It happens to be a fact that other parts of Game Theory, such as those studied by Nash, find more real world applications. The real world is full of the complications absent from classic games like chess (and dealt with by combinatorial game theory).=:
and others that don't immediately spring to mind.
How about this?
Looks like a Win for White.
Now what happens if you replace the missing Pawns?
Then who wins?
I suggest you learn about how game theory is used in the social sciences as well as in determining strategies for complex interactions between agents.
And then you can talk about it on a different thread, because it's nothing to do with this one.
How about this?
Looks like a Win for White.
Now what happens if you replace the missing Pawns?
Then who wins?
I don't see the win in the position you posted. Can you post one against Stockfish? (Any version from 8.)
I suggest you learn about how game theory is used in the social sciences as well as in determining strategies for complex interactions between agents.
And then you can talk about it on a different thread, because it's nothing to do with this one.
I know by now that you have dementia but I will explain once more. The discussion is about the nature of Theory of Games which some people still insist has some connexion to solving chess.
It cannot, because the models used it ToG do not need to be exact. It is however to do with models and as we know, models are no use in solving chess either. Basically, an algorithm is a model and so far they aren't reliable.
The discussion is on the topic "Chess will never be solved, here's why".
To those of us with dementia only combinatorial game theory is relevant to the topic.
Those who have gone beyond dementia think their mother in law and the social sciences are relevant and any old junk like, "Basically, an algorithm is a model ..." (really?), will pass as rational debate.
It would be false to claim an obvious forced win for white.
I would believe 1. e4 is best, but black has options like 1. ...g6 (to avoid the hassle of Qh5+, since 1. ...Nf6 2. e5 is suspect (but even that doesn't look a clear forced win).
Stockfish believes 1. e4 Nc6 is the best response (to stop Qe5 after Qh5+ g6, I presume) and its evaluation makes it most likely a draw.
I suggest you learn about how game theory is used in the social sciences as well as in determining strategies for complex interactions between agents.
And then you can talk about it on a different thread, because it's nothing to do with this one.
I know by now that you have dementia but I will explain once more. The discussion is about the nature of Theory of Games, which some people still insist has some connexion to solving chess.
It cannot, because the models used in ToG do not need to be exact.
With all due respect, you are getting confused again, presumably by repeating the mistake of thinking the applications of parts of Game Theory distinct from Combinatorial Game Theory are relevant to chess.
Combinatorial Game Theory is a branch of mathematics. It is rigorous and unambiguous. It does not even have the complications associated with infinite objects, as it deals only with finite structures.
It is however to do with models and as we know, models are no use in solving chess either. Basically, an algorithm is a model and so far they aren't reliable.
No, combinatorial game theory consists of theorems about finite objects.
No, your words (penultimate post) are not what an algorithm is. Compare it to a good definition (or the wikipedia article).
For example, Euclid's algorithm is a systematic procedure for finding the greatest common divisor (GCD) of two integers. He proved it worked using logic, executed it manually and in recent times it is implemented as computer code to do the same thing.
Another algorithm would be one to generate a tablebase for chess.
There are simple algorithms to play perfect chess as well. Unfortunately they require either stupendous time or stupendous precalculated data (such as a 32-piece tablebase).
optimissed chess can literally be defined by that type of game theory wdym. chess is deterministic with both players having complete information.
Looks like I'm right. If you don't understand that an algorithm is a model when it is intended do model reality
Says who? Algorithms work with abstract representations. They might be related to reality or might not. For example, Euclid's algorithm could be applied (even manually) to these two numbers:
4752395632123176451320547124
374593752375832745238459839
How is this modelling reality? It's about abstract entities called natural numbers.
in the way that assessing a chess position does, and you were once intelligent, something has gone very wrong.
@7849
Coming back to the weak solution of Checkers and the image.
Checkers has 24 men on 32 squares, Chess has 32 on 64 squares.
