Single Comment

To Derek:

If Archbishop and Chancellor have equal value, it DOES NOT IMPLY ANYTHING
for the value difference of Rook vs Bishop. They are all different pieces,
and have nothing to do with each other. In real life the value of a piece
is not the sum of the value of each of its individual moves, but also
depends critically on properties like mating potential, color-boundedness,
forwardness, speed, manoeuvrability, concentration, sensitivity to
blocking. See the considerations of Ralph Betza.

In particular, as to the R-B vs C-A difference:
A Rook has mating potential, a Bishop not. But:
A Chancellor has mating potential, and so does an Archbishop.
A Rook can stray on all colors, a Bishop can only access half the board.
But:
A Chancellor can stray on all colors, and so can an Archbishop.

Theoretical considerations like you refer to are just nonsense, with no
connection to real life. Elaborate nonsense, admittedly, but nonsense
nevertheless. No amount of _talk_ will increase the value of a Chancellor
versus an Archbishop. Only what happens on the board counts. And on the
board A+P beats C (in the presence of other material, between equal
players) by a sizable margin (like 60-40). Just like B+P is no match for a
Rook, in the presence of enough other material.

If you consider that 'flawed', because the fact that R is more valuable
than B+P 'implies' that C is more valuable than A+P, to be
'consistent', then I wonder what your concept of piece value really
means. What would you rather have (if you can choose to make a trade or
not), a piece that is more 'valuable' accoording to some contrived
reasoning, or a piece that gives you a larger probability to win the game?
If it is the latter, you should use the piece values I give, and not the
'more correct' ones of Aberg.

In real life A performs nearly as well as C in almost any combination of
material, and B gets crushed by R in almost any combination of material
except the sterile KRKB ending.