Solving Chess Kickstarter

[Brunetti]

does one need exhaustive analysis to assess this position ?

Only from a scientific point of view, but we already "know" it's won.
You can keep removing Black's pieces leaving at least one and the assessment won't change, I think.


Alex

[AlvaroBegue]

Duncan's position _is_ a certain win, I don't think it's necessary to prove it by brute force, we don't need a scientific proof for obvious facts like that. E.g., there's no need for TB's (or other exhaustive analysis) to assess K+R vs K, or KRR vs KP, KQRR vs KPP and so on.
The Qh5 example is different, I agree.

Alex

does one need exhaustive analysis to assess this position ?

[d]rnbqkb1r/pppppppp/8/8/8/8/PPPPPPPP/4K3 b kq - 0 1

The thing is by "[weakly] solving chess" people mean "prove a theorem that states what the minimax value of the initial chess position is". Even if we replace the initial chess position with some very unbalanced position, we are still talking about proving a theorem. We may have very strong intuitions that a theorem is true, and our intuitions might even be correct. However, that's not how math works: You either have a proof or you don't.

Unless you can prove some lemma that makes precise the notion that with overwhelming material advantage and barring some exceptions you are certain to win, exhaustive analysis is the only tool we have to prove this type of theorem.

[Brunetti]

However, that's not how math works: You either have a proof or you don't.

I totally agree. But *this* is not math, is chess

Alex

[mvk]

We may have very strong intuitions that a theorem is true, and our intuitions might even be correct. However, that's not how math works: You either have a proof or you don't.

In theory. In practice, mathematicians tend to leave difficult problems unsolved for centuries, but still base their work on the assumption that they are true. And those that are proved, are only proved with a lot of high-level hand waiving, and have no machine-verifiable counterpart.

[AlvaroBegue]

We may have very strong intuitions that a theorem is true, and our intuitions might even be correct. However, that's not how math works: You either have a proof or you don't.

In theory. In practice, mathematicians tend to leave difficult problems unsolved for centuries, but still base their work on the assumption that they are true.

There are many theorems in number theory that are contingent on some version of the Riemann hypothesis being true. I don't know of any other difficult problem that fits this pattern.

And those that are proved, are only proved with a lot of high-level hand waiving, and have no machine-verifiable counterpart.

That is a valid criticism of how math is currently done, but things are changing. Many important theorems have been formally verified (e.g., the prime number theorem, the four-color theorem, the Jordan curve theorem...).

[bob]

Duncan's position _is_ a certain win, I don't think it's necessary to prove it by brute force, we don't need a scientific proof for obvious facts like that. E.g., there's no need for TB's (or other exhaustive analysis) to assess K+R vs K, or KRR vs KP, KQRR vs KPP and so on.
The Qh5 example is different, I agree.

Alex

does one need exhaustive analysis to assess this position ?

[d]rnbqkb1r/pppppppp/8/8/8/8/PPPPPPPP/4K3 b kq - 0 1

Do you need a formal proof, or exhaustive proof to show that

sin^2(x) + cos^2(x) = 1?

Or can you just try a few values and see if it works?

the word "proof" is pretty well-defined. intuitive observation is not good enough. Most would agree with your position above being won for black. But that still isn't a "proof".

[bob]

First, as far as the queen goes, it is likely a loss. But until it is proven, it is just an assumption. As to any advantage for white/black, I don't think that would be the issue. If anything, it would be black's knight ending up at h5 probably.

I meant what would be black's advantage to win in this position ?

[d]rnb1kbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1

In Crafty, for example, reductions, pruning and null-move can be disabled by the user if wanted. It will be very slow to reach any reasonable depth, however.

how would do you do it with crafty in winboard?

step one: start crafty in a normal console window

type "personality list"


Now look at the output. You want to find all terms that apply to any of this selectiveness. For example:

2 null-move reduction 3

to your .craftyrc or crafty.rc file, add the following

personality 2 0

which changes item 2 to zero. Repeat for the other selective terms such as

pers 4 0
pers 5 0 {these disable LMR}

pers 6 0 {disables forward pruning}


Now you have a very accurate searcher, but a very slow one as far as reaching significant depth goes.

[duncan]

The thing is by "[weakly] solving chess" people mean "prove a theorem that states what the minimax value of the initial chess position is". Even if we replace the initial chess position with some very unbalanced position, we are still talking about proving a theorem. We may have very strong intuitions that a theorem is true, and our intuitions might even be correct. However, that's not how math works: You either have a proof or you don't.

Unless you can prove some lemma that makes precise the notion that with overwhelming material advantage and barring some exceptions you are certain to win, exhaustive analysis is the only tool we have to prove this type of theorem.

since we are talking about the slight possibilty of white winning, I would have thought the question is does overwhelming material advantage and no positional inferiority guarantee that you will not lose or is exhaustive analysis the only tool we have to prove this type of theorem (or perhaps being black might be an advantage)

[duncan]

First, as far as the queen goes, it is likely a loss. But until it is proven, it is just an assumption. As to any advantage for white/black, I don't think that would be the issue. If anything, it would be black's knight ending up at h5 probably.

I meant what would be black's advantage to win in this position ?

[d]rnb1kbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1

In Crafty, for example, reductions, pruning and null-move can be disabled by the user if wanted. It will be very slow to reach any reasonable depth, however.

how would do you do it with crafty in winboard?

step one: start crafty in a normal console window

type "personality list"


Now look at the output. You want to find all terms that apply to any of this selectiveness. For example:

2 null-move reduction 3

to your .craftyrc or crafty.rc file, add the following

personality 2 0

which changes item 2 to zero. Repeat for the other selective terms such as

pers 4 0
pers 5 0 {these disable LMR}

pers 6 0 {disables forward pruning}


Now you have a very accurate searcher, but a very slow one as far as reaching significant depth goes.

thanks for that

duncan

[duncan]

Duncan's position _is_ a certain win, I don't think it's necessary to prove it by brute force, we don't need a scientific proof for obvious facts like that. E.g., there's no need for TB's (or other exhaustive analysis) to assess K+R vs K, or KRR vs KP, KQRR vs KPP and so on.
The Qh5 example is different, I agree.

Alex

does one need exhaustive analysis to assess this position ?

[d]rnbqkb1r/pppppppp/8/8/8/8/PPPPPPPP/4K3 b kq - 0 1

Do you need a formal proof, or exhaustive proof to show that

sin^2(x) + cos^2(x) = 1?

Or can you just try a few values and see if it works?

the word "proof" is pretty well-defined. intuitive observation is not good enough. Most would agree with your position above being won for black. But that still isn't a "proof".

what about going a bit further and saying the combination of black to move gives it a positional advantage and combined with strong material advantage means black cannot lose and white will not win.
does one need exhaustive analysis to prove this. ?