What do you call "solve"?

[fern]

The discussion about chess solved or not, some day, should begin defining what is to solve, isn,'t it?
If "to solve" means that there will be a deterministic series of moves that from move one conducts to mate or draw, that seems to me irrelevant even for discussion. In fact, preposterous.
You do not need that kind of serie to solve something like chess.
In a certain sense chess is or has been already solved. It is solved each time a game finish with a determinate result coming from a decently played game. But It is solved also if the end comes from a preposterous game.
In all those ocasions chess solves itself, that is, its laws and structures give room to an end according to those rules.
Solution - to solve- is NOT the same as to know about a deterministic, previsible, one-path road.
If you see the problem in that way, you are not talking of solving or no chess, but of the very different problem of forecasting a determinate, historic, specific game from beginning to end, move by move.
There is not such a thing as an ultimate historic path equivalent, if we know it, to solve chess.

Fern.

[Dann Corbit]

The discussion about chess solved or not, some day, should begin defining what is to solve, isn,'t it?
If "to solve" means that there will be a deterministic series of moves that from move one conducts to mate or draw, that seems to me irrelevant even for discussion. In fact, preposterous.
You do not need that kind of serie to solve something like chess.
In a certain sense chess is or has been already solved. It is solved each time a game finish with a determinate result coming from a decently played game. But It is solved also if the end comes from a preposterous game.
In all those ocasions chess solves itself, that is, its laws and structures give room to an end according to those rules.
Solution - to solve- is NOT the same as to know about a deterministic, previsible, one-path road.
If you see the problem in that way, you are not talking of solving or no chess, but of the very different problem of forecasting a determinate, historic, specific game from beginning to end, move by move.
There is not such a thing as an ultimate historic path equivalent, if we know it, to solve chess.

Fern.

To solve chess is to determine for absolute certainty whether the outcome for white given the starting position is a win, a loss, or a draw.

Many games have been formally proven. Examples are tic-tac-toe (a draw), Connect 4 (a draw) and Checkers (a draw). Chess might be a draw if played perfectly but we don't know yet.

Even if we solve chess that does not mean that humans will be able to force a draw when they play because the sequences may be too difficult to memorize.

So we'll probably continue to play it just as much even when (and if) it ever does get solved.

[Dr.Wael Deeb]

Interesting thoughts from both of you,thanks

[fern]

Well, Dann, I cannot believe in that approach that implies there is a set of moves that from the beginning conduct to an specific end.
It is not a matter of numbers or difficulty to know about that set of moves. It is a matter of deeper susbtance. I mean, If you are right that set of moves should exist somewhere -Plato world of ideas, perhaps- and it is a matter of time to get it and even if we cannot get it, it is theoretically available for someone, at least for God.
I have not the words or acumen in this momnt to explain myself really well about this, but I feel this issue touches in some sense with Quantum mechanics and so about the strange relation between knowledge and reality.
I tend to think chess is solvable in practical terms, not in specifically, mathematical terms.
Cluster of positions get room to anothers that are linked in a chain that goes from beginning to end in a sense of solution. Perhaps.
But the ways to go from one to the other are or should be infinite.
In this sense, chess is unsolvable.
Just think in a tank of gas. We can know about macroscopic variables such as heat, pressure, volumen, etc.
We cannot know about specific relations or positions between each molecule of gas to the other.

My best
fern

[Dann Corbit]

Well, Dann, I cannot believe in that approach that implies there is a set of moves that from the beginning conduct to an specific end.
It is not a matter of numbers or difficulty to know about that set of moves. It is a matter of deeper susbtance. I mean, If you are right that set of moves should exist somewhere -Plato world of ideas, perhaps- and it is a matter of time to get it and even if we cannot get it, it is theoretically available for someone, at least for God.
I have not the words or acumen in this momnt to explain myself really well about this, but I feel this issue touches in some sense with Quantum mechanics and so about the strange relation between knowledge and reality.
I tend to think chess is solvable in practical terms, not in specifically, mathematical terms.
Cluster of positions get room to anothers that are linked in a chain that goes from beginning to end in a sense of solution. Perhaps.
But the ways to go from one to the other are or should be infinite.
In this sense, chess is unsolvable.
Just think in a tank of gas. We can know about macroscopic variables such as heat, pressure, volumen, etc.
We cannot know about specific relations or positions between each molecule of gas to the other.

My best
fern

There may not be any set of moves.
It may be that we have to trace down every possible path and prove them.

IOW, It may or may not be that white should lead with 1.e4. Perhaps 19 of 20 possible first moves have the same outcome and the 20th one does not.

With checkers (for instance) the game was proven from both ends.

They formally validated openings (e.g. proving that moves other than the ones listed in their openings lost).
They formally validated endgame tablebase sets.
That left only middle ground. So they had to prove all moves between opening moves up to the endgame moves. But that is much easier than searching the whole possible solution space.

Perhaps a chess solution could follow similar lines of reasoning. I don't know.

[Cubeman]

I thought that the typical 7x6 Connect 4 was a win for the first player?

[Dann Corbit]

I thought that the typical 7x6 Connect 4 was a win for the first player?

