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<i>'Archangel is Gryphon plus Bishop'. If your numbers do not show it as supeirior to Q, mustn't that be an eror in the numbers?</i> <p> The crowded-board mobility calculation for the Gryphon predicts that is very similar in value to a Cardinal. Because the Gryphon can move like F anyway, adding Bishop to its move is really only adding the longer Bishop-moves, and the Archangel is only one half-knight stronger than the Gryphon, and a piece one half-knight stronger than a Cardinal-class piece is a Queen-class piece, or so the numbers say. <p> Still, my gut instinct would think, like you, that an archangel would be noticeably superior to the queen. This is something that can only be resolved through playtesting. If the numbers are right, well, this somewhat bolsters our faith in using the mobility calculation to say two pieces are roughly the same in value. If the numbers are wrong, it is very interesting, because both the queen and the archangel are well-balanced pieces, and the first step to improving a theory is trying to identify those cases where it fails. <p> After calculating the 'forking power' for a number of these pieces, these are my second thoughts... <ul> <li>What I call 'forking power' is really only the average number of two-square combinations attacked by a piece, and therefore treats pins and forks as the same phenomenon. Perhaps this is wrong. <li>If two pieces have similar mobilities, they will almost certainly have similar FP's. Therefore, the theory can't make any predictions that couldn't also be made by invoking a multi-move mobility component to value, or simlper yet, a power-law dependence of value on mobility. I originally thought up the archangel to think of a piece with similar mobility as the queen, but vastly greater forking power. But this 'vastly greater' wasn't nearly as great as I hoped. :( <li>Not all two-square combinations of attack are created equal. Maybe two squares in the same direction are more or less valuable than two squares in different directions. <li>In short, I originally invoked this definition of forking power because it was something that would be calculated without any undue difficulty or assumption, and would be much larger for strong pieces than weak pieces, so with the right scaling factor, could be made to give the queen the right value. It may be an improvement to the theory, but I can't think of any test for it that would distinguish it from a few alternate improvements. </ul>