An interesting case is a Bishop that also attacks the square right in front of it, but cannot move there (BfcW). On 8x8 about half of the positions is won. Which is an intermediate value. It appears there also is a fortress draw here: once the bare King reaches the back-rank corner of the other shade than the (augmented) Bishop is on, there is no way to smoke it out. Since the Bishop cannot attack that corner, the King can always return there after zugzwang forced it to leave it; as long as the bare King stays on a square adjacent to the corner the other King cannot attack that square either.
If we also add a color-switching move (e.g. BfW or BfcWbmW), all corners can be attacked, and nearly all positions are won.
An interesting case is a Bishop that also attacks the square right in front of it, but cannot move there (BfcW). On 8x8 about half of the positions is won. Which is an intermediate value. It appears there also is a fortress draw here: once the bare King reaches the back-rank corner of the other shade than the (augmented) Bishop is on, there is no way to smoke it out. Since the Bishop cannot attack that corner, the King can always return there after zugzwang forced it to leave it; as long as the bare King stays on a square adjacent to the corner the other King cannot attack that square either.
If we also add a color-switching move (e.g. BfW or BfcWbmW), all corners can be attacked, and nearly all positions are won.