Chess solved?

[Dann Corbit]

Why isn't this position a piece of cake?
Power of the pawn.
Will you give up a piece for a pawn? A computer will be extremely reluctant to unless it can see clear compensation.

Philidor, who coined the expression "Pawns are the soul of chess"
has these piece values when his games are analyzed:

Code: Select all

$ ./pgnlearn philidor.pgn
Reading file: philidor.pgn
Games: 57
Created file: philidor.mat
Loading dataset...
[ 191 x 5 ]
Solving (gradient method)...
Iter 0: [ 0 0 0 0 0 ] -> 0.693147
Iter 1000: [ 0.275333 -0.440085 1.12542 -0.462062 0 ] -> 0.634309
Iter 2000: [ 0.275325 -0.440126 1.12537 -0.462237 0 ] -> 0.634309
Iter 3000: [ 0.275325 -0.440126 1.12537 -0.462237 0 ] -> 0.634309
Iter 4000: [ 0.275325 -0.440126 1.12537 -0.462237 0 ] -> 0.634309
Iter 5000: [ 0.275325 -0.440126 1.12537 -0.462237 0 ] -> 0.634309
Iter 6000: [ 0.275325 -0.440126 1.12537 -0.462237 0 ] -> 0.634309
Iter 7000: [ 0.275325 -0.440126 1.12537 -0.462237 0 ] -> 0.634309
Iter 8000: [ 0.275325 -0.440126 1.12537 -0.462237 0 ] -> 0.634309
Iter 9000: [ 0.275325 -0.440126 1.12537 -0.462237 0 ] -> 0.634309
Iter 10000: [ 0.275325 -0.440126 1.12537 -0.462237 0 ] -> 0.634309

PIECE VALUES:

Pawn:   100
Knight: -159.857
Bishop: 408.741
Rook:   -167.887
Queen:  0
Press ENTER to finish

which is, I suppose what we would expect from someone who loves the pawn (a bishop is a bit like a giant pawn, and you can put one in a pawn structure and it will mostly act like one, at least defensively).
It appears that for Philidor, the queen was worthless and the knight and rooks merely impediments.



A bit silly, perhaps, but the point remains, the pawn is formidable when formed in connected formations.

[corres]

...

Chess is solved.
The result is draw.

[Dann Corbit]

...

Chess is solved.
The result is draw.

Definitely a win for black

[mmt]

The main problem is that the white pieces in the start position are not developed, so you have to spend a fair number of moves getting out from behind the white pawns before all that extra material helps any. And the black pawns help slow down the mate some also,
4k3/8/8/8/8/8/PPPPPPPP/RNBQKBNR w KQ - 0 1 is a mate in 6 or less.

Yeah, the way to prove mates in positions with multiple pieces missing is not to fight for small positional or material advantages but to develop pieces in just a few ways depending on black's actions. And not to mind sacrifices to open things up. So let's say always start with 1.e4 2.d4 3.Qg4 4.Bc4 5.Nc3 6.Bf4 7.Nh3 8.O-O with just contingencies for black's moves that could capture white's pieces. You will still have many positions to analyze because black could play it in various ways but you will get much closer to a mate without having to look at 99.999% of positions. I think you could write a special version of a chess program that would prove a mate with a queen advantage - make it consider a very narrow range of white's moves, try to limit black's choices, try to open up the position.

[corres]

...

Chess is solved.
The result is draw.

Definitely a win for black

Maybe "A" win.
But any more?

[chrisw]

I once ran SF Matefinder on this position for over a day:

[d]r3k2r/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1
It reached a depth of 51 but couldn't find a mate. Existing programs are not optimized to be most efficient when there is a huge advantage but this shows that we are far from solving chess.

Should be possible to direct the search a little.
Do something like make your own white pawns worth zero each, and your knights and bishops worth initially less than one pawn, but worth progressively more as black pawns are removed. Then you favour both fewer pawns and more open files, keeping some minor pieces and allowing Queen and rooks some mobility.

[towforce]

The main problem, as I see it, is that the fundamental nature of chess is exponential.
So I think that a solution will have to deal with that level of complexity.
Any simpler sort of solution would be some kind of stroke of good fortune (like a forced solution nearby).

The "stroke of good luck" that is very likely to exist in chess would be an unexpected emergent pattern. They do tend to arise in complex systems - even when you try to design them out (and nobody has done that in chess).

Do you mean this "stroke of good luck" to be related to chess in general (i.e. the basic rules of moving, winning and drawing) or do you mean all that plus the specific (opening) position we have?

