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This gave me an idea for a variant I would like to playtest: White moves and chooses two possible moves to make on his following turn. Black moves and does the same. White then plays one of his possible moves, and so on. If only one of the moves is legal, then that move must be played. If neither of the chosen moves can be legally played, then that player loses. This might be called Psychic Chess.
Another more convoluted idea is that a player gives a certain number of possible moves, say four, but must pick one (secretly) that he must then play on his next turn. Obviously, there is some luck involved in this game. This may make for fun over-the-board play, and the game could be named Multiple Choice (or Multiple Guess?) Chess.
There's an error in this page. It says that Choice Chess 'differs only in one aspect from Choice Chess'. I think it's supposed to say 'differs only in one aspect from Compromise Chess'.
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And the Diagram here is really the same as that for Refusal Chess, except that it announces in advance what his second choice is.
Perhaps this gives away too much? Even though it is usually quite obvious what the best move is that you should not allow it to play, it might be better to randomly decide which move it will play automatically, and which it presents as an alternative.