Will computers ever solve chess?

If both While and Black play perfectly it is a draw. The is no "solving chess".

That tempo advantage would never be enough to win a game, and it is also impossible for someone to remember all the winning lines for white. Chess will always continue to be remarkable and fun as it is now.

Most experts agree it is extremely likely that chess is a draw with perfect play. Some point out that the two other possible values are not disproven. No-one can genuinely be certain, only very confident based on the evidence of large numbers of imperfect games with all three results.

White is not in zugzwang

Bam now white is playing as black.

White can lose a tempo whenever he wants.

And yet it has been pointed out numerous times that we do, in fact, already have mathematical ways to investigate endgames for a variety of piece combinations without enumeration.  We already know a good deal of invariants for these kinds of solutions over all of the individual pieces and a variety of combinations.

So the evidence is that this way is indeed possible.  All of the rules have known invariants and define subcollections of the game state space that we can mathematically investigate.  Progress is made all the time in combining the invariants and subcollection descriptions to more complex positions, using combinatorial techniques for various bijections.

So it seems like the impetus should be to provide some mathematical explanation why such a program cannot work.  It cannot be through complexity-space arguments or embedding a turing machine in chess, as that can proven not to work (because of the 50 move rule giving deterministic finalisation).  In fact, I know of no mathematical argument that would cast doubt on such an approach.  It seems purely a guess.

you cant count something which uncoutable

I don't think so, and even if they do, which is not unreasonable to think per se, it will take them much longer to understand the complex algorithm that lies beneath that discovery. To dissect or not to dissect? There are "virtual frogs" dissection programs you can find on the web as well, if you search for them. Nevertheless since I didn't learn much from it, and thousands of others didn't learn much from it, proves that a frog is better alive than dead.

I am surprised (but also pleased) to hear that people are actively working on this. Do they ever publish their findings?

Interesting question! Lets forget about positions that are obviously impossible, for example material combination like one side having 10 queens or 6 queens with 4 pawns still on the board,or positions where both sides are in check.

The first thing that comes to mind then are all positions that contain an impossible pawn structure, for example any position containing white pawns on a2 b2 and a3. Other candidates would be positions with one side still having all pawns on their starting squares while the other side has a material combination that requires promotion (e.g. 2 queens).

I can' think of any impossible positions that don't exploit the limited mobility of pawns though. Anyone else? But we can safely say there must be an awefull lot of positions like this, altough it would be very difficult to give an exact number.

There are positions with Bs outside of pawn structures that are impossible.

But there are also positions that don't rely specifically on pawn structures. There are positions where the last move had to be a check, but there's no check that could possibly have been delivered, and so on. These positions are known to problemists.

I don't immediatly see what clustering of pieces would be really impossible to achieve, except when exploiting pawn structure again, like having all pawns on their starting squares while there are minor pieces outside. So can you give an example of the kind of position you have in mind, one that cannot be reached by any legal move order no matter how illogical?

 Can you give an example? I frankly don't see how a position can have the property "the last move was necessarily a check".

I'm thinking of retrograde problems. I'll see if I can dig some up. Take a look at the works of Raymond Smullyan for some such problems. You can create positions that are illegal based on retrograde analysis that way.

 Ah thanks, I see what you mean now: you could exploit a double-check that cannot have been achieved in one move by the opponent

So that gives us three classes of impossible positions so far: impossible pawnstructures, impossible double-checks, and pieces that cannot be outside of your own pawnstructure (or inside the pawnstructure of the opponent)

Anything else?

But isn't - after

White playing as White and Black lost a tempo as well as he wanted?

 Good point, make that "impossible double-or-more-checks"

Crazy positions like this (from http://timkr.home.xs4all.nl/chess2/diary.htm):

But that link gives an exact line on how to reach this from the starting position, so how is it impossible?

Yeah, there is a long history of the application of mathematics to chess.  The original endgame proofs have been formalised to varying degrees.  As an example, "Proving Correctness of a KRK Chess Endgame Strategy by using Isabelle/HOL and Z3" by Filip Maric, Predrag Janicic, Marko Malikovic shows a fully formal proof that involves no enumeration.  Additionally, work like "Stratification and control of large systems with applications to chess and checkers" by Opens overlay Richard Bellman shows other methods of invariant decompositions that, in particular, are useful for pawn endgames.

Various frameworks have been developed for representation in general analysis over the years.  For instance, "Multi-dimensional structure in the game of chess" by R. H. Atkin was an earlier space decomposition that provided a way to describe positional connectedness compactly.  More recently, "Multilinear algebra and chess endgames" shows a decomposition theorem in tensor algebra that is useful in separating rule-dependency (and thus invariant application).

Generally, this has always been an active area of research at different levels of formality.  The 8-queens problem and the knight's tour are problems that mathematicians have used to extract useful invariants and mathematical structure descriptions that have application to game analysis.  All of the 3 piece endgames (and several 4) were known prior to enumeration due to formal reasoning.

That's the better question, "will people ever solve chess?". No way, as long as psychology, fear, confidence (and over-confidence), bluffs, intimidation, stress, self-doubt, performance anxiety, and all other emotions are involved. 🏁

s23bog wrote:

I take issue with the title of this thread.  I think it should read, "Will people ever solve chess?"  Now, whatever tools we use to accomplish that task is fairly inconsequential.