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H. G. Muller wrote on Sat, May 3, 2008 06:32 PM UTC:
Well, I got that from the beginning. But the problem is not that the A
cannot be defended. It is strong and mobile enough to care for itself. The
problem is that the Knights cannot be threatened (by A), because they all
defend each other, and can do so multiple times. So you can build a
cluster of Knights that is totally unassailable. That would be much more
difficult for a collection of all different pieces. This will be likely to
have always some weak spots, which the extremely agile Archbishops then
seek out and attack that point with deadly precision.

But I don't see this as a fundamental problem of pitting different armies
against each other. After an unequal trade, andy Chess game becomes a game
between different armies. But to define piece values that can be helpful
to win games, it is only important to test positions that could occur in
chames, or at least are not fundamentally different in character from what
you might encounter in games. and the 4A-9N position definitely does not
qualify as such.

I think this is valid critisism against what Derek has done (testing
super-pieces only against each other, without any lighter pieces being
present), but has no bearing on what I have done. I never went further
than playing each side with two copies of the same super-piece, by
replacing another super-piece (which was then absent in that army). This
is slightly unnatural, but I don't expect it to lead to qualitatively
different games, as the super-pieces are similar in value and mobility.
And unlike super-pieces share already some moves, so like and unlike
super-pieces can cooperate in very similar ways (e.g. forming batteries).
It did not essentially change the distribution of piece values, as all
lower pieces were present in normal copy numbers.

I understand that Derek likes to magnify the effect by playing several
copies of the piece under test, but perhaps using 8 or 9 is overdoing it.
To test a difference in piece value as large as 200cP, 3 copies should be
more than enough: This can still be done in a reasonably realistic mix of
pieces, e.g. replacing Q and C on one side by A, and on the other side by
Q and A by C, so that you play 3C vs 3A, and then give additional Knight
odds to the Chancellors. This would predict about +3 for the Chancellors
with the SMIRF piece values, and -2.25 according to my values. Both
imbalances are large enough to cause 80-90% win percentages, so that just
a few games should make it obvious which value is very wrong.

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