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Derek Nalls wrote on Thu, May 1, 2008 02:47 AM UTC:
As far as playtesting goes ...

Admittedly, my initial intention was just to amuse myself by 
disproving the consistency of Muller's unusually-high archbishop 
material value in relation to other piece values within his CRC set.
If indeed his archbishop material value had been as fictitious as it 
was radical, then this would have been readily-achievable 
using any high-quality chess variant program such as SMIRF.
No matter what test I threw at it, this never happened.

Previously, I have only used 'symmetrical playtesting'.
By this I mean that the material and positions of the pieces
of both players have been identical relative to one another.
This is effective when playing one entire set of CRC piece values
against another entire set as, for example, Reinhard Scharnagl & I
have done on numerous occasions.  The player that consistently 
wins all deep-ply (long time per move) games, alternatively playing 
white and black, can be safely concluded to be the player using 
the better of the two sets of CRC piece values since this single 
variable has been effectively isolated.  However, this playtesting
method cannot isolate which individual pieces within the set 
carry the most or least accurate material values.

In fact, I had no problem with Muller's set of CRC piece values
as a whole.  The order of the material values of all of the CRC 
pieces was-is correct.  However, I had a large problem with his
material value for the archbishop being nearly as high as for
the chancellor.  

To pinpoint an unreasonably-high material value for only one 
piece within a CRC set required 'asymmetrical playtesting'.  
By this I mean that the material and positions of the pieces 
of both players had to be different in an appropriate manner to
test the upper and lower limits of the material value for a certain 
piece (e.g., archbishop).  This was achieved by removing select
pieces from both players within the Embassy Chess setup so that 
BOTH players had a significant material advantage consistent
with different models (i.e., Scharnagl set vs. Muller set).  
This was possible strictly because of the sharp contrast between the 
'normal, average' and 'very high', respectively, material values 
for the archbishop assigned by Scharnagl and Muller.  The fact
that the SMIRF program implicitly uses the Scharnagl set to play
both players is a control variable- not a problem- since it is 
insures equality in the playing strength with which both players
are handled.  The player using the Scharnagl set lost every game 
using SMIRF MS-173h-X ... regardless of time controls, 
white or black player choice and all variations in excluded pieces 
that I could devise.

I thought it was remotely possible that an intransigent, positional 
advantage for the Muller set somehow happened to exist within the 
modified Embassy Chess setup that was larger than its material 
disadvantage.  This type of catastrophe can be the curse of 
'asymmetrical playtesting'.  So, I experimented likewise using a 
few other CRC variants.  Same result!  The Scharnagl set lost every 
game.

I seriously doubt that all CRC variants (or at least, the games I tested)
are realistically likely to carry an intransigent, positional advantage 
for the Muller set.  If this is true, then the Muller set is provably, 
ideally suited to CRC, notwithstanding- just for a different reason.

Finally, I reconsidered my position and revised my model.

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