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H. G. Muller wrote on Sat, May 3, 2008 08:18 PM UTC:
| And by that this would create just the problem I have tried to 
| demonstrate. The three Chancellors could impossibly be covered, 
| thus disabling their potential to risk their own existence by 
| entering squares already influenced by the opponent's side.

You make it sound like it is a disadvantage to have a stronger piece,
because it cannot go on squares attacked by the weaker piece. To a certain
extent this is true, if the difference in capabilities is not very large.
Then you might be better off ignoring the difference in some cases, as
respecting the difference would actually deteriorate the value of the
stronger piece to the point where it was weaker than the weak piece. (For
this reason I set the B and N value in my 1980 Chess program Usurpator to
exactly the same value.) But if the difference between the pieces is
large, then the fact that the stronger one can be interdicted by the
weaker one is simply an integral part of its piece value.

And IMO this is not the reason the 4A-9N example is so biased. The problem
there is that the pieces of one side are all worth more than TWICE that of
the other. Rooks against Knights would not have the same problem, as they
could still engage in R vs 2N trades, capturing a singly defended Knight,
in a normal exchange on a single square. But 3 vs 1 trades are almost
impossible to enforce, and require very special tactics.

It is easy enough to verify by playtesting that playing CCC vs AAA (as
substitutes for the normal super-pieces) will simply produce 3 times the
score excess of playing a normal setup with on one side a C deleted, and
at the other an A. The A side will still have only a single A to harrass
every C. Most squares on enemy territory will be covered by R, B, N or P
anyway, in addition to A, so the C could not go there anyway. And it is
not true that anything defended by A would be immune to capture by C, as
A+anything > C (and even 2A+anything > 2C. So defending by A will not
exempt the opponent from defending as many times as there is attack, by
using A as defenders. And if there was one other piece amongst the
defenders, the C had no chance anyway. 

The effect you point out does not nearly occur as easily as you think.
And, as you can see, only 5 of my different armies did have duplicated
superpieces. All the other armies where just what you would get if you
traded the mentioned pieces, thus detecting if such a trade would enhance
or deteriorate your winning chances or not.

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