The FAD
The FAD (pronounced "fad", of course) combines the powers of Ferz and Alfil and Dabaaba.For example, from e4 this piece can go to
- d5, f5, f3, or d3 with its Ferz move; or
- c6 (even if d5 is occupied), g6, g2, or c2 with its Alfil move; or
- e6 (even if e5 is occupied), g4, e2, or c4 with its Dabaaba move.
This is a short-range colorbound jumping piece that is comparable in value to the FIDE Rook, perhaps a half of a Pawn weaker.
The Pawnless endgame of two FAD versus King is an easy forced checkmate, and the help of the friendly King is not needed.
Mathematically, this piece should be clearly stronger than the Bishop, but in its one test between two masters, the Bishops did rather well.
Although the result of a single game is not a conclusive proof of anything, it seems that the FAD is in general slightly stronger than the Bishop, but not enough to decide the game or create a tangible advantage.
However, if you can keep both FADs on the board while playing an endgame of attrition, sooner or later they will probably run amok and produce a sudden win by checkmate; this is not a bad advantage to have.