It looks to me like the main effect of the Joker would be to restrict your opponent’s moves. Since you never know what it’s going to be, you can’t make long-term plans with it. All you could do would be to put it in a position where, say, it could make a valuable capture if it were a Queen or Rook, and thereby disincentivize your opponent from moving their Queen or Rook.
Since its strength scales with the strength of your opponent’s pieces (thereby bringing the players closer together), it can’t really effectively attack directly, and it encourages players to use less-valuable pieces, it would probably result in considerably lengthened games.
The rules for it also need to be considerably fleshed out before it could be used in actual play. As that link points out, it’s unclear if it can promote when moved as a pawn to the back rank (probably not, since it’d be too easy to get it there, but then, your opponent could keep your Joker paralyzed once it got to the back rank by just moving pawns). It’s also unclear what a Joker can do in response to an opponent moving his Joker: Does it mimic whatever the other one was mimicking, does it remain mimicking whatever it was previously mimicking, or is it unable to move at all? Or, when mimicking a pawn, under what circumstances can it move forward two ranks: When it hasn’t yet moved in the game, or when it’s on the second rank, or when the pawn it’s mimicking has done so?
All of them. Make the board 160 by 160. And add some Settler pieces that can found cities…
Rather than go through all 142 pieces, I thought of what additional movement patterns would fit in best with the existing pieces. There’s the superQueen, moves like a knight or queen. I guess you’d have one of them, and two regular queens, but it seems too powerful.
I’ve read somewhere discussion of a piece that can move like a queen, but only one or two squares. I thought it was called Prime Minister, but it’s not listed as that in the link. That seems more balanced in power. I think I’d put them in the center, and have King and Queen next to them. No Queen side castling, but King side is unchanged.
The obvious choices (and Capablanca agreed with me) would be the Rook-Knight and Bishop-Knight composites - the Queen-Knight is just too powerful. (Each of these three has several names, for instance Chancellor, Archbishop and Amazon respectively.) The Joker strikes me as too puzzle-oriented.
Even the rook-knight and bishop-knight would be pretty powerful. I estimate that a bishop-knight would be somewhat more powerful than a rook (it gains a lot from being able to change what color square it’s on), and of course the rook-knight would be more powerful than a rook, as well. Especially so since either one can use a knight-move to deploy immediately, on the first turn (even quicker than a queen). Given that rooks are already highly powerful pieces, and that their main limitation is the difficulty in deploying them, I think it’d rock the game pretty hard to add either of them.
Realistically, the Archbishop is the most likely piece to become standard (noting the fact that any new piece has very little chance of doing so). It’s similar to the existing pieces and an archbishop would be a closer balance to a rook by being able to play both colors.
But that said, there’s plenty of other possibilities:
The Archer: A replacement for the Pawn. Can move diagonally forward one space into an empty square or can capture an opposing piece one or two squares directly in front of it. Can be promoted like a Pawn if it reachs the eighth rank.
The Shield: A defensive piece. Can move like a Queen but cannot capture or be captured.
The Wizard: It can move and capture one square in any direction (like a King) but it can also exchange places with any other of the player’s pieces on the board.
The Spy: Can move like a Queen to empty squares. Can capture in adjacent squares like a King. But pieces captured by a Spy are not permanently removed from the game. The player that captured a piece with his Spy can bring it back on to the board in his first rank and play them as his own. Bringing a captured piece back counts as a complete move.
The Chariot: Can move like a Queen. But the player moving a Chariot must count all of the pieces (friendly and opposing and including the Chariot itself) in the row, column, or diagonal line that the Chariot is in. The Chariot will then move exactly that number of squares and any piece, friendly or opposing, in a square the Chariot passes through is removed. The Chariot can also be forced to move off the board and if so it is removed.