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The same idea was also recently posted to the CV subreddit, where it recieved a bit of discussion; in particular it was noted that the game is practically guaranteed to reach the endgame
Some years ago I read about a similar variant proposal in a forum of a game site. The author named it 'stale chess':
Win by stalemating the opponent; it is forbidden to give check.
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A similar idea was posted here under Modest Proposals - Various Authors. [QUOTE]
Sacred King Chess Peter Aronson This game is played just like usual Chess, except you may not move one of your pieces in such a way as to give check to the opposing King. However, the usual rule against moving into check still applies. Victory is by bare King (reducing your opponent to nothing but a King) or by stalemate. You do not get a chance to capture your opponent's last non-royal piece after they capture yours. This tends to be a longish game. Your King is very effective in defending your pieces, since captures that would put it into check are not allowed.
A ZRF has been written for this game:
sacred-king.zip. [ENDQUOTE]
1.Kd1 stalemate victory!