Meet the Furlrurlbakking!

The Furlrurlbakking, or frlRrlbK for short (?), is a piece that moves and captures with the forward and sideways half of the Rook's powers or the sideways and rear parts of the King's powers.

Here is a complete example of its power: from e4, a White Furlrurlbakking can go to f3, e3, d3, or

d4, and if d4 is empty can continue to c4, and so on through b4 and a4;
e5, and if e5 is empty to e6 and on to e7 and e8;
f4, and if f4 empty, g4 and h4.

This piece is as strong as a FIDE Rook, or at most a tiny tiny bit weaker or stronger. The retreating move of the Rook contributes such a small percentage of the Rook's value that it is hard to make a mistake when designing a piece such as this!

Here is a composed position: White has King h1, frlRrlbK on b7; Black has King h8 and Pawn a5. White to play can still draw by checking with the frlRrlbK on b8, then a7 and a8:

if Black goes to the sixth rank, (frlRrlbK)a7-b6+ catches the Pawn.
if Black comes all the way to b8 with his King, the same move (frlRrlbK)a7-b6+ catches the Pawn.

Here is another one: White has frlRrlbK on f7, Black has Kh8 and Pawn h7; White plays (frlRrlbK)f7-f8 mate.

Okay, so these are not great endgame studies, but they *are* original!

Meet the Furlrurlbakking!

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