To H.G.:

I'm not sure how you measured an Archbishop's relative point value for every case that you mentioned. Did you always base your measurements on, say, the outcomes of a large number of games that were play-tested which involved a variant using that piece? If so, the results might at least somewhat depend on the average strength of the players involved, even if all/many were computer playing engines, though I would assume you took that into account if that was always your method. Hopefully the method can be described briefly, if you are happy to do that.

To John:

It looks like you have a valid point about saying an Amazon = Q + N is fundamentally different than objecting that a Q is greater than a R + B, in comparing by analogy. I hadn't thought about a B's limitations when a piece by itself.

[edit: though a vital follow up question could be: are 2 Queens only = 2 Rooks + 2 (different coloured) B's, or are 2 Q's in fact = 2 Rs + 2 (different coloured) Bs + 2 Pawns? Looking at your last post before this one of mine, I assume you now would put the 2Qs value as closer to the latter.]

[edit: Another follow up question could be: are 2 Amazons = 2 Qs + 2 Knights? The reason I thought of asking is that either Amazon might (using just its bishop and/or rook type powers) be able to double attack the 2 enemy knights, or else attack one enemy knight and another enemy piece. In fact, a single Amazon could do the latter in case of having a Queen and Knight for it, so again the real question becomes: is an Amazon really just = Q + N (or even less)? To strengthen my doubts a little more, I would note a single Amazon can also use its knight type power to double attack an enemy queen and another enemy piece, say even another queen, though such a queen might often have a good chance to move and guard the other piece that is being double attacked by the Amazon. As an aside, fwiw long ago I read in some chess book that it is the great mobility and double attacking capability of a queen that makes it such a powerful chess piece, and a knight of course is awesome at forking.
]


In any case, I hope it's not too objectionable to anyone if I leave my own estimates for Sac Chess pieces (which I admitted were tentative) the way they are for at least a little while longer. I can edit my submission to change my estimates after I think about it more if necessary, and perhaps have even play-tested variants using Amazons or Archbishops myself at some point. 

[edit: I had forgotten that I've already played a quite small number of games of Seirawan Chess (8x8 chessboard variant, with first rank drops of Hawks [aka Archbishops] and Elephants [aka Chancellors] in the opening phase) and it seemed to me based just on these games (two of them with a fellow chess master) that the Chancellor seemed at least as dangerous a piece as the Archbishop, especially after the opening phase, if nothing else. Also, I wonder if there really has been enough human experience playing with such fairy chess pieces yet for even a very strong human chess player to really know how to defend (when necessary) against their unusual movement capabilities.]