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Lyudmil Tsvetkov

Joined: 12 Jun 2012
Posts: 5989

Post subject: Re: Redundant knight    Posted: Sat Jun 21, 2014 8:48 am

hgm wrote:
Lyudmil Tsvetkov wrote:
[d]2bq2k1/pppppppp/8/8/8/8/PPPPPPPP/1N1Q2K1 w - - 0 1
Anyone doubting in the redundancy theory should look at the above position.

Indeed, they should look at the above position, play it some 10,000 times between equally strong opponents, (possibly permuting the back-rank pieces to force game diversity), and then compare the result with that for the same position(s) without Queens. Then they would know if the extra Queen is worth more to white than to black.

Point is that you have not done that at all, and that anything you say about it is just a fabrication of your imagination.

Quote:
[d]8/5n2/3nk3/8/8/2R1B3/4K3/8 w - - 0 1
Another proof for the redundancy of knights. Did you know that this is won ... in 222 moves for white?

How is this proof for Knight redundancy? The hypothesis that Bishops are stronger than Knights when not hindered by Pawns (as is already extensively discussed in Larry Kaufman's paper on empirical piece values), plus the obvious fact that Rooks are stronger than Knights, is by itself perfectly capable of explaining this 'cursed win'. This position gives exactly zero evidence for Knight redundancy. It only tells us that Knights are pretty weak pieces.

Redundancy can never be demonstrated from single positions. It only can be demonstrated from comparing positions that have an extra pair of pieces to an equivalent position that has not. You would have (the beginning of) a case if BRNKNN was won, and KRKN (deleting a Knight on each side) was draw. Only the beginning of a case, because piece values are in general not determined by how well the pieces perform in Pawnless endings, but by how well they combat and support Pawns. To make a real case you would not only have to see what extra Knights do to KRKN, but what they do to a representative mix of material combinations where one side already has a Knight (so that the second Knight is 'redundant'), and the other has not. With KRBKNN there aren't even equal pieces on each side that you could delete...

Larry Kaufman already showed based on investigations of his large database that Q+N have and advantage over Q+B, although small. Of course, those were just master games. I would be happy if someone conducts an investigation of a large computer games database to reassess the same factor on a higher level. I am certain the conclusion will be confirmed.

Concerning 2 knights endgames, first you talked of pawn span, and now you claim that it is minimal number of pawns, actually non-existent, that gives white the decisive advantage in RB vs NN. Sliding pieces really become increasingly stronger as pawns come off, but that is far from insufficient to explain how it is possible to win such an endgame with only 150cps material edge. You need to consider also other factors.

[d]4q3/5n2/3nk3/8/8/2R1B3/4K3/4Q3 w - - 0 1
You might also want to take a look at the below position. It is the same as the main RB vs NN endgame, but you add one queen each side. I bet here already black's drawing chances are much better. Why? Simply because if black still has the full redundancy of the knights, white already gets 2 more partial redundancies that did not exist earlier, namely the partial redundancy of Q and R as linear pieces and the partial redundancy of Q and B as diagonal pieces.

OK, you can not check a million database or play hundred thousand games to check the theory of redundancy, but you can certainly compare the below 2 positions that are relatively simple. Are there differences in score for the 2 positions and what they are attributed to?

[d]8/5n2/3nk3/8/8/2R1B3/4K3/8 w - - 0 1
[d]4q3/5n2/3nk3/8/8/2R1B3/4K3/4Q3 w - - 0 1