Schaeffer used Chinook and a 10-men endgame table base,
for Chess Stockfish and a 7-men endgame table base are available.
Checkers is most complicated with 23 men, Chess with 26 men.
For Chess the ICCF Finals draws can be used as seeded lines.
Just like Checkers: stored boundary < relevant search space < legal search space
@7849
Coming back to the weak solution of Checkers and the image.
Checkers has 24 men on 32 squares, Chess has 32 on 64 squares.
Schaeffer used Chinook and a 10-men endgame table base,
for Chess Stockfish and a 7-men endgame table base are available.
Checkers is most complicated with 23 men, Chess with 26 men.
For Chess the ICCF Finals draws can be used as seeded lines.
Just like Checkers: stored boundary < relevant search space < legal search space
"For Chess the ICCF Finals draws can be used as seeded lines."
not necessarily. there is no proof that that is the line.
@8042
There is statistical proof that ICCF WC Finals draws are > 99% certain to be perfect games with optimal play from both sides. They also represent 2 years of play with engines piloted by ICCF (grand)masters. So at least these games are suitable as seeded lines.
If one of these falls under the < 1% cases with 2 errors that undo each other, then that will become apparent during the solving process: then there will appear some line that does not end in a 7-men endgame table base draw.
"If one of these falls under the < 1% cases with 2 errors that undo each other, then that will become apparent during the solving process: then there will appear some line that does not end in a 7-men endgame table base draw."
, yes, and there are10^17 possible lines, taking up 10^17 positions each.
your explanation of what weakly solving chess isnt far off from how it would be done. however, you dont really know what that entails. at best only a couple orders of magnitude can be confidently reduced.
@8045
"there are10^17 possible lines, taking up 10^17 positions each"
++ No, there are 10^17 relevant positions in total. The whole tree has 10^17 nodes: either branching points or leaflets.
@8045
"there are10^17 possible lines, taking up 10^17 positions each"
++ No, there are 10^17 relevant positions in total. The whole tree has 10^17 nodes: either branching points or leaflets.
yeah, 10^17 in the final tree. but you have to find that tree first.
@8047
"you have to find that tree first"
++ Yes: for black play the top 1 Stockfish move after 17 s calculation on a 10^9 nodes/s cloud engine, for white explore the top w (e.g. w = 4) Stockfish moves.
Let us take an example with this ICCF game as seeded line.
1 e4. Grandmaster E with cloud engine e will work on this.
Grandmaster D with cloud engine d will work on 1 d4.
Grandmaster C with cloud engine c will work on other first moves that do not transpose, notably 1 c4 and 1 Nf3.
Grandmaster E and cloud engine e will never have to look at any position with a white pawn on e2, shrinking the search space.
1...e5. Grandmaster E selects this. It is probably that 1...c5 draws as well and 1...e6 and/or 1...c6 might draw as well, but a weak solution only calls for one strategy to achieve the game-theoretic value of the draw.
From now on no positions with a black pawn on e7 are relevant. This shrinks the search space.
2 Nf3. Grandmaster E will study alternatives 2 Nc3, d4, Bc4 later with other seeded games if they do not transpose. There is no need to investigate 2 Ba6?
2...Nc6. Grandmaster E selects this. It is probable that 2...Nf6 draws as well, maybe even 2...d6 draws, but a weak solution only calls for 1 strategy to achieve the draw.
3 Bb5. Grandmaster E will study alternatives 3 Bc4, 3 d4, 3 Nc3 later if they do not transpose. There is no need to investigate 3 Ba6, Nd4, Nxe5, Ng5, Nh4, or Ng1.
3...Nf6. Grandmaster E selects this.
It is probable that 3...a6 draws as well, but a weak solution only calls for 1 strategy to draw.
4 O-O. Grandmaster E will study alternatives 4 d3, d4, Qe2 with other seeded games. From now on no positions with white castling rights need to be considered. That shrinks the search space.