If you mean the former (i.e. the stroke of good luck covers all chess positions), there are theoretical CS reasons why that should not be the case.

What are these cs (Computer Science?) reasons, please?

[duncan]

We're not quite devoid of proof: we know that it's not possible to force material gain in the first 30 or so moves from the starting position. We didn't know that in the last century.

Where do you get that idea from? We certainly do not know that.

If it's possible to make material gain early from the opening position, then where's the sequence of moves that achieves it?

Do you understand the difference between knowing that something is true and not having a counterexample?

Two facts that are factual:

1. As long as something like Moore's Law holds, we continue to be able to do bigger tree searches as time passes

2. No way has yet been found of winning material from the starting position

That forced win of material from the starting position is not possible at any depth is speculation on my part, not fact - but I feel confident that it's correct.

So do you actually agree that the following statement has no basis in fact?

We're not quite devoid of proof: we know that it's not possible to force material gain in the first 30 or so moves from the starting position.

And why did you ask me for a counterexample when I asked you where you base that "knowledge" on? Just to troll a bit more?

Do you know the maximum amount moves it is not possible to force material gain from the starting position. 15 ?

[chrisw]

Perhaps you’ld like to present an audit of your skills, qualifications, experience and achievements in this field alongside the (non-demonstrated) emergent properties and the work you do far did to discover these properties?
Absent that, there’s zero reason to take any of these opinions of yours even marginally seriously.

I've got a better plan: ignore your poncey self-righteousness, and instead do what I want to do, at a time when I choose to do it.

So, the skills audit, unsurprisingly, is a sheet of blank paper.

Many mathematicians who have discovered ways to map patterns in multi-dimensional space in better ways than were known previously went on to make a fortune in financial markets,

Except you’re not a mathematician either.
It’s generally held btw that there is no long term successful method of gaming the markets using “patterns” in historical market behaviour.

so maybe I'll do that

Again, a track record would allow for taking you seriously.

rather than jump to the whims of somebody who is talking to me as if I'm a piece of shit on their shoe!

No whims involved, I was just querying whether there was any base, experiential or otherwise, to your “I believe that, in my opinion bla di bla wild claim bla bla”.

[towforce]

The main problem, as I see it, is that the fundamental nature of chess is exponential. So I think that a solution will have to deal with that level of complexity. Any simpler sort of solution would be some kind of stroke of good fortune (like a forced solution nearby).

The "stroke of good luck" that is very likely to exist in chess would be an unexpected emergent pattern. They do tend to arise in complex systems - even when you try to design them out (and nobody has done that in chess).

Do you mean this "stroke of good luck" to be related to chess in general (i.e. the basic rules of moving, winning and drawing) or do you mean all that plus the specific (opening) position we have? If you mean the former (i.e. the stroke of good luck covers all chess positions), there are theoretical CS reasons why that should not be the case.

What are these cs (Computer Science?) reasons, please?

Please don't go shy on me - I am genuinely interested in what you have in mind!

I have come to realise that I'm actually in the wrong place to discuss ideas for solving chess: a large number of members of this forum have fallen head-over-heels in love with the AB process. Most of the time, "process over product" is ABSOLUTELY the way to go: loving the process that's going to get you want you want is almost always more productive than thinking "I would like to have {product}". In this case, however, it has resulted in attacks against someone thinking about doing things a different way. Questioning whether an idea will work is completely legitimate, and is actually valuable feedback ( ), but in this thread, some have taken this too far: in particular, Chrisw has decided to launch a highly personalised ad-hominem attack against me, with the aim of shutting down discussion about what would amount to a "paradigm shift" away from AB. This has, as he intended, inhibited everyone from further discussion. However, your thoughts about CS reasons, whether or not they're right, are actually of EXTREME importance to me, and at the very least I'd be genuinely grateful if you'd give me a hint as to what you had in mind.

So I'll make you a deal: if you'll share your thoughts about the CS reasons why there wouldn't be a relatively quick way to accurately evaluate all chess positions, then even if it turns out to be not applicable or wrong, while I cannot speak for anyone else, I will make a firm promise that, beyond either acknowledging that you're right or sharing thoughts about why you're not right, you won't get ANY negative feedback from me - and ESPECIALLY not an ad-hominem attack. All you'll get from me (beyond discussion as to whether the reasons you had in mind apply in this case) is warm, positive feedback for being willing to share your thoughts!