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Kevin Pacey wrote on Sat, Jan 28, 2017 11:56 PM UTC:

Thinking now (once again in a non-empirical way) about adding a non-capturing wazir component to a given piece in order to make a compound piece of the two, it might heavily depend on what piece is being added to in this way, in my humble opinion. If a non-capturing wazir component is added to a bishop to make a new compound piece (call it a 'bishopwa'), then the bishop loses its handicap of being colour-bound, which I'd guess is worth more than adding a pawn to the bishop's value (I don't know if this is close to a refutation of Dr. Muller's rule of thumb, but it might be a notable exception to it).

The observed problem in practice with the knightwa being hounded by enemy bishops or knights might be reduced in an endgame, where the knightwa might show any special advantages it has more often... but how to get past the opening and middlegame successfully for the knightwa side? That I haven't fully figured out a plausible strategy for. If I did, I'd feel more comfortable with the relatively high value I'm getting for a knightwa, using my primitive methods, which I'm having some doubts about right now (such as, if a Q=B+R+P in value, what is wrong with having knightwa=N+non-capturing wazir+P in value, rather than just knightwa=N+non-capturing wazir in value? Or at least an answer that's something in between these estimates?).

What I can suggest so far as an opening/middlegame strategy for the knightwa side in a chosen setup is to trade his bishops for some of the other side's minor pieces, perhaps at the earliest opportunity that arises, if any. After that, he might generously(?) (if necessary) give up just one of his knightwas for a remaining enemy minor piece, following which there'll be even less ways to harass his surviving knightwa, and he can hope it turns out to be a surprisingly valuable piece as the game further unfolds. Also, it seems a good idea not to allow the side with the extra pawn in the chosen setup to, at little cost, get to a pawn structure where he can eventually force the undoubling of his extra pawn, again at little cost.

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