I really like this idea. I think it would be a great way to learn as well
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I loved Danny's "Hand and Brain" games with John Urschel, and my life goal is now to get to be directed in a game by Danny just like that. I know it can never happen, though, so I'd like to request the next best thing: a Hand and Brain mode for live chess on this site.
This would be a new kind of chess, like chess 960 or four player chess. In this variation, an engine would determine the best move for each player, but only tell that player the piece to move. (Perhaps the relevant pieces would be highlighted on the board, and no other pieces could even be moved.) The challenge of the game would be to see which player could better divine the truth of the engine.
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I think this would not only be tons of fun, but it could be a super powerful training tool. Please consider making it happen!