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