4...Nxe4. Grandmaster E selects this. It is possible that 4...d6 draws as well, but a weak solution only calls for 1 strategy to draw.
From now on no positions with 32 men are relevant. That shrinks the search space.
5 d4. Grandmaster E will study alternatives 5 Re1, Qe2 with other seeded games.
From now on no positions with a white pawn on d2 are relevant. That shrinks the search space.
5...Nd6. Grandmaster E selects this. Other moves might draw, but only 1 way to draw is needed.
6 Bxc6 Grandmaster E will study alternatives 6 dxe5, Bg5, Ba4 with other seeded games.
From now on no positions with 31 men are relevant. That shrinks the search space.
6...dxc6. Grandmaster E selects this. No need to consider 6...bxc6: only 1 way to draw needed.
From now on no positions with 30 men are relevant. That shrinks the search space.
7 dxe5 There are no valid alternatives to consider.
From now on no 29-men positions are relevant. That shrinks the search space.
7...Nf5 Grandmaster E selects this. Only 1 way to draw needed.
8 Qxd8+. Grandmaster E will investigate alternative 8 Qe2 with other seeded games.
From now on positions with 28 men are no longer relevant. That shrinks the search space.
8...Kxd8. Only legal move. From now on postions with 27 men or with black castling rights are no longer relevant. That shrinks the search space.
Now that 26 men are reached, grandmaster E may decide to launch his engine e.
9 h3. Engine e investigates alternatives from its top w moves (e.g. w = 4) after 17 s of calculation at 10^9 nodes/s.
9...Be7. Engine e takes the move from the seeded game.
If it leads to a 7-men endgame table base, then it is right in retrospect.
10 Nc3. Engine e investigates alternatives from its top w moves (e.g. w = 4) after 17 s of calculation at 10^9 nodes/s.
10...Nh4 Engine e takes the move from the seeded game.
If it leads to a 7-men endgame table base, then it is right in retrospect.
11 Nxh4 Engine e will investigate alternatives from its top w moves (e.g. w = 4) after 17 s of calculation at 10^9 nodes/s.
After this move positions with 26 men are no longer relevant. That shrinks the search space.
11...Bxh4 Engine e takes the move from the seeded game. If it leads to a 7-men endgame table base, then it is right in retrospect.
After this positions with 25 men are no longer relevant. That shrinks the search space.
12 Be3 Engine e will investigate alternatives from its top w moves (e.g. w = 4) after 17 s of calculation at 10^9 nodes/s.
12...h5 Engine e takes the move from the seeded game. If it leads to a 7-men endgame table base, then it is right in retrospect. After this positions with a black pawn on h7 are no longer relevant. That shrinks the search space.
etc. ...
57 Bxa1 Engine e investigates alternatives from its top w moves (e.g. w = 4) after 17 s of calculation at 10^9 nodes/s.
@8047
"you have to find that tree first"
++ Yes: for black play the top 1 Stockfish move after 17 s calculation on a 10^9 nodes/s cloud engine, for white explore the top w (e.g. w = 4) Stockfish moves.
Let us take an example with this ICCF game as seeded line.
1 e4. Grandmaster E with cloud engine e will work on this.
Grandmaster D with cloud engine d will work on 1 d4.
Grandmaster C with cloud engine c will work on other first moves that do not transpose, notably 1 c4 and 1 Nf3.
Grandmaster E and cloud engine e will never have to look at any position with a white pawn on e2, shrinking the search space.
1...e5. Grandmaster E selects this. It is probably that 1...c5 draws as well and 1...e6 and/or 1...c6 might draw as well, but a weak solution only calls for one strategy to achieve the game-theoretic value of the draw.
From now on no positions with a black pawn on e7 are relevant. This shrinks the search space.
2 Nf3. Grandmaster E will study alternatives 2 Nc3, d4, Bc4 later with other seeded games if they do not transpose. There is no need to investigate 2 Ba6?
