#2841
"One thing I am sure about that chess can’t be solved in a human mind, Which means no human can handle every position’s response."
++ I am not so sure about that. Allen solved Connect Four by brute force supplemented by knowledge, but Allis solved it with a set of 9 rules.
For chess it is beneficial to incorporate knowledge into the brute force method as well.
It may also be that chess can be weakly solved by a set of rules.
For example Lasker formulated a set of 4 rules about the opening.
1) Play only d- and e-pawns.
2) Play knights before bishops.
3) Do not play the same piece twice.
4) Do not pin the KN with the QB before the opponent has castled O-O.
One can think of many more rules.
- Do not sacrifice pawns or pieces without good reason.
- Do not trade BxN without good reason.
- Castle O-O unless you intend to advance your h- or g-pawn.
- If you have 1 bishop, then place your pawns on the other color.
Connect Four is a simpler game, but maybe for chess a set of say 64 rules might suffice as a strategy for black to achieve the draw against any opposition.
Maybe for chess a comprehensive set of rules can be formulated after chess is weakly solved.
Chess will never be solved, here's why
Anyone who thinks a human could reach >3600 rating and be invulnerable to top engines by "a set of say 20-50 rules " is surely delusional.
Over a century of effort by top players has not got to 2900.
#2852
"Over a century of effort by top players has not got to 2900."
++ Rating is relative.
If all humans study and become stronger, then they all stay at the same rating.
The main limit of the humans is that they get tired, low on time, emotional...
This was clear in the last World Championship match. In the first 5 games Nepo had better chances, but did not use them to the fullest extent. Then in game 6 Nepo lost a table base draw when he was tired and low on time. Then Nepo became sort of disheartened and blundered a pawn, then a bishop, then his king in otherwise drawn positions.
Even without engines a human ICCF grandmaster is immune to all these human deficits: he does not get tired, he never runs low on time, he has time to control his emotions.
His only vulnerability is that he may become ill during the game.
@Elroch makes good posts.
'Somebody' is again having his worry about 'more intelligent'.
Hoping to bait perhaps.
I didn't even bother to read his post 2850.
And - we've got posts from a titled player that could use some attention maybe. Are chess titles enormously important? Usually not - but sometimes it helps.
#2827
"So the first thing is to see how that would play out in the example he gives."
++ You can see for yourself if you do not believe. Run the position on your desktop for 17000 s/move = 4.7 h/move. There is no doubt at all what you will find: a draw.
I did say proof.
I ran this White win on my desktop for 2048 seconds a move and (surprise!) I got a draw.
I also ran it at all times 2ⁱ for i=0,1,2...,10 and got 10 draws out of 11.
Further I checked the blunder rates for the different times and got the following graph.
The blue line is a linear regression. It apparently shows the blunder rate increasing with time overall.
So much for running SF14 for 17000 s/move being any sort of proof.
You may say that a similar degradation doesn't apply to the human element of the ICCF matches.
This is a diagram posted by von der Lasa in 1843 together with an analysis purporting to show the position with either side to move is a win.
The position was debated by the best analysts of the time for about a century; Berger, Sacconi, Grigoriev, Fine and Chéron among others. Not until 1925 was a correct analysis produced (unpublished) by Grigoriev and general agreement reached only in 1952 after Chéron published a correct analysis.
The position with Black to move is in fact drawn.
So you're saying that a combination of humans, who take a century to get a correct analysis of the above position, and engines, the best being SF14 which fails in one of the most completely and accurately analysed positions with 5 men on the board can prove in 5 days that this position is drawn.
Forgive me for being sceptical. That's not just no proof, it's ridiculous.
Is it a draw at a best current level of play - yes. But would it be a draw with perfect play?
#2856
"I ran this White win on my desktop for 2048 seconds a move and (surprise!) I got a draw."
++ This is irrelevant. Whenever a position with 7 men or less is reached, is is looked up in the 7-men endgame table base. The engine cannot find the checkmate unless you give it enough time. So the engine is happy with its +5 advantage and even happier when it can win the pawn getting +6. The evaluation function cannot handle the knight pair. You come up will all kinds of irrelevant positions that do not happen. I checked two KRPP vs. KRP and the engine plays table base perfectly.
"You may say that a similar degradation doesn't apply to the human element of the ICCF matches." ++ No, of course not. In ICCF they can claim the table base win, even if it exceeds 50 moves. Such table base win claims do not happen however. Table base draw claims however are common.
"So you're saying that a combination of humans (...) and engines (...) can prove in 5 days that this position is drawn." ++ Yes, of course, that is what they did.
"Is it a draw at a best current level of play - yes. But would it be a draw with perfect play?"
++ Yes, with perfect play from both sides it surely is a draw.
#2842
"it is highly likely that there are positions with multiple light squared bishops that are reached by 100% optimal play."
