Single Comment

'I only think color balance for pieces matter if the pieces are colorbound. It doesn't matter to me what colors non-colorbound pieces end up on since those pieces can change color at will.'

The color-bound pieces imbalance (e.g., queen and archbishop both on dark or light spaces) is measurably a much more efficacious fault than the color-changing pieces imbalance (e.g., chancellor and archbishop both of dark or light spaces) although I classified both as 'minor faults' in the overall scheme consisting of only 4 distinct faults.

As measured by the movement capabilities for each power piece taken one-at-a-time on an otherwise empty board at its opening position [an ideal, potential maximum evaluation to reveal space-based imbalances rather than an actual, obstructed condition existing upon the very first move of the game by white], a color-bound pieces imbalance often results in a number for one color that is appr. twice as high as the other color in CRC. For example, 39 dark spaces can be occupied while only 20 light spaces can be occupied on the first move. So, it is NOT merely a trivial fault (instead of a minor fault).

A color-changing pieces imbalance typically only throws the numbers (from a total of appr. 55-59) out of balance by 2-4 more than they would otherwise be since a perfect balance never exists anyway with any CRC positions. Still, when you have a vast number of positions to choose from (12,000+ according to Reinhard Scharnagl), why tolerate this imbalance, either. Logically, I cannot tolerate the former fault. So, I will not tolerate the latter fault of a similar nature, either. Thereby, I maintain consistent standards for the model.

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'... I no longer think it's essential that each and every pawn in the opening setup is defended. I think it's a good idea for white to be unable to threaten mate on his first move, since otherwise Black can be prevented from making natural developing moves in the opening; having all pawns defended stops these kinds of threats.'

Yes but ...

An undefended pawn can, with perfect play by white (the player with the first-move-of-the-game advantage) over a number of moves irrefutably result in a stolen pawn despite perfect play by black. [{proven to us by someone}* using a powerful, multi-CPU computer with one proposed CRC opening setup.] Ultimately, this material disadvantage is probable to lead to the eventual defeat of black. This is too unfair to black. The potential amplification of the pre-existing and marginally, unacceptably-high advantage for white is the reason that an undefended pawn is unconditionally classified as a fatal fault for any CRC position under my system.

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'I am not sure every pawn around the king has to be defended two times or more. FIDE chess has had, for over 500 years, the King Bishop's pawn defended by only the king, and this has not stopped FIDE chess from becoming the most popular Chess variant that we will ever have.'

Yes but ...

Standard Chess is the most stable FRC position available.

[You can quickly verify this fact by creating a select FRC scheme in a likewise manner as you created a select CRC scheme.]

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'However, I can see why one may not want these weakly defended pawns in a Capa setup, since there is 18 pawns more power (2 more pawns, the archbishop, and the marshall/chancellor) on the board than in FIDE Chess.'

Exactly.

My analysis of fault-free and faulty positions exists entirely within the relative context of what resources are available with a given piece set and class of games. Consequently, I demand higher standards of the CRC piece set on the 10x8 board defensively than of the FRC piece set on the 8x8 board.

Since I have only developed one tool to date, the select CRC analysis tool, I realize this fact was unexplained and undemonstrated.

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Whatever piece set and gameboard with 100's-1000's of possible opening setups is presented, my goal is to customize a method to it by:

1. Focusing upon a highly-selective set of positions based upon your well-defined, easily-used criteria as potentially most favorable, interesting, least asymmetrical and worthwhile to investigate in detail- existing in a number manageable for one person in terms of the time and work required.

2. Applying an extremely-selective filter so that only one to a maximum of a few of the very strongest positions available survive with a rating of fault-free.

The very best possible game(s) out of the vast number within a class should exist there. This is due to the fact that the number of pawn backups (in chess variants related to standard Chess) impose mathematical limitations upon what is possible, despite the vast number of tactical, offensive multi-move options available, to effectively imbalance the game to the further advantage of white (the player with the first move of the game).

*Edited - JG