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I wonder if a game could be devised where you could pocket any piece
execept the king, but there was a cost.  For example, using the beginner's
piece values, perhaps in order to pocket a piece, you had to sacrifice 1/3
of its value. This would give:

Pawn = free
Knight or Bishop = pawn
Rook = 2 pawns
Queen = 3 pawns, Knight, or Bishop

Non-material costs could be used instead (double move for enemy, etc.)

I just thought of this--Demotion Pocket Chess.  You can pocket a piece, but
it drops as the next lower-valued piece.

Queen becomes Rook
Rook becomes Bishop or Knight
Bishop or Knight becomes Pawn

A pawn could be pocketed (to get it out of the way) but drops as nothing =
allows player to pass a turn!

The cost of pocketing a Queen seems too high--perhaps demote the Queen to
a Cardinal and the Cardinal to a Rook? This idea would work well with a
Capablanca variant.

I forget whose idea it was or where I saw it, but the idea was you could
pocket any piece (as a move) and place a pocket piece (as a move), and
there was no restriction about how many pieces you could have pocketed,
but immediately following your drop, your opponent got a double move.

My reaction at the time was that the rule changes were only of tactical
value because in most situations the doublemove response should be able to
easily answer the dropped piece (not to mention that the teleportation of
the dropped piece required two tempi to complete, and in the meantime, the
piece did had only second-order usefulness.  It defended nothing and
attacked nothing, but could only threaten to defend or attack things. 
Granted, it threatened to attack and defend EVERYTHING, but I still think
the doublemove response is overkill.)

Thanks to Mike, Peter, and Sam, I think my original question might be
leading to a couple of very good new variants (or more, since there might
be more demotion sequences that are interesting).  I'm glad I provided the
initial nudge, though I take none of the credit for whatever games get
developed here.  I might suggest that pawns remain pawns even when
pocketed, though, since otherwise there will be little reason to pocket
them; if so, we would need to restrict where they can be dropped otherwise
threats to drop pawns one step from promotion might be unbalancing.
Perhaps of the above three can whip up a ZRF for playtesting?  Perhaps
modifying the Tauschach ZRF will make the job easier by providing a
starting point?

There does not seem to be a pocket knight preset :)! Is there one, but I cannot find it?

Edit: King is now KilO2jirO2 so that it can't castle with Pocket Knight. Thx HGM!

Clever solution to the drop problem!

It never occurred to me to use the Universal Leaper move for mimicking drops. An alternative over defining it as an initial move would be to define a captureMatrix that has the Pocket Knight promote to Knight whenever it moves (captureMatrix=/////N). The Pocket Knight can then be simply mU, and you would not need so many inaccessible ranks to isolate it from the board.

I also was thinking about how clever that solution is. I now have a way to represent the Anvil (icU)!

Addendum: If the Interactive Diagrams had a rule that pieces could move out of the "hand" with an iU move (or perhaps an atom specifically designated for the purpose), that might be a more generalized solution.

If the Interactive Diagrams had a rule that pieces could move out of the "hand" with an iU move (or perhaps an atom specifically designated for the purpose), that might be a more generalized solution.

This is one of the things that has been on the to-do list for very long: an atom to indicate dropping. The plan was to use @ for this as if it were a capital. Of course directional and some other modifiers and ranges would be meaningless in this case, so the corresponding lower-case letters could be recycled for drop-specific meanings. Like j meaning that you cannot drop on first rank (somewhat similar to its use for ski-pieces, if you imagine the dropped piece to come from behind the baseline), and a range behind the @ indicating the maximum rank you can drop. The f (for 'file') could mean that only a single piece of the type can be in a file (and ff two pieces), while the s could limit you to a single piece per square shade, and b for the entire board.

The problem is that it doesn't bring very much as long as the AI doesn't know how to use the drops, and currently it doesn't search deep enough to see the advantage of drops, and will be overwhelmed by the large number of drops that would in general be possible. Limitations on what you can drop in the same file or shade are by definition a legality matter, and since the Diagram highlights all pseudo-legal moves you would not see that even in manual play. Limitations on the ranks you can drop can now be specified by a morph parameter (exempting the normal moves), so for that you won't need it either.

And then there is the issue of evaluation. The AI uses the Pocket Knight in a pretty stupid way, dropping it as quickly as possible. While the best use is of course to keep in in your pocket as long as possible. This behavior comes from the built-in drive to centralize pieces, and in the representation here the Pocket Knight is furthest from the center. So it gets an enormous bonus for brining it into play.

This exposes a flaw that might have a general fix: in a sense pieces that have an initial move are not the same pieces as those that no longer have it. Basically the first move always is a demotion. Now the value of a one-time move is of course not nearly as large as when you can use it forever. But it would contribute some, and especially when it is an extremely powerful move like U, even the small fraction it contributes can be significant compared to positional bonuses like centralization. So moving pieces with initial moves should incur a penalty, the magnitude of which could be calculated by repeating the value guestimate with the initial move enabled.

All that's worth considering, and if I were better (more practiced) at programming I'd offer to lend a hand.

I'll just hope that you and I both live long enough that I can one day drop an Anvil into a game. :)

(Though the icU ikcU solution is still possible!)

Perhaps I should treat U as a special case, and give a significant penalty (like nearly one Pawn) for moving a piece that has such a move. Even if it was not an initial move. Because it will always be a wasted move; after it you cannot reach any square that you couldn't reach already. So there must be some tactical reason before considering it.

There is the issue of captures, though, in case of mU. In particular when you are in a location where you have zero captures, like the Shogi hand. My first Shogi engine initially had that flaw: it kept hoarding pieces in hand, because these were worth more there, but this eroded its board control so much that his defenses easily collapsed under attack. So I added a non-linear term that discouraged holding too much material in hand.

Regarding all that, two advantages of a drop/mU are that the piece's presence in a particular spot can block attacks; and its location can be the launching point for a potential capture, which drops normally cannot do (my Anvil being that rare and probably unique exception). So, an mU (or @) should be given greater weight for any given turn on the basis of those two things.

And any initial move, drop or otherwise, should have a lowered effect on the piece's net value (if it doesn't already). After all, you only get one shot at it.

Since when did the AI ​​stop using Pocket Knight in such a stupid way? I noticed that now the AI ​​doesn't drop it as quickly as possible.

I suppose I implemented the idea I described earlier in this thread, to give U moves a penalty in the positional range. I don't remember when I did that. (Or in fact that I did it at all.)

BTW: K-side castling is done with the pocketed Knight, instead of the Rook! Better move the pocket squares to 2nd rank.