++ That is nonsense.
Optimal play is to promote to a queen, not to a second same color bishop.
There are very rare exceptions where promotion to a bishop is necessary to avoid stalemate. Some sick artificial constructions prove nothing. The sick artificial constructions cannot be reached from the initial positions by optimal play themselves. In none of the ICCF WC draws occurs a single underpromotion. 99% of these ICCF WC draws are ideal games with optimal moves.
There is an important point which is that underpromotion to a bishop can only be optimal while promotion to a queen is not in a WINNING position. Thus such positions can only occur in 100% optimal play if the value of chess is a win for one side or the other. This is possible, but generally believed to be unlikely, so let's assume it is not so.
So underpromotion to a bishop or rook can never be essential in a drawing position but positions where underpromotion to a bishop or rook can still be relevant, because where such a move is the only way for one side to win, the other player may need to realise this when they play a move that (eventually) reaches this position. If they assume queening, they may get to the position expecting a draw and then lose.
Take one of your "sick, artificial constructions". To avoid irrelevancy, assume it is reachable by legal moves from the opening position.
Perform retrograde analysis on this position, finding for each ply all the positions for which an optimal move leads to a position that is a smaller number of ply of optimal moves to the chosen underpromotion position. Note that the retrograde analysis only needs consider moves from a position that is legally reachable from the opening position.
Typically the number of such positions grows exponentially as the number of ply increases.
For this to become relevant to the selection of an optimal strategy, all that you need is that at some point there is a legal move from a position reached by optimal play that gets you to one of these positions reached by retrograde analysis.
While it is plausible that retrograde analysis would dry up early in the process (this can only happen when co-operation is needed to reach a position - at least one move by each player which changes the value of the position, so is suboptimal) it becomes rapidly less likely as the number of precursor positions grows. And remember we only need one example to work, and we have a lot of choice.
The above applies to all underpromotions to bishop or rook (the colour is not crucial), but of course for underpromotions to knights, the relevance is broader. Underpromotion to a knight can be necessary to achieve a draw as well as to achieve a win (while if underpromotion to a rook or bishop achieves a draw, queening will always get at least as good a result).
#2856
"I ran this White win on my desktop for 2048 seconds a move and (surprise!) I got a draw."
++ This is irrelevant. Whenever a position with 7 men or less is reached, is is looked up in the 7-men endgame table base.
It's relevant because we don't have 14 man tablebases. Exactly the same would apply if we did. The only difference would be you wouldn't be able to hide behind the impossibility of checking your assertions.
The engine cannot find the checkmate unless you give it enough time.
From what I said concerning the reliability of its evaluations as a function of time, it's quite likely that "enough time" would mean enough time to completely search the game tree from that position to the shortest mate. A lot longer than 17 seconds. A lot longer than 5 years.
So the engine is happy with its +5 advantage and even happier when it can win the pawn getting +6. The evaluation function cannot handle the knight pair. You come up will all kinds of irrelevant positions that do not happen. I checked two KRPP vs. KRP and the engine plays table base perfectly.
Positions that are not in the KRPP vs. KR endgame may not happen at your local chess club, but they will happen in your computation if the starting position is a draw, when it would be necessary, for a proof, to exclude all potential wins. What occurs in practical play is not relevant.
In any case the KNNKP endgame does occur in practical play.
KNNKP endgames almost never occurred before Troitzky published his analysis of the White wins. Nobody understood them so they avoided them.
This is not the case any more. a few years ago the endgame was in progress at the same time at two adjacent tables in a major US tournament.
SF14 does play certain endgames perfectly. It probably plays KRK not only perfectly but perfectly accurately, but I think you would need to try more than two positions to be at all confident about KRPPKRP. It plays just about all KNNKP ply 0 positions perfectly accurately so long as the mate depth doesn't exceed about 20.
"You may say that a similar degradation doesn't apply to the human element of the ICCF matches." ++ No, of course not. In ICCF they can claim the table base win, even if it exceeds 50 moves.
There are three pieces additional to the kings in von der Lasa's position, eleven in your purported draw. More of the additional pieces would need to be eliminated from the latter than even exist in the former before either player could claim a tablebase anything.
You say "of course not". That's laughable. Just look at the von der Lasa position and your ICCF "draw".
Such table base win claims do not happen however. Table base draw claims however are common.
Draws are common in SF14 v SF14 whenever it's out of its depth. The games I referred to are a case in point.
The same is true of humans. The KQKRR endgame has always been regarded as drawn unless there is an obvious short mate, but the Nalimov tablebase says 98% of positions are wins under basic rules and Syzygy says 73% of ply 0 positions are wins under competition rules.
Müller & Lamprecht evaluate it as generally drawn subject to some constraints, based on the results in the occurrences in a 1.7 million game database of recorded games. So in practical play it is a draw.
