j_king:

i'm not sure that we're disagreeing.  i looked over some of your old posts and it looks like you agree that solving chess by a using a position tree is theoretically possible but currently impossible given our current means (storage space and calculating time, etc.).  so thanks for the wikipedia links but judging by what you have been saying, i do not disagree with any of the facts presented in them.

on the other hand - i think it is interesting to consider the possibility of solving chess by means other than using a position tree.  i'm NOT talking about an equation that would calculate the best possible move by considering all the possible positions for move 1, and for move 2, and for move 3, etc.  and then telling you the best move on move 1 (which is essentially a position tree approach).  i AM talking about an completely new way to approach the "best move" criteria. 

you asked me for an example and i'll try.  imagine if it was discovered that there was no way to stop fool's mate.  you would have "solved" chess in creating an unbeatable line for white and you would not have had to calculate all possible chess positions.  now, obviously that's not the best example since fool's mate is easily stopped, but it's the best i can come up with.  i'm not claiming to have solved chess here, i do, however, think that it is solveable.

on the other hand - if (as many people believe) chess is a neutral game where perfect play will always end in a tie, then solving chess is much simpler given that you could play from the beginning for a game ending in either three fold repetition, stalemate, or a draw.

johnny263 wrote:

j_king:

i'm not sure that we're disagreeing.  i looked over some of your old posts and it looks like you agree that solving chess by a using a position tree is theoretically possible but currently impossible given our current means (storage space and calculating time, etc.).  so thanks for the wikipedia links but judging by what you have been saying, i do not disagree with any of the facts presented in them.

on the other hand - i think it is interesting to consider the possibility of solving chess by means other than using a position tree.  i'm NOT talking about an equation that would calculate the best possible move by considering all the possible positions for move 1, and for move 2, and for move 3, etc.  and then telling you the best move on move 1 (which is essentially a position tree approach).  i AM talking about an completely new way to approach the "best move" criteria. 

you asked me for an example and i'll try.  imagine if it was discovered that there was no way to stop fool's mate.  you would have "solved" chess in creating an unbeatable line for white and you would not have had to calculate all possible chess positions.  now, obviously that's not the best example since fool's mate is easily stopped, but it's the best i can come up with.  i'm not claiming to have solved chess here, i do, however, think that it is solveable.

Well, to be formal, another poster did point out the difference between an algorithm and a function.

The reason why that is important is because from a blank board, White has approximately 20 moves available. The Fool's mate example requires a very specific sequence of moves in order to be possible. In order to "solve" chess, this equation would have to produce a Fool's mate 100% of the time by playing Black. That is simply not possible if White doesn't follow the specific sequence.

A function simply cannot exist that can solve chess.

The only avenue I can see which one may pursue besides the modern algorithms we've been developing for over fifty years is a state-machine approach. Such a machine would probably be enormously complex; relying on sets of algorithms for determining the next move of play based on its current state. However; even if such a machine were possible, it would only be able to weakly solve chess as by the conditions of solvability I linked to in my previous posts.

"Solving" chess is a goal pursued since some time in the mid-30's. Some of the greatest minds in computer science and mathematics have thrown their weight at it. However, it's complexity will be (thankfully) out of the bounds of a strong solution for the foreseeable future. If it were solved already, it would be an awfully boring game -- which we do know without a doubt that it is not. :)

I love it - every math genius in the room poked there head up at this question, and me also - however, I have the answer...

NO!

Now instead of investing hours in a formula, learn how the pieces move.  Your opponent will lose on time trying to apply the equations!

Haha well from a mathematical point of view there's two main thought that come to my mind the first is;

As mentioned by Jonny236 chess is generally accepted amoungst the mathematic community as being a nuetral game - however any concievable 'golden strategy' would be so much more complex than the equivelant strategies for Naughts and Crosses and Checkers that it would be impractical to apply this set of rules to a human Vs human game of chess.

Personally I believe that the reason there is yet to be a strategy of this form is that chess is a dynamic game - the true relative value of each piece and each square changes based on every move that is played aswell as every move that is NOT played. It is constantly evolving and as such any set of rules that is applied to a game with have to take account of this fact.

The second idea that springs to mind is also only really applicable to a computer but how about an algorythmic probabalistic analysis of games that then defines the optimal move based on a data set collected of previous games - assuming that you can get a large enough uncorrupt set of data this seems to be the strongest method for writing a super chess programme.

A similar programme would be something like 'sender base' the online threat management database created by Ironport of Cisco. The way in which this works is hundreds of thousands of networks are installed with an 'Ironport' which monitors and detects all digital attacks against said network - it then records the information of ALL successful and unsuccessful digital attacks against the network and stores this information on the 'sender base' database. This data is then compiled and used to probabalistically analyse the probability of an 'email' or 'ping' etc being malicious.

Similar if you could inbed a algo based programme into a popular online chess site you would be able to collect a massive data set of moves, sequences of moves and entire games that could then be combined to create an unbiased analysis from a purely probability driven pov. Obviously this would take the role of a modern day IBM project LOL.

This is just an idea but I'd be really interested in hearing what the other 'maths and chess' crowd's thoughts are on such a thing?

Ta for listening to my rabble!

Sam