I have implemented a new meaning of the o modifier on non-final legs. On a final or only leg the legacy meaning of 'cylindrical piece' remains valid. On non-final legs it means the move is allowed to step off board. This is treated similarly to hopping, where you step on an occupied square, and will terminate the current leg to continue with the next.

Why would this ever be useful? Well, it turns out there are several applications. One is the Reflecting Bishop, which bounces from the board edge. To 'sense' the edge you can optionally extend the Bishop move with a Ferz step in the same direction. And if that lands off board, you can retrace that with another Ferz step, and then continue as a Bishop at right angles. So [B?foF-bF-sB]. The ? indicates this 'hook move' extension of the trajectory is optional, and that you can terminate after a normal B move as well.

Another example is the Edgehog: this moves as a Queen, but only from or to an edge square. To describe these moves you need to sense for the edge at the start or the end of the move, respectively. When a back-and-forth King step can hit an off-board square you are on the edge, and can continue with the real move in the next (and in this case final) leg: [oK-bK-Q]. Or for moving to an edge [mcQ-oK-bK]. (There has to be an explicit c on the Q move there, as otherwise the latter would not be able to capture, being a non-final leg.) This works, but is a bit inefficient for the AI, which is still too stupid to recognize that moves that go through a different path to the same square are really the same move. So it would search each Edgehog move 3 times, reaching the destination through the three different off-board square the oK step can reach. This would needlessly drive up its thinking time. This can be cured by probing more selectively (directionwise) for the edge: [vvssoK-bK-Q][mcQ-foK-bK]. This limits initial probing to orthogonal directions, (which, except for the corner case, hits only a single off-board square), and probing on the target square to the forward direction.

Off-board detours also make it possible to describe the Ultima Withdrawer and Advancer. These are given an extra back-and-forth step at the start or the end of their trajectory, respectively. With this step they must either capture an enemy, hop over a friend, move through an empty square, or stray off board. Without the latter, it would not be possible to describe moves that dissociate them from the edge. There is one problem: we cannot use the p for describing the hopping, because that would also allow hopping over an enemy piece, and thus make the capture of it optional. While the capture must be a mandatory side effect of the move. Fortunately we can use the 'friendly capture + unload' trick to describe friendly hopping. But this forces us to describe it as a separate move from the real capture, as the latter should not be unloaded. So we get [omcK-bK-fmQ][dK-buK-fmQ] for the Withdrawer, the first move describing moving away from the edge, and empty square or an enemy (and capturing the latter), the second moving away from a friendly piece.

Similarly, the Advancer will be [Q-fomcK-bK][Q-fdK-buK]. These descriptions are not very intuitive; it would probably be preferable to have some method to describe the captures here as Fire-Demon style 'burning', but in a specific direction, rather than through all K steps. This still has to be designed, though.