I suggest the reason you have so few tablebase win claims is that practical players, human or machine, are usually out of their depth in terms of perfect play in the most closely matched positions with more than 5 men on the board.
Of course SF14 is not at all out of its depth when it comes to practical play, But practical play has nothing to do with solving chess. We don't have the slightest idea how practical play at the present best levels compares with perfect play (and won't have while a solution is not available).
"So you're saying that a combination of humans (...) and engines (...) can prove in 5 days that this position is drawn." ++ Yes, of course, that is what they did.
They proved sweet FA.
"Is it a draw at a best current level of play - yes. But would it be a draw with perfect play?"
++ Yes, with perfect play from both sides it surely is a draw.
You never produced your perfect White win under basic rules against Syzygy from the position I posted here viz:
It has half the number of men on the board than there are in the position you're so confidently claiming drawn.
Until you can start meeting some of the challenges that have been raised there is no reason to take your bald statements of "fact" seriously.
@Elroch made another good point there - with this argument:
" If they assume queening, they may get to the position expecting a draw and then lose."
He explained it carefully.
Its one of many refutations of the '5 years' arguments.
One could argue endlessly over the semantics of 'refutation' though.
As to what @tygxc can/will do about that ... I guess there'll just be more sidestepping.
[snip]
There is an important point which is that underpromotion to a bishop can only be optimal while promotion to a queen is not in a WINNING position.
[snip]
Depends how we interpret "optimal". From a winning position, underpromotion to a knight might make a checkmate either quicker or easier, while not affecting the ultimate result. But it's a minor point.
I think my sentence was a bit obscure. We are not in disagreement. The point is that underpromotion to a bishop or rook can never be essential (and can never be the only good move) in a drawing position because the only thing that can "go wrong" is to stalemate the opponent, and that can never be disadvantageous if the position is a draw. Under promotion to a knight can be the only good move in a winning or a drawing position.
Obviously - Elroch's point about the underpromotions is not and was not a question.
So the accusation is unfounded.
#2867
"underpromotion to a bishop or rook can never be essential (and can never be the only good move) in a drawing position because the only thing that can "go wrong" is to stalemate the opponent, and that can never be disadvantageous if the position is a draw. Under promotion to a knight can be the only good move in a winning or a drawing position."
++ Yes, good point.
Underpromotion to a knight happens once in a while,
but usually to a knight previously captured and never in multiples.
#2863
"It's relevant because we don't have 14 man tablebases. Exactly the same would apply if we did. The only difference would be you wouldn't be able to hide behind the impossibility of checking your assertions."
++ It is very well possible to check my assertions. Take a 7-men KRPP vs. KRP and run your desktop for 17000 s/move and you can check the engine against the table base.
"Positions that are not in the KRPP vs. KRP endgame may not happen at your local chess club, but they will happen in your computation if the starting position is a draw, when it would be necessary, for a proof, to exclude all potential wins."
++ I did not say only KRPP vs. KRP occurs, I said it 1) occurs most frequently and 2) is most relevant. That is not the local chess club, it is grandmaster practice and ICCF play and TCEC play.
The reason why it occurs most frequently is that unlike other pieces the defending player benefits from avoiding a rook trade. Rooks can move or capture to 14 squares wherever they stand. Other pieces are more powerful in the center and thus cannot avoid a trade.
The reason why it is most relevant is that other 7-men balanced positions are either more decisive, like KPPP vs. KPP, KNPP vs. KNP, KBPP vs. KNP, KNPP vs. KBP, KBPP vs. KBP with same color bishops, or less decisive like KBPP vs. KBP with opposite colored bishops.
"In any case the KNNKP endgame does occur in practical play." ++ Yes, but it is 5 men only and thus has been looked up in the 7-men endgame table base long before it occurs.
"you would need to try more than two positions to be at all confident about KRPPKRP."
++ "No number of experiments can prove me right, one can prove me wrong" - Einstein
If I try 20, or 200, or 2000 positions you will still not believe me.
Try to find a counterexample yourself. You will fail to find one.
"It plays just about all KNNKP ply 0 positions perfectly accurately so long as the mate depth doesn't exceed about 20."
++ Yes, that is right. The evaluation function fails for KNN vs. KP. So the engine plays perfectly only if its search depth exceeds the depth to mate. The engine plays positions with mate in 60 perfectly if only you give it enough time to reach depth 120 ply.
"eleven in your purported draw" ++ It is not my draw, it is the draw between two ICCF grandmasters with their multicore engines.
"More of the additional pieces would need to be eliminated from the latter than even exist in the former before either player could claim a tablebase anything."
++ The two ICCF grandmasters had no doubt that if they had continued play in their position for more months, they would ultimately reach a 7-men table base draw or a 3-fold repetition.
