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H.G.Muller

Joined: 10 Mar 2006
Posts: 21875
Location: Amsterdam

Post subject: Re: Redundant knight    Posted: Sat Jun 21, 2014 7:54 am

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...
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Subject Author Date/Time
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
Re: Redundant knight 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
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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