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Larry, if you go through the comments for this page, you'll find some comments by HG Muller on piece values there. In general, he values the minister at 6.33 pawns and the High Priestess at 6.50. The guard, he values for the endgame at 3.2, but more like 2.8 at setup. And he makes the comment that all the pieces in this game that are analogs to pieces that can mate in regular Capa can mate in this game. Start about in the middle of the 30 comments.

Mats, you've made an interesting point in saying that one needn't exhaust one's brain in this game, which fits kind of next to Larry's comment about being able to recover in this game. In FIDE, tactics, from the nature of the pieces being generally infinite sliders, is always active. While you certainly could use a strategy, it's 'positional play', aka: tactics, which often determines the game, and always has at least an indirect effect on the outcome. In Great Shatranj, strategy is always active, but tactics tends to happen more sporadically, with intense bursts for 5 - 10 turns at a time, followed by a bit of strategic picking up of the pieces. In closed games, given that no piece here has a blockable move, I suspect the tactics would be more varied, intense, and far-reaching. These pieces are made for close-in, with wide, short footprints. The High Priestess attacks 8 forward squares [and 8 rearward], every turn, unblockably. Does the B+N?