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loseyourname
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Why does this thread have no posts in it?
selfAdjoint said:I don't think the OP meant solvable through brute-force enumeration. For example checkers has a decision rule expressible in a sentence or two. Indeed one can ask questions like is chess NP-complete? For example could you show that solving chess would involve solving the traveling salesman problem (which given their definitions, doesn't seem intuitively outrageous to me)?
pallidin said:Chess provides for the aspect of "selective-suicide" during a thrust towards an achieved objective. That type of involvement renders computer computation very, very dificult.
If there are other moves that you can make that gain long term advantages that can be exploited, then it's not statistically the "best" move, now, is it?Even if you decided what is statistically the "best" move in every given situation there are other moves you can make that gain long term advantages that can be exploited.
Computers can do that, by the way. The scoring systems computers use account for a lot more than just material value. For example, see http://www.frayn.net/beowulf/theory.html.Someone already mentioned sacrifices to control the center.
Rach3 said:That doesn't make sense - chess doesn't scale on the size of an input. There's no meaning to the "computational complexity of chess" - it's simply O(1).
If there are other moves that you can make that gain long term advantages that can be exploited, then it's not statistically the "best" move, now, is it?
No it's not -- they were talking about perfect play. It takes O(1) time to, given a board position, return one of the following:-Job- said:I don't agree. In this case the input to the problem is the algorithm(s) that each player is using.
No it's not -- the size of an algorithm has little bearing on how long the algorithm will run.The problem of determining which player wins, black or white, is solvable in a deterministic manner (assuming that no player is running a randomized algorithm) and its complexity is dependent on the size of the algorithms.
A computer can't compute that (yet). They simply compute something they hope is a decent approximation.Renge Ishyo said:The "best" move is simply the one that when compared to other possible moves yields the highest stastical probability of leading to a sequence that will win the game.
No it doesn't. A decent chess program will remember all of the relevant analysis it did from the previous turns, and continue analysis from that point.The problem is that the computer "re-evaluates" the entire situation after every move.
Why not? It's easy enough to implement a heuristic that rewards having a good pawn line when the opponent doesn't have any knights.It cannot say to itself, "making this move puts me in a disadvantage in this way, but I want to get rid of both his knights early on anyways so that I can build my pawn line freely without worrying about them jumping it."
Creativity is usually a bad thing. In fact, computers are well-known for punishing "creative" play.It wins on percentages, it loses to creativity.
Hurkyl said:No it's not -- they were talking about perfect play.
... by which the "chess" problem, being solved in determining "who wins", is the problem of determining which player will win. So i don't see where you're coming from, but whatever, rather than get into a quote cycle, i'd rather argue the following:Greg825 said:Theoretically this would result in only one possible outcome from the beginning of the game (white wins, loses, or a draw) if both players play optimally (like tic-tac-toe), which is why I'd call it "solved".
chroot said:If you presented all the members of the grandmaster community with an entire chessboard in some specific state, would they generally all be in agreement about which move to make next?
- Warren
ecolitan said:Chess is a boring program for computers, if you want a real challenge try to make a computer play GO.
chroot said:Yes, chess is theoretically solvable.
This is, in fact, one of the most naive approaches to developing a chess computer. You simply create a database of every possible board configuration, and compute the move to make in each configuration. Standard metrics can be used to compute the best move given each position. You end up with an enormous database which is the "solution" to chess, since you will have considered every possible move for every possible configuration, and determined the best for each.
This is not the case. Here's from wiki:Hurkyl said:But if you meant to talk about strategic play, then yes, humans are currently better than computers in the strategic domain for chess.
http://en.wikipedia.org/wiki/Human-computer_chess_matchesHuman-computer chess matcheswiki said:After convincing victories in two matches in 2005 and 2006, it appears that chess programs can now defeat even the strongest chess players.
Since 2007 Rybka has played some odds matches against grandmasters. Jan Ehlvest first lost a pawn-odds match, then later lost a match when given time, color, opening, and endgame advantages.[citation needed] Roman Dzindzichashvili then drew a match when given pawn and move odds.[citation needed]
In September 2008, Rybka played an odds match against Vadim Milov, its strongest opponent yet in an odds match. (Milov at the time had an Elo rating of 2705, 28th in the world). The result was a narrow victory to Milov: He had won 1½-½ when given pawn-and-move, and 2½-1½ (1 win, 3 draws) when given exchange odds but playing black. In two standard games (Milov had white, no odds), Rybka won 1½-½.
I didn't say "humans are better than computers" -- I said "humans are better than computers at strategic play". Conversely, computers are better at tactical play.jimmysnyder said:This is not the case.
This article is almost, but not quite relevant to your point. It would be relevant if the human-computer team (computer for tactics, human for strategy) consistently beat pure (strategy deficient) computer. However, that is not what the article is about.Hurkyl said:See this link; it describes something I was saying earlier.
In the context of games, a game is considered "solvable" if there exists a known optimal strategy or set of moves that will always result in a win, draw, or loss for a player.
No, chess is not considered a solvable game. While there are certain openings and strategies that are known to be advantageous, the complexity of the game makes it impossible to determine a guaranteed winning strategy for every possible game.
Yes, computers can solve games like chess by using algorithms and brute force techniques to analyze all possible moves and determine the best course of action. However, this does not necessarily mean that the game is "solvable" in the traditional sense.
Studying the solvability of games like chess can provide insights into the complexity of decision making and the capabilities of artificial intelligence. It can also help inform strategies and improve gameplay for human players.
Yes, there are certain games that are considered unsolvable, meaning that there is no known optimal strategy or set of moves that will always result in a win, draw, or loss. Examples include Go and checkers, which have a significantly higher number of possible game states compared to chess.