Will computers ever solve chess?

The "brute force" aspect is purely a matter of processing and memory storage. You're assuming today's technology limits tomorrow's methods.

As for algebra, I mean really, who knows? I acknowledge it might not be possible, but I don't know how anyone can say for certain it isn't. It's not neat enough? That just means it will be a ludicrously complex equation. Chess is a mathematical game, I don't see why it can't be solved using algebra, in the same sense that heat dissipation can be calculated using algebra, despite the enormous complexity of fluid dynamics. But I have to admit I'm just making assumptions here, it's essentially instinct that tells me it can, in theory, be solved this way.

No, heat dissipation can be APPROXIMATED with numerical difference models (not really algebra, but mathematical computations). To do it perfectly, you would need to solve the quantum mechanical equations for the entire system. This would have decillions of parameters (a decillion is a bit less than Avogadro's constant), so is hideously impractical (but not quite as bad as chess).

This is how I like to be argued with.

Perhaps heat dissipation wasn't the best example, considering chess doesn't have quantum properties to take into account. but I still feel algebra has something to offer. I think this because chess is essentially goemetry.

Of course technology has its limits... so does chess.

As a mathematician, this is a very interesting question. Mathematical intuition leads to a very strong belief that the arbitrary nature of chess means it is almost certain there are no dramatic shortcuts. By contrast, it is perfectly normal in mathematics to come to conclusions about an infinite sets of objects with a concise proof. There are very few theorems about chess, just empirical results and approximations arising from large numbers of examples (eg what can be said precisely about rook endings comes from large tablebases of itemised examples, not from mathematical reasoning of any depth).

I have not said that chess cannot be solved either, Sherlock.  I can torch as many straw men as you want to throw up, so you might want to try some other tactic at this point.  It hasn't worked in the 100+ pages since you joined this thread.  Now show me all your supporting papers claiming it will happen in our lifetimes.  Maybe you are forgetting that your "analysis" earlier in this thread claimed it could be solved in as little as 18 years?

Let's be clear:

My position:  Chess cannot be solved with current technology, nor with any reasonably foreseeable technology...so talking about solving Chess right now amounts to fantasy/a call for "magic".  Soft science fiction vs. hard science fiction.

Your position (glossed over and backed off from many times but still not something you admit you were even possibly wrong about):  Chess will be solved, and in as little as 18 years (by your own direct analysis), and most definitely possible in our lifetimes.

You no longer spout that nonsense, because you know it will be picked apart every time.  But you still believe it, for some inane reason.

 It cannot be solved. The number of atoms in the observable Universe will never be even reasonably approached by any calculating device.

Although some positions have a lot of candidate moves there are also a lot of positions only allowing one move or a choice of 2 or 3 so as openings are advancing and endgame positions are also converging on the middlegame it only takes a few small steps for chess to fall to computer analysis

The openings can go in boundless directions: change one move and the whole thing changes. Very similar with the middlegames. The endings is the only place where advances have been made, but as it reaches a certain level of complexity progress will stop.

How did you arrive at this conclusion?

It's a matter of the complexity of chess (a quantifiable thing). Here is a simple guide to (weakly) solving chess as efficiently as possible.

1. Find a strategy by highly efficient approximation methods (eg a la AlphaZero) that allows you to pick moves which have an extremely high probability of being optimal. It is likely that this could be achieved at far less cost than truly solving chess (this has been true for some other games).

2. By brute force, deal with literally every possible position that an opponent could get to by the legal moves available when playing against your strategy as both black and white.

3. If either your worst result against the zillions of combinations of responses is a draw with both black or white or you have won every single game with one of the colours (sounds unlikely), your approximate strategy is actually perfect as desired and you have solved chess,

The problem is that the complexity of this is loosely speaking the square root of the complexity of chess (there is always just one option for the moves for one side, the entire range for the other), and this is too big to be practical.

This is not a bad description of how checkers was solved and the rough idea of square root complexity was verified.

This topic is four years old, but alive and well.  I've seen some ancient threads that are ongoing, but where the OP has died ... (or at least his account has)

Very well thought out @Elroch. I think that's an excellent and viable method of how chess might be solved. Two points I have in mind:

1) If there is a forced win for one side, I haven't seen anyone estimate in how many moves that is possible. One can argue that it could be in as few as 14 moves or so (this can be debated but has not been ruled out AFAIK). That represents a range way outside opening book knowledge. But it's enough moves to take chess to a point where very little is known. It's quite conceivable that a perfectly-played forced win is lurking in that zone somewhere.

2) It's not a bad idea to compare chess with certain aspects of checkers. But there's a few key differences. One is the win condition. In checkers nearly all the pieces need to be eliminated to win a game. In chess, checkmates can exist with a majority of pieces still on the board.

3) Another difference is that in checkers all pieces have the same capability. There is no single piece which dominates. Chess has queens which are significantly stronger than the other pieces. Is it possible that one side can use the dominant pieces (queen and rook) to push around the other pieces to force a win? Checkers has no such dominant pieces - chess does.

Nice analysis.

lol.😝

Thanks, vickalan.

There are two ways in which a side in a powerful position can use this to their advantage (reducing the computation needed) and these are a natural part of an optimal strategy. The first is to limit the number of legal moves available to the opponent. The second is to shorten the games. But the latter applies mostly in winning positions, which are almost certainly not critical. Drawing positions are likely to be a large fraction of those that need to be analysed.

Games where one side deliberately (or accidentally - thinking of the second player who just tries every move some time). aims to extend the game as long as possible before conceding a draw may well dominate the complexity (because they are long and balanced). Note that the length of games is a powerful effect on their contribution, because if you have roughly N choices at each step, N^A is a lot bigger than N^B if A is a moderate amount bigger than B (and if A is a lot bigger, it it ENORMOUSLY bigger).

That being said, it's not really the games that matter to the complexity, but the positions (as there are far fewer of them), but those long games may contribute a lot of positions not seen in shorter games.

The first phrase is a fact, not a conclusion, and if the second phrase were not true, then there would be papers talking about how the solving of chess is imminent as soon as we break X computing barrier that is set to fall in a few years...so, since the existence of "published papers" with suppositions about solving chess (someday, some way) is your standard of scientific proof, I guess there's no more to be said on the subject...surely, when the time comes, papers will just show up to back up your position .

How did you arrive at the conclusion that it will take 18 years, Vickylan?  What about the 18 years claim?  Vickylan?  Eighteen years?  You know...the analysis you did, the 18 years one.  Vickylan?  Maybe you could address your earlier analysis.  I believe you said that the 10^46.7 number could be reduced so far that Chess would be solvable in about 18 years. 

Or are you just going to try to pretend forever that you never said that?  It's a bit embarrassing that you can't own up to it.  I mean, really.  It's right there for everyone to read.

In the meantime, I think I may just stick to replying to your questions from now on with "18 years, Vickylan...", since you seem to ask so many questions that I answer, but you cannot seem to address any yourself.

Vickylan 

It will never be found that chess is a win for either side.

You can forget about trying to compute that chess is a win.

This is because chess a draw if neither side makes a mistake.

I would be inclined to say it's a draw from the starting position, but it's not a certainty. It's possible white is winning, while there's even the very slightest chance that white begins the game in zugzwang, although that is a ludicrously low probability.

But there can be no certainty without the game actually being solved.

Computer ? Fischer ? Tal ? Think......

This is the absolutely precise description of the state of knowledge: by contrast, ponz expresses a very strong belief as a certainty!