2...Nc6. Grandmaster E selects this. It is probable that 2...Nf6 draws as well, maybe even 2...d6 draws, but a weak solution only calls for 1 strategy to achieve the draw.
3 Bb5. Grandmaster E will study alternatives 3 Bc4, 3 d4, 3 Nc3 later if they do not transpose. There is no need to investigate 3 Ba6, Nd4, Nxe5, Ng5, Nh4, or Ng1.
3...Nf6. Grandmaster E selects this.
It is probable that 3...a6 draws as well, but a weak solution only calls for 1 strategy to draw.
4 O-O. Grandmaster E will study alternatives 4 d3, d4, Qe2 with other seeded games. From now on no positions with white castling rights need to be considered. That shrinks the search space.
4...Nxe4. Grandmaster E selects this. It is possible that 4...d6 draws as well, but a weak solution only calls for 1 strategy to draw.
From now on no positions with 32 men are relevant. That shrinks the search space.
5 d4. Grandmaster E will study alternatives 5 Re1, Qe2 with other seeded games.
From now on no positions with a white pawn on d2 are relevant. That shrinks the search space.
5...Nd6. Grandmaster E selects this. Other moves might draw, but only 1 way to draw is needed.
6 Bxc6 Grandmaster E will study alternatives 6 dxe5, Bg5, Ba4 with other seeded games.
From now on no positions with 31 men are relevant. That shrinks the search space.
6...dxc6. Grandmaster E selects this. No need to consider 6...bxc6: only 1 way to draw needed.
From now on no positions with 30 men are relevant. That shrinks the search space.
7 dxe5 There are no valid alternatives to consider.
From now on no 29-men positions are relevant. That shrinks the search space.
7...Nf5 Grandmaster E selects this. Only 1 way to draw needed.
8 Qxd8+. Grandmaster E will investigate alternative 8 Qe2 with other seeded games.
From now on positions with 28 men are no longer relevant. That shrinks the search space.
8...Kxd8. Only legal move. From now on postions with 27 men or with black castling rights are no longer relevant. That shrinks the search space.
Now that 26 men are reached, grandmaster E may decide to launch his engine e.
9 h3. Engine e investigates alternatives from its top w moves (e.g. w = 4) after 17 s of calculation at 10^9 nodes/s.
9...Be7. Engine e takes the move from the seeded game.
If it leads to a 7-men endgame table base, then it is right in retrospect.
10 Nc3. Engine e investigates alternatives from its top w moves (e.g. w = 4) after 17 s of calculation at 10^9 nodes/s.
10...Nh4 Engine e takes the move from the seeded game.
If it leads to a 7-men endgame table base, then it is right in retrospect.
11 Nxh4 Engine e will investigate alternatives from its top w moves (e.g. w = 4) after 17 s of calculation at 10^9 nodes/s.
After this move positions with 26 men are no longer relevant. That shrinks the search space.
11...Bxh4 Engine e takes the move from the seeded game. If it leads to a 7-men endgame table base, then it is right in retrospect.
After this positions with 25 men are no longer relevant. That shrinks the search space.
12 Be3 Engine e will investigate alternatives from its top w moves (e.g. w = 4) after 17 s of calculation at 10^9 nodes/s.
12...h5 Engine e takes the move from the seeded game. If it leads to a 7-men endgame table base, then it is right in retrospect. After this positions with a black pawn on h7 are no longer relevant. That shrinks the search space.
etc. ...
57 Bxa1 Engine e investigates alternatives from its top w moves (e.g. w = 4) after 17 s of calculation at 10^9 nodes/s.
that doesnt work lmao. you prove absolutely nothing, literally by the second move you have a false assumption
It shouldn't be beyond the capabilities of @Optimissed to understand that the only part of the broad subject of Game Theory that is relevant to chess is Combinatorial Game Theory. While the other parts involve rigorous analysis of abstractions (in the way I referred to earlier), combinatorial game theory is intuitively simpler to comprehend.