I would appreciate very much if someone posts engine analysis, even if brief, on the above 2 positions. I guess that the score of black will be better in the second position with added queens.
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Lyudmil Tsvetkov Fri Jun 20, 2014 10:38 am
H.G.Muller Fri Jun 20, 2014 11:03 am
Lyudmil Tsvetkov Fri Jun 20, 2014 11:54 am
H.G.Muller Fri Jun 20, 2014 4:01 pm
Lucas Braesch Fri Jun 20, 2014 11:21 am
Lyudmil Tsvetkov Fri Jun 20, 2014 12:03 pm
Lyudmil Tsvetkov Fri Jun 20, 2014 11:37 am
Louis Zulli Fri Jun 20, 2014 11:50 am
Lyudmil Tsvetkov Fri Jun 20, 2014 12:13 pm
Lyudmil Tsvetkov Fri Jun 20, 2014 12:36 pm
Louis Zulli Fri Jun 20, 2014 1:27 pm
Lyudmil Tsvetkov Fri Jun 20, 2014 2:09 pm
Arjun Temurnikar Fri Jun 20, 2014 2:32 pm
Louis Zulli Fri Jun 20, 2014 4:12 pm
Louis Zulli Fri Jun 20, 2014 4:21 pm
Lyudmil Tsvetkov Fri Jun 20, 2014 4:30 pm
Robert Hyatt Sat Jun 21, 2014 2:51 am
Lyudmil Tsvetkov Sat Jun 21, 2014 6:53 am
Arjun Temurnikar Fri Jun 20, 2014 1:41 pm
Lyudmil Tsvetkov Fri Jun 20, 2014 2:26 pm
Arjun Temurnikar Fri Jun 20, 2014 3:03 pm
Lyudmil Tsvetkov Fri Jun 20, 2014 3:40 pm
Arjun Temurnikar Fri Jun 20, 2014 4:43 pm
Joerg Oster Fri Jun 20, 2014 2:33 pm
Lyudmil Tsvetkov Fri Jun 20, 2014 3:12 pm
Arjun Temurnikar Fri Jun 20, 2014 3:19 pm
Arjun Temurnikar Fri Jun 20, 2014 3:35 pm
Lyudmil Tsvetkov Fri Jun 20, 2014 3:51 pm
Lucas Braesch Fri Jun 20, 2014 6:47 pm
Arjun Temurnikar Fri Jun 20, 2014 7:23 pm
Lyudmil Tsvetkov Sat Jun 21, 2014 1:31 am
Bernhard Bauer Sat Jun 21, 2014 5:31 am
Lyudmil Tsvetkov Sat Jun 21, 2014 6:57 am
H.G.Muller Sat Jun 21, 2014 7:54 am
Matthew R. Brades Sat Jun 21, 2014 8:04 am
Lyudmil Tsvetkov Sat Jun 21, 2014 8:57 am
Re: Redundant knight Lyudmil Tsvetkov Sat Jun 21, 2014 8:48 am
H.G.Muller Sat Jun 21, 2014 9:19 am
Lyudmil Tsvetkov Sat Jun 21, 2014 10:00 am
Bernhard Bauer Sat Jun 21, 2014 5:22 am
Lyudmil Tsvetkov Sat Jun 21, 2014 7:07 am
Lyudmil Tsvetkov Sat Jun 21, 2014 9:30 am
H.G.Muller Sat Jun 21, 2014 9:45 am
Lyudmil Tsvetkov Sat Jun 21, 2014 10:21 am
H.G.Muller Sat Jun 21, 2014 11:31 am
Lyudmil Tsvetkov Sat Jun 21, 2014 11:38 am
Lyudmil Tsvetkov Sat Jun 21, 2014 11:38 am
H.G.Muller Sat Jun 21, 2014 11:52 am
Arjun Temurnikar Sat Jun 21, 2014 2:23 pm
Kevin Hearn Sat Jun 21, 2014 10:30 am
Lyudmil Tsvetkov Sat Jun 21, 2014 11:16 am
Bernhard Bauer Sat Jun 21, 2014 11:36 am
Lyudmil Tsvetkov Sat Jun 21, 2014 12:10 pm
H.G.Muller Sat Jun 21, 2014 12:16 pm
Lyudmil Tsvetkov Sat Jun 21, 2014 11:59 am
Lyudmil Tsvetkov Sat Jun 21, 2014 12:58 pm
H.G.Muller Sat Jun 21, 2014 12:11 pm

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