#122
400 moves:
Chess will never be solved, here's why
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Jan 23, 2022
0
#123
tygxc wrote:
#122
400 moves:
Definitely not 400 moves.
This needs 1098 ply (549 full moves).
and the position you show needs more than 400.
This is the fastest possible way for White to convert to a reduced number of men and still win.
and that still leaves 7 men on the board and no mate yet.
If Haworth's law holds good up to 32 men the longest mate with 32 men would be a little short of three (American) trillion moves.
Jan 23, 2022
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#125
https://en.wikipedia.org/wiki/Endgame_tablebase#Tables
apparently KQN vs KRBN has a longest win of 545
Jan 23, 2022
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#126
technical_knockout wrote:
sorry i mean once all the pawns are off.
If all the pawns are off, then you're down to 16 men. Haworth's law would almost certainly be a huge overestimate in this case, because the rate of increase in the length of pawnless endgames appears to stall (starting with the increase from 6 to 7 men). So the answer is probably nobody has a good guess at the maximum length of a mate once all the pawns are off.
But what's the significance of the requirement that all the pawns are off?
Jan 23, 2022
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#127
chess will never be solved because there are lots variations and more and more we can't even imagine about that
Jan 23, 2022
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#128
tygxc wrote:
#120
"I can't see anything but a draw, but if two grandmasters who have been looking at it for months can't that's not surprising. It doesn't mean there is no win with perfect play."
++ It is a draw. Even in over the board classical play this would be drawn, despite time trouble, fatigue.
I would say it's pretty obviously a draw with play at the human or SF level but there could still be a mate in a thousand moves or two lurking.
"The starting position has equal material and symmetrical pawns. Would they have done better to have called it quits then?" ++ But there are many possibilities: pawn moves, captures... Rook endings are known to be drawish, even more so with equal and symmetrical pawns.
I wasn't being totally serious, but there are people who know the starting position is a draw too.
"Was the >50 moves meant to mean outside the 50 move rule, or just a suitably large number?" ++ Because of the 50 moves rule. The 50 moves rule itself was devised to be suitably large.
But it doesn't limit the length of mates to 50 moves. E.g. the following position is mate in 85 under basic rules or mate in 128 under competition rules.
Hence the question.
"I didn't understand the significance of the link." ++ The first thing to do in KNN vs. KP is to block the pawn with a knight so as to make it immobile.
The Wikipedia article covers various endgames, you didn't specify.
But you shouldn't believe everything you read in Wikipedia. Blocking the pawn with a knight is not always the first thing you do. How would that work in the first position in #27 for example? (Also less obviously in the above position. You're not interested in blocking the pawn on a5; you need to force it to a3.)
#132
This is what solved game means:
https://en.wikipedia.org/wiki/Solved_game
Jan 23, 2022
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#130
MARattigan wrote:
E.g. the following position is mate in 85 under basic rules or mate in 128 under competition rules.
I am probably missing something obvious here, but how? Is it as artificial as a diversion around a position that has been previously reached twice?
Jan 23, 2022
0
#131
significance: was wondering how that applies towards whether the current 50-move rule ought to be revised to accomodate known technically won positions... just easier than thinking about it with pawns on (would seem to unduly complicate the basic question).
#135
This is how ICCF handles it:
2. As concerns a 7-piece tablebase claim, if the tablebase indicates a win, this
supersedes the 50-move rule. (All ICCF events allow 7-piece tablebase win/draw
claims.) In a position that is not solvable by the certified ICCF tablebase, the 50-move
rule as described by ICCF Laws of Correspondence Chess is valid even in case such a
solvable position will arise immediately after the 50th move. In case the solvable won
position arises and is claimed before a draw according to the 50-move rule, the win will
be awarded.
https://webfiles.iccf.com/rules/2022/ICCF%20Rules%20update%20for%201-1-2022.pdf
Ugh idk
Jan 23, 2022
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#134
Elroch wrote:
MARattigan wrote:
E.g. the following position is mate in 85 under basic rules or mate in 128 under competition rules.
I am probably missing something obvious here, but how? Is it as artificial as a diversion around a position that has been previously reached twice?
No you have to play it differently with the 50 move rule in effect. If you take any fastest route it will include a phase that falls foul of the 50 move rule. So you have to force the pawn forward prematurely to avoid that but still have a mate. Horribly difficult and I don't even plan to try learning the endgame under competition rules.
The same would apply in an increasing number of positions with extra men on the board. (Perfect opening theory is probably very different depending on whether it's for basic rules or competition rules.)
Luckily the Nalimov approach is good enough in practical play.
You can see the details here: http://galen.metapath.org/egtb50/
#138
"Perfect opening theory is probably very different depending on whether it's for basic rules or competition rules"
Probably not at all.
Opening play largely stays the same even with more radical rules changes.
https://arxiv.org/pdf/2009.04374.pdf
Jan 23, 2022
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#136
tygxc wrote:
#138
"Perfect opening theory is probably very different depending on whether it's for basic rules or competition rules"
Probably not at all.
Opening play largely stays the same even with more radical rules changes.
https://arxiv.org/pdf/2009.04374.pdf
Well that's back to using AZ to verify.
As I said playing Nalimov is sufficient in practical play. E.g. to win "frustrated wins" against the SFs under competition rules. But not against Syzygy.
KNNKP mates can be at most 128 moves deep. You wouldn't expect AZ to give a correct answer on perfect play in the opening where there are likely to be mates a trillion or more deep. You would expect it to give a correct answer for its own level which would be good enough for practical purposes.
#141
At least it is a scientific approach. It even corresponds with the human knowledge derived from millions of human games. The engine reinvented the Berlin, the Grünfeld etc. with no external input but the Laws of Chess by playing 700,000 games against itself.
Here is another AlphaZero paper on opening theory
https://arxiv.org/pdf/2111.09259.pdf
Jan 23, 2022
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#139
#141
It's essentially going through the same process that humans have used over the centuries, so you'd expect it to come up with much the same openings.
#143
You may well believe 1 Nh3 wins in 800 moves or even 1 e4 b5 wins for black in 700 moves, but there is no evidence at all to support that.
The consensus among experts is that chess is a draw and the results of classical, ICCF and TCEC games corroborates that.
With or without 50 moves rule should make no difference.
Bigger rules changes make no difference either.
No, no-one knows. But it has a known upper bound.