++ "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.
And in a tinier sample of a few thousand games by perfect players: ICCF WC draws.
Set of all legal positions 4.79 * 10^44; set of legal, sensible, reachable, relevant positions 10^17.
You are the only one in the world stating such things, but you write them as everyone thought the same. You say that sometimes things are "known" but not proven. Is there a way that coud prove you that those statements above are not so "known" as you think?
#2875
"You are the only one in the world stating such things."
++ Yes, somebody has to be a pioneer.
Here is an overview of ICCF WC finals:
WC Total Decisive Draw D E Ideal
32 125 17 108 0.14 0.13 106
31 133 14 119 0.11 0.10 118
30 136 9 127 0.07 0.07 126
29 136 13 123 0.10 0.09 122
28 136 20 116 0.15 0.14 113
27 136 16 120 0.12 0.12 118
26 136 25 111 0.18 0.18 107
25 120 22 98 0.18 0.18 94
24 136 35 101 0.26 0.24 93
23 136 50 86 0.37 0.33 70
22 136 70 66 0.51 0.42 37
Total 1466 291 1175 0.20 0.19 1102
Progress over years is clear: a drop in the error rate E.
Each ICCF WC Finals yields over 100 ideal games with optimal moves i.e. perfect play.
In total we have 1102 ideal games with optimal moves i.e. perfect play.
#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.
When you are talking about 10^44 positions, then "very rare exceptions" can be millions or billions of positions that you are summarily dismissing. Every single recorded chess game in human history would be "very rare exceptions" by your reasoning, since there are far less than 1 trillion games recorded.
The way you clumsily hack 10^44 to 10^17 shows amply well that you do not really grasp exponents at a fundamental level. You know the math on the page, but you lack the imagination to understand how unfathomably large the numbers are.
Somebody has to be a pioneer.
Progress over years is clear: a drop in the error rate E.
But do you think you have proven that the increasing draw rate is due to a drop in the error rate (I don't think you estimation of the error rate is correct)? And do you think that an engine that in self-play draws 70% of the times, plays perfectly about (applying your formula) 60% of times, so it can be beaten no more than 40% of times by any other engine?
#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.
You must write a book on your system of logic sometime.
You said
I did not say only KRPP vs. KRP occurs, I said it 1) occurs most frequently and 2) is most relevant.
KRPP vs. KRP is an endgame classification not a position.
Try a random sampling of the the games in the ICCF tournaments you keep posting and count in how many of those samples KQRRBBNNPPPPPPPP vs. KQRRBBNNPPPPPPPP occurs and in how many KRPP vs. KRP occurs.
Before you do would you like to propose a wager that KRPP vs. KRP will occur more frequently than KQRRBBNNPPPPPPPP vs. KQRRBBNNPPPPPPPP? I'd be happy to take the bet.
And there 'somebody' goes again. Breaking the rules.
Again - Elroch's point about underpromotions was not a question.
So therefore the accusation against him by 'the guy' was unfounded.
All Elroch is doing, is asking questions which he knows full well cannot be answered. I disagree with tygxc, of course: but the argument is already over and repeating it is a sign of weakness. It indicates a misplaced sense of hopefulness.
Obviously - Elroch is doing far more than asking questions.
So the accusation is unfounded. And is in the same category as phony authority - obsessions about intelligence levels - other unfounded accusations - rulebreaking ... and even complaining that the forum topic continues ... all coming from the same person (not I) plus he's been there before and was asked 'lets see how long you can go'.
Not long. Just repeating his same cycles over and over.
He's even back to the 'cabal' stuff too. Imaginary conspiracies.
Changing the avatar isn't going to change his behaviour either.
But @tygxc (who is Not that person) - makes his points in a civil way.
The other guy could learn from that - but fails to do so.
And now - getting back to the main topic - there's lots of posts to respond to - and to consider.
No need to be intimidated by somebody who even threatens to go to the moderators over use of common english pronouns 
And in a tinier sample of a few thousand games by perfect players: ICCF WC draws.
Set of all legal positions 4.79 * 10^44; set of legal, sensible, reachable, relevant positions 10^17.
You are the only one in the world stating such things, but you write them as everyone thought the same. You say that sometimes things are "known" but not proven. Is there a way that coud prove you that those statements above are not so "known" as you think?
Good post. Questioning - but without breaking the rules.
and the reply from @tygxc :
"++ Yes, somebody has to be a pioneer."
Not exactly a 'proof'
But done without rancour.
"All Elroch is doing, is asking questions which he knows full well cannot be answered"
Unfounded. Wrong. False. And maybe 'malicious' too.
Whether he 'the guy -not Elroch) quibbles about the semantics of 'accusations' or not.
While he (not I and not Elroch) continues with more accusations and projections.
Regarding 'own medicine' - perhaps others can give him some of his - which is to run to the moderators when he's talked back to.
But not for the same reason. More like - report rule breaking.
Folks - he has a 'history' with the moderators.
Including being muted by the moderators. That's right.
Also - multiple times the moderators have had to explain to him that the others did nothing wrong.
How does somebody like him get stopped?
By breaking his power. That includes being exposed. Or reported.
When he is - he cools it for a bit - but is soon back into the same cycle.
Jesus... Considering how much of a cesspool of bile and ignorance this thread has become, I wouldn't be surprised if it gets locked pretty soon.
Jesus... Considering how much of a cesspool of bile and ignorance this thread has become, I wouldn't be surprised if it gets locked pretty soon.
There's lots of good posts.
As for talking back to insulting behaviour - that's allowed.
Just got to be careful not to also break the rules - which is what the insulting person wants.
#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.
When you are talking about 10^44 positions, then "very rare exceptions" can be millions or billions of positions that you are summarily dismissing. Every single recorded chess game in human history would be "very rare exceptions" by your reasoning, since there are far less than 1 trillion games recorded.
The way you clumsily hack 10^44 to 10^17 shows amply well that you do not really grasp exponents at a fundamental level. You know the math on the page, but you lack the imagination to understand how unfathomably large the numbers are.
Critical. But without rule breaking.
And in-subject ... as opposed to a personal attack.
I happen to agree with the four other persons politely but critically responding to @tygxc
Good points they make. But he keeps sidestepping adroitly.
Has @tygxc ever been right once and them wrong?
But he parries every thrust.
Its quite a demonstration that he's kept up (civilly - unlike the other guy) - month in and month out.
@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.
Didn't explain it particularly clearly,
It was clear enough for several people. I (genuinely) welcome questions if it was not clear enough for you.
though and it is not a refutation, in itself, of the 5 years argument.
The true relevance is that it means one of @tygxc's attempts to make the problem smaller and thus possibly accessible "in five years" (based on a rash guess about ignoring large classes of positions) is unreliable.
Just "unreliable" suffices in this case, since @tygxc needs his claim to be 100% reliable for it to be part of something close to a proof.
#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: