Comments/Ratings for a Single Item

Note that even a King and Commoner (nonroyal piece moving like a King) can checkmate a lone King on an 8x8 board, without using something like the King-Kaiser Faceoff rule. So a Kaiser and Duke can easily checkmate a lone King. Also the Checkmating Applet tells me that a Kaiser and two Eagles can checkmate a lone King in twenty moves or less. Dividing the Fairy Stockfish endgame values listed in the game by 2.76 yields:

Pawn=77, Knight=309, Bishop=332, Rook=500, Queen=972.

Soldier=98, Eagle=389, Cardinal=515, Tower=536, Duke=417.

I would guess that the minimum values are: Eagle=450, Cardinal=500, Tower=650, Duke=550. At least, I am reasonably certain that an Eagle and a Duke are a match for a pair of Cardinals. A final note: in a game of Empire Chess gaining Pawns seems more important than hanging on to all those higher valued pieces. My immediate goals would include trading an Eagle for Knight+Pawn and trading a Cardinal for Bishop+Pawn.

For the few divergent pieces I once tested the rule of thumb that their total value is the weighted average of the non-capturing and capturing components, where the later count twice as much as the former. So mQcN was around 5 (N=3, Q=9 scale), mNcQ around 7. The Tower and Cardinal can also be written as mQcR and mQcB, so I would expect values 6.3 and 5 for those.