Yes, although that's more a resulting artifact of solving chess. The process of building it is the act of solving.
The future of computer Chess
Sort:
May 26, 2009
0
#83
richie, after Nf6 i would go for the line e5 d5 Be2 Ne4 Nf3 and i think white still has good chances!
Wait -- gumpty, I think you just solved it!
I have no wish to communicate further with people whose idea of logic revolves around sarcasm.
I have a similar prejudice.
Well, the good news is that there are treatments for self loathing.
Ricardo_Morro wrote:
I have no wish to communicate further with people whose idea of logic revolves around sarcasm.
Seriously though, if you want to continue to discuss this on its logical merits then I'm happy to do so.
I really do think that you've got the logical linkage between determining if a position is legally attainable and solving chess backwards -- solving chess will allow you to determine if a position is legal, not the other way around....
May 27, 2009
0
#90
I think Gumpty's answer is closer than anyone else's, and he was in the wrong thread.
For some clarity to the issue: for chess to be solvable, it is either a forced win for one side or a draw can be forced. A forced win must end in checkmate; therefore if it is a forced win, it must be a forced checkmate. Therefore, if chess is solvable and not a draw, then the initial arrangement of the pieces must be a forced checkmate in x moves. There may or may not be multiple solutions.
If the game is forceably a draw in y moves, we must ask whether "best play" involves seeking the shortest possible draw or the longest possible draw. Take the case of the forced mate: best play for the aggressor is to seek the shortest possible mate while best play for the defender is to delay mate as long as possible. But if both players are on an equal footing--since the game will end in a draw--how do we decide which draw is optimum?
If a drawn outcome is known in advance, the best strategy might be for each side to move its king knight out and back to its home square three times and declare the draw.
Both these cases, forced win or forced draw, have logical implications that must be examined carefully, with regard to hidden assumptions.
Unknowability of outcome is a condition of the game of chess as we understand it. It is that which provides the two sides with motive: something in which computers are notoriously lacking. It must be provided by their human hosts. There is a reason only small children can amuse themselves very long with tic-tac-toe.
Why do we have to ask if best play involves seeking the shortest or the longest possible draw? If the outcome with best play is a draw in either scenario, then either path is actually on equal footing with respect to the quality of their respective next moves.
The fact is that whether the draw is drawn out or is claimed at the soonest possible opportunity is irrelevant: It is enough to know that the position is drawn.
Yes, but even if both sides in this solved-chess scenario are capable of playing perfectly (which, in your second case, would result in a draw), they would not know that the other player is so capable. The other side may well make a mistake. Otherwise, there would be no point in these perfect players playing a game at all.
In that case, just moving the knight back and forth wouldn't be best play - it would always be to pursue mate (and avoid one's own mate) until a repetition is forced.
After reading all these replies I think it's pretty obvious what will happen in the future. Even if Chess is solved all the computers will still let Wookies win. </end star wars dorkiness>
If the game of chess is a forced mate, both computers have a way to choose moves: one side chooses the line that leads to the shortest possible mate of its opponent, while the other side chooses the line that delays mate as long as possible. This leads to a game (or games, if there are multiple solutions of the same length) that is optimal, ie, is best play for both sides.
But if chess is a forced draw, then on what principle do the computers choose between lines? We cannot even distinguish one as the aggressor, "striving for mate," since the mate does not exist. In this case we have logical trouble because "best play" is undefined. Play could only proceed with a "random generator" enabling the computers to choose between equally drawn lines.
Ricardo_Morro wrote:
If the game of chess is a forced mate, both computers have a way to choose moves: one side chooses the line that leads to the shortest possible mate of its opponent, while the other side chooses the line that delays mate as long as possible. This leads to a game (or games, if there are multiple solutions of the same length) that is optimal, ie, is best play for both sides.
But if chess is a forced draw, then on what principle do the computers choose between lines? We cannot even distinguish one as the aggressor, "striving for mate," since the mate does not exist. In this case we have logical trouble because "best play" is undefined. Play could only proceed with a "random generator" enabling the computers to choose between equally drawn lines.
As I stated before: In this situation repetition is bound to occur as the game would continue indefinitely. Eventually the "random generator" would exhaust its candidate moves for a given repeated position and have to begin repeating lines -- this is detectable, and as a result can be declared drawn.
And what does a random generator do to the concept of "best play"? It seems that in some sense to solve the game is to destroy it, for once solved it is no longer a game.
To return for a moment to the example of tic-tac-toe, which by analogy was used to shoot down my application of Godel's theorem. Even though it is easy to list all possible games of tic-tac-toe (it only being a maximum of 9 moves long), there are still things within its system that cannot be known. For example, given a concluding position, is it possible to know what order the x's and o's were put in the boxes? No, the best we could do would be to say one of several possible ways. So if we made the statement, "the order or moves was such-and-such," we could not know whether it was true or false, and that would be an undecidable proposition.
So Godel's theorem applies even to tic-tac-toe. The question for chess, a much more complex logical system, is this proposition: "Given any position, it is possible to know whether the outcome will be a win or draw." If this proposition is true, chess is solvable. If it is not true, chess is not solvable. But what if this proposition is undecidable?
TheGrobe wrote:
By that same logic Tic-Tac-Toe cannot be solved, but it clearly has.
You're misapplying Gödel's incompleteness theorem.
Ah, "but In mathematical logic, Gödel's incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest." (Taken from Wikipedia.) Is Tic Tac Toe a "trivial formal system"? But on the other hand, there are no "undecidable propositions" in chess, because any given move is either correct or incorrect.
richie_and_oprah wrote:
bondiggity wrote:
For a proof to be complete, you need to address every possible condition. For chess to be completely solved and declared draw, then every single possible line of play will have to be analyzed as ending in draw.
Incorrect.
Only best play needs be shown to draw, as in Tic-Tac-Toe and draughts.
Mistakes lead to decisive results.
Even a cursory look at large databases (40 million games+) gives more evidence than that evidence which is used to justify and accept biological evolution. I am puzzled by people that accept the one, with much less evidence, but continue to argue the other.
Who is to say that h3 or a3 are incorrect moves, in the larger scheme of things?
I think the only way to "solve" chess is to have a complete 32 piece tablebase.