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Is a crowned bishop (moves like B or K) as powerful as a rook?



 
 
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  #1  
Old July 3rd 03, 01:26 PM
Neil Fernandez
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Default Is a crowned bishop (moves like B or K) as powerful as a rook?

I was wondering to what extent the inferiority of the B's strength
relative to the R's is explained by the fact that the B can only reach
half the board.

Does this account for all or almost all of the inferiority, or less than
almost all? Or maybe if this factor could be 'counter-balanced' exactly,
the B would become theoretically stronger than the R?

Which led to the following question. If a B were allowed to move one
square orthogonally as well as an unlimited number of squares
diagonally, how would its strength compare with that of a R?

I'll test this, but wondered what other people thought about it :-)

A B given these extra powers has been called a Crowned Bishop in variant
chess, and is called a promoted bishop in shogi.

Neil

--
Neil Fernandez
  #2  
Old July 3rd 03, 11:52 PM
Neil Fernandez
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Default Is a crowned bishop (moves like B or K) as powerful as a rook?

In article , Neil Fernandez
writes

[...]

If a B were allowed to move one
square orthogonally as well as an unlimited number of squares
diagonally, how would its strength compare with that of a R?

I'll test this, but wondered what other people thought about it :-)


Answering my own question here (!)
My software suggests that a crowned bishop (C) may be slightly stronger
than a rook. Interestingly White can mate with K + C against K.

Neil

--
Neil Fernandez
  #3  
Old July 4th 03, 02:25 AM
Harold Buck
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Default Is a crowned bishop (moves like B or K) as powerful as a rook?

In article ,
Neil Fernandez wrote:

In article , Neil Fernandez
writes

[...]

If a B were allowed to move one
square orthogonally as well as an unlimited number of squares
diagonally, how would its strength compare with that of a R?

I'll test this, but wondered what other people thought about it :-)


Answering my own question here (!)
My software suggests that a crowned bishop (C) may be slightly stronger
than a rook. Interestingly White can mate with K + C against K.



I'd be interested to hear how you determined that using your software,
and how much stronger the C seems to be.

Can white mate with a K + (another piece that moves like a K but which
can't be checked) against K? I'd guess yes, but I'm not sure.

--Harold Buck


"I used to rock and roll all night,
and party every day.
Then it was every other day. . . ."
-Homer J. Simpson
  #4  
Old July 4th 03, 04:37 AM
John Lawson
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Default Is a crowned bishop (moves like B or K) as powerful as a rook?

Also check out the series of articles by Ralph Betza on the values of
chess pieces at http://www.chessvariants.com/.

http://www.chessvariants.com/piececl...al-values.html

is the beginning of the series.

John Lawson

Neil Fernandez wrote in message ...
In article , Neil Fernandez
writes

[...]

If a B were allowed to move one
square orthogonally as well as an unlimited number of squares
diagonally, how would its strength compare with that of a R?

I'll test this, but wondered what other people thought about it :-)


Answering my own question here (!)
My software suggests that a crowned bishop (C) may be slightly stronger
than a rook. Interestingly White can mate with K + C against K.

Neil

  #5  
Old July 4th 03, 11:44 AM
Neil Fernandez
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Posts: n/a
Default Is a crowned bishop (moves like B or K) as powerful as a rook?

In article
s.com, Harold Buck writes
In article ,
Neil Fernandez wrote:

In article , Neil Fernandez
writes

[...]

If a B were allowed to move one
square orthogonally as well as an unlimited number of squares
diagonally, how would its strength compare with that of a R?

I'll test this, but wondered what other people thought about it :-)


Answering my own question here (!)
My software suggests that a crowned bishop (C) may be slightly stronger
than a rook. Interestingly White can mate with K + C against K.


I'd be interested to hear how you determined that using your software,
and how much stronger the C seems to be.


Hi Harold. I wouldn't say it was a determination, rather I just got
a first indication. I hacked the non-variant chess program
published by Zillions for their gaming system
(http://www.zillions-of-games.com) by turning all four bishops
into crowned bishops. I then used the facility of that program to
estimate the point-value of each piece. For example, at the
starting position it gives the pawn on a2 a value of 1853 points,
and the pawn on e2 a value of 1867. There is little variation for
pieces of the same type. Taking the mean for crowned bishops and
dividing by the mean for pawns gave a figure of 4.6, and taking the
mean for rooks and dividing by the mean for pawns gave a figure of
4.9. So according to this software, the crowned bishop is worth 0.3
pawns more than a rook in the starting position. I also played a
few games against the program, and let the program play itself too.
In a couple of games the program readily exchanged a rook for a
crowned bishop, without incurring any disadvantage, and my overall
feeling was that the crowned bishop was no weaker than a rook.

Can white mate with a K + (another piece that moves like a K but which
can't be checked) against K? I'd guess yes, but I'm not sure.


This combined wazir-fers is sometimes called a counsellor, man,
non-royal king, or prince in variant chess. Not sure of the answer
though.

Neil

--
Neil Fernandez
  #6  
Old July 4th 03, 12:22 PM
Neil Fernandez
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Posts: n/a
Default Is a crowned bishop (moves like B or K) as powerful as a rook?

In article , Neil Fernandez
writes
In article
s.com, Harold Buck writes
In article ,
Neil Fernandez wrote:

In article , Neil Fernandez
writes


[...]

I hacked the non-variant chess program
published by Zillions for their gaming system
(http://www.zillions-of-games.com) by turning all four bishops
into crowned bishops. I then used the facility of that program to
estimate the point-value of each piece. For example, at the
starting position it gives the pawn on a2 a value of 1853 points,
and the pawn on e2 a value of 1867. There is little variation for
pieces of the same type. Taking the mean for crowned bishops and
dividing by the mean for pawns gave a figure of 4.6, and taking the
mean for rooks and dividing by the mean for pawns gave a figure of
4.9.


Oops - I typed this the wrong way round. The program gives 4.6 for the
rook and 4.9 for the crowned bishop.

Neil

--
Neil Fernandez
 




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