"The KQKRR endgame has always been regarded as drawn unless there is an obvious short mate, but the Nalimov tablebase says 98% of positions are wins under basic rules and Syzygy says 73% of ply 0 positions are wins under competition rules."
++ That is 5 men only, so it will have been looked up in the 7-men endgame table base before it occurs. Do you claim the engine plays KQ vs. KRR badly?
"So in practical play it is a draw."
++ That is practical play between humans, tired and short of time. Nepo lost a table base draw to Carlsen in the world championship match when he was tired and short of time.
"the reason you have so few tablebase win claims is that practical players, human or machine, are usually out of their depth in terms of perfect play in the most closely matched positions with more than 5 men on the board."
++ I do not understand this argument.
5 men do not happen in ICCF: they claim when they reach 7 men.
7-men tablebase draw claims happen frequently. 7-men tablebase win claims do not happen. The reason why 7-men tablebase win claims do not happen is that the defending side steers clear of such pitfalls and heads towards a safe haven.
"We don't have the slightest idea how practical play at the present best levels compares with perfect play" ++ Oh yes, we do. 99% of ICCF WC drawn games are ideal games with optimal moves, so these ICCF WC draws show what perfect play looks like.
I already gave 2 examples of such perfect games. Here is a 3rd example: it ends in a perpetual check, i.e. a draw by forced 3-fold repetition of the position.
Here is a 4th example, ending in a 7-men endgame table base draw claim:
++ "No number of experiments can prove me right, one can prove me wrong" - Einstein
So why you keep quoting Capablanca, Fischer, Sveshnikov, and using ICCF games and all the cumulated experience of centuries, as supporting evidence for your claims, is a mystery. You have also refused so far any experiment that people here think proves you wrong, so maybe you had better state clearly beforehand, what sort of experiment could do that, in your opinion.
[snip]
++ I did not say only KRPP vs. KRP occurs, I said it 1) occurs most frequently and 2) is most relevant.
[snip]
Oh, I see now, @tygxc is attempting a proof by ignoring less common examples.
Just to clarify, all examples that can occur are relevant to a proof, not just the most common ones.
@tygxc
In point of fact KQRRBBNNPPPPPPPP vs. KQRRBBNNPPPPPPPP occurs most frequently, not KRPP vs. KRP.
And that is one thing that would remain true with perfect play.
#2867
"underpromotion to a bishop or rook can never be essential (and can never be the only good move) in a drawing position because the only thing that can "go wrong" is to stalemate the opponent, and that can never be disadvantageous if the position is a draw. Under promotion to a knight can be the only good move in a winning or a drawing position."
++ Yes, good point.
Underpromotion to a knight happens once in a while,
but usually
"usually"? So what? It's what happens that matters, not how often.
to a knight previously captured and never in multiples.
In a tiny sample of a few hundred million positions occurring in games by imperfect players.
If you are looking for rare examples, the best way to miss them is to ignore 99.9999999% (or more) of the relevant population. The set of all positions that can be reached by optimal play is enormously larger than your sample.
I have provided an argument why it is extremely likely that multiple underpromotions to knights can occur in optimal play from drawn or won positions and that multiple underpromotions to bishops and rooks can occur from winning positions. (More strongly my argument indicates that if chess is a draw the former is extremely likely to occur from the opening position and that the latter can occur by a single mistake from the opening position).
#2871
"In point of fact KQRRBBNNPPPPPPPP vs. KQRRBBNNPPPPPPPP occurs most frequently, not KRPP vs. KRP."
++ That is not even true: there are more 26-men positions than 32-men positions.
We cannot verify 32-men positions or 26-men positions.
KRPP vs. KRP occurs most frequently and is most relevant among the 7-men positions we can verify as they count 7 men and thus are at the boundary of the 7-men endgame table base.
#2872
"In a tiny sample of a few hundred million positions occurring in games by imperfect players."
++ And in a tinier sample of a few thousand games by perfect players: ICCF WC draws.
"The set of all positions that can be reached by optimal play is enormously larger than your sample."
++ Yes, that is right: set of all legal positions 4.79 * 10^44; set of legal, sensible, reachable, relevant positions 10^17.
Sample of positions from imperfect games 10^8. Sample of positions from perfect games 10^5.
However, knowledge about stars was also derived from observing a small sample of the total.
Tromp also estimated the number of 4.79*10^44 legal positions from a sample of only 10^6 and he also provided the interval of 95% confidence +- 0.04 * 10^44.
"it is extremely likely that multiple underpromotions to knights can occur in optimal play from drawn (...) positions" ++ Do you mean multiple underpromotions to knights or multiple underpromotions to knights not previously taken?
"the former is extremely likely to occur from the opening position" ++ Why? I do not see that.
Looks like projection of projection again.
Especially on the 'authority' stuff.
'Somebody' definitely wants 'authority' (not I) but he hasn't been getting it and doesn't like that and its been showing. A lot.