Thus, in Half Chess, all the distance-moving pieces travel half as far (rounded up) as in FIDE Chess, but the Knight is replaced by the Crab of DemiChess. This is a simple change to make, and yet it leads to a situation which I find highly pleasing.
In Half Chess, the pieces move either half as far or in half as many directions as in FIDE Chess, and the pieces are worth half as much as in FIDE Chess. The pieces move in the same general way as FIDE Chess, merely half, and retain the same relative values -- the Crab is worth three half-Pawns, the Halfling Rook is worth either 4.5 or 5 half-Pawns, and so on. (The King and Pawns have their fighting power doubled, as compared to FIDE Chess.) Surely this game is at least half as interesting as FIDE Chess!
It is half, and it is Chess. The pieces move in their natural Chess patterns, but only half, and their relative values are natural. Therefore, it may be a useful "first Chess Variant" for getting chessplayers interested in variant games.
Because the rule of half is so simple, it is clear that Almost Half Chess, replacing the Half Queen with the Half Chancellor, is a good game, and it is clear that if one side plays with the Half Queen and the other side plays with the Half Chancellor, we have a simple game of Half Chess with Different Armies.
In fact, two other simple plug-ins are available: instead of the Crab, one side could use a Half Fibnif (bFffN); instead of the Half Rook, a Half Crooked Bishop; and all we lack for a proper game with different armies is a Bishop substitute.
The Lobster from DemiChess would be okay, but there is already a rearward F in the army (in the Half Fibnif) and the Lobster is a jumper rather than a runner; and thus although the Lobster may have the right value it is not perfect enough for this exceptionally aesthetic army.
I want to suggest the use of a Halfling Cannon, but I'm not sure of the value.
Alternatively, the Halfling bAADD is somewhat pleasing: it jumps 2 squares Rookwise, over obstacles if need be, then if that square was empty can continue jumping the same way, that is, in the opening position it can jump from f1 to f3 (over the P at f2), and because f3 is empty it can continue to f5 as part of the same move, but because it's a halfling it cannot continue moving to capture the Pawn at f7; in addition, it can jump two squares diagonally to the rear. This piece can see only half the squares of one color, which means that the Bishop's defect of being colorbound is doubled in the AADD! Half the visibility for this halfling makes it seem very appropriate for a Half Chess Different Army. The Halfling bAADD ain't half bad.
And so, we have half-Chancellor, half-crooked Bishop, half-Fibnif, and half-bAADD, for an army that is expected to be properly competitive against the "orthodox" Half Chess army.
Remember, of course, that the piece values given here are theoretical, and have not been playtested. For example, I haven't even worked out the fastest possible checkmates.
If Black plays 1...Ke8-f8, the R on g7 is attacked, because the R on c7 cannot move far enough to protect it. Rc7-e7 protects but gives stalemate, Rc7-d7 does not protect, and Rg7-h7 allows Kf8-g8 and the King escapes from confinement. Thus we see that W must play Rc7-f7+, but after Kf8-e8, what next?
If W makes a tempo move (we assume he has a King on the board somewhere, and we assume it cannot come in and help), Black plays Ke8-d8, and then after Rg7-g8+ he simply plays Kd8-c8 and laughs at the shortness of the Halfling Rook. (In fact, the King inwardly quakes with terror at the thought of what would happen if the Halfling's leash should break, but conceals his fear and assumes an exterior air of aloof amusement as the slavering jaws of the Rook snap shut inches from his face.)
Instead, W must cut off the K with Rf7-d7, forcing Ke8-f8, and now he can play Rg7-h7 so if Kf8-g8 then Rd7-g7+ (from c7 to g7 would have been too far for the Halfling), make a tempo move, and give mate. The trick is to get the Rearmost Rook (the one that's farthest from the K) onto the edge of the board so that it can make a move 4 squares long.
Of course, after 1...Ke8-f8 2 Rc7-f7 Kf8-e8 3 Rf7-d7 Ke8-f8 4 Rg7-h7 Kf8-e8 (instead of moving the K to g8), W simply needs to make a tempo move to reach the same position as before.
This was surprisingly complicated.
With K+zF+B I think that you can only force mate in the corner where the corner square is the same color as the xF.
The method of confining the King to the proper corner is left as an exercize for the unwary.