the other player could force a draw. Reading the linked article[1] though made it more clear what it's about, and I agree with what you said. [1]: http://www.math.harvard.edu/~elkies/FS23j.03/zermelo.pdf http://www.math.harvard.edu/~elkies/FS23j.03/zermelo.pdf
V-2 6y ago
The same could be argued for tic-tac-toe (which is obviously and trivially solved). There are many positions in which there's more than one move that is perfectly playable.