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Multiple choice chess

Since you would always choose the worse move for your opponent , this game has another name: frustration chess.

Intresting idea! But I think the most of the games would end in a draw, as no tactics will be played.
Might not be that easy, you could anticipate that you'll be allowed to choose for your opponent as well.
End-game K+R vs K looks like draw, but K+Q vs K is still won. Tactics could be tricky in a different way.

Actually this chess variant exists already -
it's played like that -
whenever you play your move, your opponent may object and you have to play another move.
Your opponent may object ONCE per turn - so that you always get to play AT LEAST your second-preferred move (the opponent says - "No!", or "I disagree" or words to that effect, and HITS YOUR CLOCK)
Of course, you can trick him and play the second-best move FIRST, so that if he objects, THEN you play the best line... so he can't just automatically object to whatever you say.
This is a very exciting chess variant - I recommend it with five minutes. Excitement and laughs aplenty.

I think I knew the one u mentioned but thought that it was allowed only once in the entire game, which would also make sense.
The player who's turn it is must name two legal moves, the opponent may choose. Then the opponent names two legal moves and so on...
(Sometimes there is only one legal move - than just play that move.)