Interesting. So, the Archbishop is the only piece whose value you feel needs tweaking from its computed "safe check" value. I'd like to challenge that position, in the hope that the ensuing discussion will lead to greater understanding. First, two Bishops often work well together and I am not sure that it is obvious that an Archbishop should be worth more than a Bishop pair. I would be willing to grant that an Archbishop should be worth more than a Knight and Bishop for the same reasons that a Queen should be worth more than a Rook and Bishop, one of which would be that an Archbishop and Queen can "change the color of the Bishop." When discussing this, we should not forget that the actual value of a particular piece is dynamic and depends strongly on the position. Since the Archbishop is a jumping piece, one finds that it often joins the battle earlier than the Rooks and Bishops, so in the initial phases of the game, the Archbishop should be considered more valuable than a Rook or Bishop pair. In the endgame, however, the jumping capability is less important and it would not be surprising to find that a Bishop pair or even a Rook could be equal to an Archbishop. Of course, I still would not exchange an Archbishop for a Rook in the opening or middlegame, since my opponent's Arcbishop might checkmate me before I made it to the endgame :-). The issue of "dynamic value" also applies to the situation of a Rook versus two minor pieces. Certainly very few good chessplayers would play Bxf7+ Rxf7 Nxf7 Kxf7 as White for the reasons given. However, notice that this assumes that the exchange took place in the early to middle phase of the game, before the Rooks would be free to roam on open files and ranks; a Rook is very nearly the equal of two minor pieces in the endgame (and a Rook and Pawn is considered fully equal to two minor pieces in the endgame). I believe the reason a Rook is downgraded from 6 to 5 in 8x8 chess has more to do with the fact that two minor pieces can attack a square twice (unless, of course, the two minor pieces are a Bishop pair :-) ) rather than the actual strength of the Rook compared to two minor pieces, and that this is why a Rook is considered to be worth less than two minor pieces. In fact, one could argue that the Rook is the only 8x8 piece whose value was tweaked from the "safe check" value, since the "safe check" value of the other pieces are essentially the accepted values.