You are right, I should have looked it up. I thought I remembered it correctly but did not.

http://en.wikipedia.org/wiki/Solved_game

[fern]

Is possible to explore every posible path?
I mean, in terms of practical time and processor resources compared with the number of possible paths.
Maybe so or maybe not.
Anyway, my feeling still is the problem is far more complicated.
I have the idea that transformation occurs at every node. I mean, when an answer is given to one move that begin a path, something change in such a manner that there is not anynmore that supposed path to explore as it was before the so called first move was played.
It is difficult to explain, but I tried it in my thesis in sociological causation.
I demostrated -I believe I did- there that even in a closed cluster of causal factors, -say, in a matrix of a determinated number of free spaces to be filled- the result of filling this or that changes the overall matrix, so a new causal situation arises instead of a degree of closing of the pre existent one.
Ok, this is difficult to explain without some maths and I am no going to do it again here....
I became old and lazy regards
Fern

[Uri Blass]

The discussion about chess solved or not, some day, should begin defining what is to solve, isn,'t it?
If "to solve" means that there will be a deterministic series of moves that from move one conducts to mate or draw, that seems to me irrelevant even for discussion. In fact, preposterous.
You do not need that kind of serie to solve something like chess.
In a certain sense chess is or has been already solved. It is solved each time a game finish with a determinate result coming from a decently played game. But It is solved also if the end comes from a preposterous game.
In all those ocasions chess solves itself, that is, its laws and structures give room to an end according to those rules.
Solution - to solve- is NOT the same as to know about a deterministic, previsible, one-path road.
If you see the problem in that way, you are not talking of solving or no chess, but of the very different problem of forecasting a determinate, historic, specific game from beginning to end, move by move.
There is not such a thing as an ultimate historic path equivalent, if we know it, to solve chess.

Fern.

To solve chess is to determine for absolute certainty whether the outcome for white given the starting position is a win, a loss, or a draw.

By this definition you may solve a game without knowing the best moves
in order to win games practically.

Imagine the following game that is similiar to chess and start from the opening position of chess but white has the following advantages relative to chess:

1)The target of white is not to lose and a draw is considered as a win for white.

2)White has the right to make a null move in the first move.

It is clear that white can win the game(if white does not lose in normal chess then white win in this game and if white lose in normal chess then
white win by starting with null move).

Inspite of it I can say that it is clear that I cannot say what is the best move for white and the knowledge that white wins does not help me to have a program to play the game perfectly.

Uri

[Sven]

Is possible to explore every posible path?
I mean, in terms of practical time and processor resources compared with the number of possible paths.
Maybe so or maybe not.
Anyway, my feeling still is the problem is far more complicated.
I have the idea that transformation occurs at every node. I mean, when an answer is given to one move that begin a path, something change in such a manner that there is not anynmore that supposed path to explore as it was before the so called first move was played.
It is difficult to explain, but I tried it in my thesis in sociological causation.
I demostrated -I believe I did- there that even in a closed cluster of causal factors, -say, in a matrix of a determinated number of free spaces to be filled- the result of filling this or that changes the overall matrix, so a new causal situation arises instead of a degree of closing of the pre existent one.
Ok, this is difficult to explain without some maths and I am no going to do it again here....
I became old and lazy regards
Fern

I don't see your point, especially not why you see a connection between a game like chess and some sort of sociological causation. Things are quite different in chess IMO.

In games like chess you are not dealing with a matrix but with a tree consisting of nodes connected by edges, where the root node represents the initial position of the game, leaf nodes represent final (end of game - mate or draw) positions, intermediate nodes represent non-final positions, and edges represent chess moves made on the board. Illegal moves/positions are discarded, i.e. are logically "removed" from the tree. For the remaining tree the following strict rules apply (from my understanding of game theory, applied to chess):

- Each node has one of the values "unknown", "win", "draw", or "loss", where "win" and "loss" are relative to the moving side at that node.

- Initially all nodes have the value "unknown".

- "Evaluating" a leaf node means replacing "unknown" by one of the other three values according to the chess position that belongs to that node.

- Transpositions are special cases that lead to additional "leaf nodes" since the value of a node that corresponds exactly to another node that has already been evaluated can be remembered and taken from that memory instead of evaluating it again (TT hash).

- Threefold repetitions (leading to "draw" value) are another special case of additional leaf nodes, these can be detected by analyzing the path from the root node to the current node.

- The value of any intermediate node P can be derived from the values of its direct successors:

a) If at least one of the successors of P has the value "loss" then P's value is "win". The edge leading from P to that particular successor can be remembered as an optimal move.

b) If a) is not true but at least one of the successors of P has the value "unknown" then P's value is "unknown".

c) If a) and b) are not true but at least one of the successors of P has the value "draw" then P's value is "draw". The edge leading from P to that particular successor can be remembered as an optimal move.

d) If neither a) nor b) nor c) are true, which means that all successors of P have the value "win", then P's value is "loss". All edges to any direct successor are optimal.

- Based on the rules given above the value of the root node can be determined exactly, and if it is different from "unknown", an optimal sequence of moves is given since there is an optimal move at the root node as well as at each node on the path to a leaf node that is reached by making an optimal move. (Note that things like "shortest mate" like in endgame tablebases are not covered by these very simple rules. Note further that an optimal move never crosses a node with value "unknown".)

The "only" open point for chess is therefore to replace all "unknown" values by one of "win", "draw", or "loss", which can be done by evaluating as many leaf nodes as necessary to obtain a value different from "unknown" for the root node.

A very abstract algorithm to evaluate a node P (EDIT: an intermediate node) would look like this:

Code: Select all

If (value(P) is "unknown") {
    For (all successors of P) Do Until (value(P) is not "unknown") {
        evaluate(successor);
        update value(P) "according to rules a-d";
    }
}
return value(P);

I would consider this as kind of a proof that chess can be solved, although it does not tell us how long this could take, or how it could be achieved. But formally it is possible since we have "only" a game tree to process.

Sven