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Variant request: Bronstein chess

An idea would be that castling is only possible when king is "in-between" rooks applying classical chess rules
That you can only castle when King/Rook have not moved, king not in check and so on.
@ellum But where should the king and the rook go if they are not on the e and a/h files respectively?
The king just moves 2 squares left/right?
The original Bronstein rules are cool, makes it related to classic chess (you can only castle when your king is on e1/e8 with rooks in a corner). This would effect the theory of the game in interesting ways as there may be formations that beat the classical setup (rooks starting at e1-d1) but if we give the classical king the option to castle it changes the evaluation.
I would be thankful for any variation of the castling rules, even my lest favorite with no castling at all.
@boorchess Even with castling, the classical setup is at a large disadvantage against the other setups without castling. I did a quick computer analysis (Stockfish 9), here are the scores of various white starting positions against a classical black setup:

Position Score Depth
BKNRRNQB +1.94 34/48+
BQNRRNKB +1.80 35/48
KBBRQRNN +1.79 31/43+
KNBRQRNB +1.66 33/42+
KNBRRBNQ +1.58 31/43+
QNBRRBNK +1.30 32/44

An advantage of 1.5 pawns is often enough for a GM-level player to convert. So leaving the castling for the classical setup only is kind of pointless, because it is not really viable.
but does the engine understand that it can not castle with hybrid setups ? I do not put much stock in engine evaluations of starting positions in chess.
Also the original rule set says King at e1 and rooks in the corner. You can put the minor pieces and knights (and one of the rooks) anywhere you like and still be able to castle.

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