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Hi, all. Good to see you back, Derek. I'm glad to see you're still working on the algorithm!

I'm inclined to agree with H.G. that it almost certainly is based on effectinveness against pawn formations. Typically, we look at the bishop and the rook and decide that the rook is more valuable because it has better mobility, based on some calculation (e.g., how many spaces can it slide to, on average, if each square has an x percent chance of being occupied.) But this approach only gives an 'instantaneous' mobility accessment. Because of the pawns, (and perhaps for other reasons,) this isn't good enough.

Because they're the weakest piece in the game, pawns make good obstacles. Any pawn that is defended generally can't be chased off or taken. And, since their move is so slow, the obstacles can be lasting, especially considering pawns can become locked with enemy pawns quite easily. In essence, pawns become the 'terrian' of the chessboard, and how well a piece can navigate this terrain is very important to determining the real mobility of a piece. Unfortunately, calculations of instantaneous mobility don't really reflect this.

There's already plenty of evidence that a piece's position relative to the pawns affects its value. A knight fortified in the center behind enemy pawns gets a very large bonus for being a 'posted knight.' A bishop that is on the same color as the player's pawns trapped in a locked formation is a 'bad bishop' and gets a huge penalty. Of course, with both of these, it isn't a bonus or penalty intrinsic to the general value of the piece, but rather because of its circumstance... But I think we can consider an Archbishop Bonus the same way. The more pawns there are on the board, for example, the larger the bonus. I have to believe that in endgames where the pawns are mostly gone, the gap in value between the archbishop and chancellor widens greatly, in favor of the chancellor (as instantaneous mobility calculations would suggest.)