[auemejjt] Combinational turn-based Bughouse

Continuing on previous musings of turning Bughouse chess into an untimed 2-player turn-based game:

If you are to move on both boards, you cannot pass.  For long stretches of the game, therefore, the same player will have the privilege to pass; the other player has the privilege of deciding which board progresses.  The situation flips when that one player passes.

To prevent infinite stalling, easiest would be to forbid 2 consecutive passes; however, I feel this alters the strategic feel of the game too much.  If one player's optimal "move" at a certain point in the game is to pass, then the other player's optimal move is to force them to move, by the nature of it being a zero-sum game.  I think forcing the passing player to move can usually be too easily accomplished with a throwaway move on the other board, followed by a pass.  For example: Player X faces immediate mate (mate in 1.5) on the board 1 to move, and needs to capture a certain piece on board 2 (that has player Y to move) to avert it.  Player X passes, forcing player Y to play (because consecutive passes are forbidden) on board 2.  Player Y plays one move (of likely several) that avoids giving up that certain piece.  Player X then responds on board 2.  Player Y passes, forcing player X to play on board 1, yielding a winning mate in 1 for Player Y.

However, we can elaborate on this: after one player passes, the other player may not pass for the (say) next 4 moves.  In other words, if one board stalls for waiting for some capture to occur on the other board, then, on this other board, the player must execute a 4-move (actually 4.5 move) tactical combination to accomplish this task.  4-move chess problems can stump strongest human chess players (problem solvers), so this yields a rich game.  We want a device to count down the "power play" on the unfrozen board.

Things might get tricky in a Bughouse "endgame", defined loosely as when both players are facing immediate mate on separate boards.  Judiciously pull the "pass" lever at the right moment to force zugzwang on your opponent.

Compose bughouse chess problems assuming these rules.

Things might be interesting with more than two boards.