4 ms·

No, the paper only "weakly solves", so it doesn't give a perfect strategy of the type you talk about. Imagine finding a pamphlet written by God that contains a

No, the paper only "weakly solves", so it doesn't give a perfect strategy of the type you talk about. Imagine finding a pamphlet written by God that contains a listing of a perfect game of chess. Armed with it, you will still lose easily to Magnus Carlsen. He will deviate fro| the sequence and you won't know the perfect responses to his moves.

leoff 3y ago
> Imagine finding a pamphlet written by God that contains a listing of a perfect game of chess How would you go to prove that this is the perfect game of chess, if you didn't explore all of it's possible sequences? If they did solve the game, there's no way around knowing all possible outcomes - starting from a fixed given position.
- bluGill 3y ago
  You don't, you trust that God has proved.
  - kreetx 3y ago
    I don't get then, how the paper "solves Othello": how does it determine the perfect game (why is it perfect)?
    - bluGill 3y ago
      The claim (see other threads, it is not clear if the paper really shows this) is that you can follow their plan or any deviation from it known results. That is no matter what I play if you understand their paper you can ensure you don't lose. If I also know their paper I can force a draw, but I won't win.
- Scarblac 3y ago
  Not the perfect game, a perfect game. There will be a huge number of them, many of them very boring and unremarkable
Asraelite 3y ago
"Weakly solved" does actually imply that perfect strategy. I think you're referring to "ultra-weakly solved", which seems to be what the paper did.
- cvoss 3y ago
  A "weak solution" demonstrates perfect play from the initial state and merely implies the existence of a perfect strategy for the entire tree of game states, but, crucially, need not actually produce said strategy. Doing so would be a "strong solution." An "ultra-weak solution" is even less. It gives the win/lose/draw outcome of the perfect strategy, without producing that strategy, nor even producing the game of perfect play from the initial state. This is all covered in the second paragraph of the paper's introduction.
  - Asraelite 3y ago
    So are the definitions in the Wikipedia article then wrong? https://en.wikipedia.org/wiki/Solved_game https://en.wikipedia.org/wiki/Solved_game And if a strategy for perfect play only from the initial position is a strong solution, then what do you call the even more strongly solved case of a strategy for perfect play from any position? The second paragraph of the paper isn't super specific about its definition for "weakly solved", but I read it as agreeing with my statement. It also calls checkers "weakly solved", a game for which a strategy to beat any possible move is known.
charcircuit 3y ago
>He will deviate fro| the sequence and you won't know the perfect responses to his moves. Even if you don't know the moves you will know that you are in a winning / drawn position. Magnus can not find a way to get to a winning position unless you make a mistake.
- Scarblac 3y ago
  That'll be very little help if the perfect game you have starts with 1.e4, but Magnus plays 1.d4. Yes, you're not losing, congratulations. You're still on your own against Carlsen now.
  - sudosysgen 3y ago
    You can just evaluate whether or not a given move will change from a +1 or 0 position to a 0 or -1 position and play it from there. Perfect play in a perfect game means that the objective won't change - in optimal control theory this is called Pontryagin's Maximum Principle or the Bellman optimality criteria. A "value to go" function is enough to find the optimal solution.
    - Scarblac 3y ago
      Yes, but we were talking about a scenario where someone was just given the moves of a single perfect game. Not an oracle that gives you the -1/0/+1 of any position.
      - sudosysgen 3y ago
        Weakly solving a game requires a proof of optimality, which means an evaluation of all variations to prove their value. A sequence of moves in one perfect game isn't weakly solving a game.
- vasco 3y ago
  > unless you make a mistake. That's the easiest part.

leoff 3y ago

> Imagine finding a pamphlet written by God that contains a listing of a perfect game of chess How would you go to prove that this is the perfect game of chess, if you didn't explore all of it's possible sequences? If they did solve the game, there's no way around knowing all possible outcomes - starting from a fixed given position.

bluGill 3y ago
You don't, you trust that God has proved.
- kreetx 3y ago
  I don't get then, how the paper "solves Othello": how does it determine the perfect game (why is it perfect)?
  - bluGill 3y ago
    The claim (see other threads, it is not clear if the paper really shows this) is that you can follow their plan or any deviation from it known results. That is no matter what I play if you understand their paper you can ensure you don't lose. If I also know their paper I can force a draw, but I won't win.
Scarblac 3y ago
Not the perfect game, a perfect game. There will be a huge number of them, many of them very boring and unremarkable

Asraelite 3y ago

"Weakly solved" does actually imply that perfect strategy. I think you're referring to "ultra-weakly solved", which seems to be what the paper did.

cvoss 3y ago
A "weak solution" demonstrates perfect play from the initial state and merely implies the existence of a perfect strategy for the entire tree of game states, but, crucially, need not actually produce said strategy. Doing so would be a "strong solution." An "ultra-weak solution" is even less. It gives the win/lose/draw outcome of the perfect strategy, without producing that strategy, nor even producing the game of perfect play from the initial state. This is all covered in the second paragraph of the paper's introduction.
- Asraelite 3y ago
  So are the definitions in the Wikipedia article then wrong? https://en.wikipedia.org/wiki/Solved_game https://en.wikipedia.org/wiki/Solved_game And if a strategy for perfect play only from the initial position is a strong solution, then what do you call the even more strongly solved case of a strategy for perfect play from any position? The second paragraph of the paper isn't super specific about its definition for "weakly solved", but I read it as agreeing with my statement. It also calls checkers "weakly solved", a game for which a strategy to beat any possible move is known.

charcircuit 3y ago

>He will deviate fro| the sequence and you won't know the perfect responses to his moves. Even if you don't know the moves you will know that you are in a winning / drawn position. Magnus can not find a way to get to a winning position unless you make a mistake.

Scarblac 3y ago
That'll be very little help if the perfect game you have starts with 1.e4, but Magnus plays 1.d4. Yes, you're not losing, congratulations. You're still on your own against Carlsen now.
- sudosysgen 3y ago
  You can just evaluate whether or not a given move will change from a +1 or 0 position to a 0 or -1 position and play it from there. Perfect play in a perfect game means that the objective won't change - in optimal control theory this is called Pontryagin's Maximum Principle or the Bellman optimality criteria. A "value to go" function is enough to find the optimal solution.
  - Scarblac 3y ago
    Yes, but we were talking about a scenario where someone was just given the moves of a single perfect game. Not an oracle that gives you the -1/0/+1 of any position.
    - sudosysgen 3y ago
      Weakly solving a game requires a proof of optimality, which means an evaluation of all variations to prove their value. A sequence of moves in one perfect game isn't weakly solving a game.
vasco 3y ago
> unless you make a mistake. That's the easiest part.