I heard that in formal games you have to move the piece that you touch first. What if the piece cannot move, as in there are no legal moves that involve that piece? What would happen in that circumstance?
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The laws of FIDE state in article 4.5 that "If none of the pieces touched can be moved or captured, the player may make any legal move."

d4zed
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10@akostadinov that probably refers to the opponent's piece. If you touch one of their pieces and you can capture it, then you need to make a move that captures it. I guess. – terdon Nov 18 '21 at 14:05
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4@akostadinov, it's in the articles right before: "4.3 Except as provided in Article 4.2, if the player having the move deliberately touches on the chessboard: [...] b. one or more of his opponent’s pieces, he must capture the first piece touched which can be captured" . – ilkkachu Nov 18 '21 at 15:06
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5Wow, lo and behold! When I was growing up (born mid-80's), we were taught that the "If you touch it, you must move it" rule had been done away with. There were some people who still thought the rule was in effect and would try to hold you to it, but many said it was an older rule that had been discarded. It's interesting to see official rules here, in Article 4 in general, saying that it is currently in effect. – Panzercrisis Nov 18 '21 at 20:15
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4@Panzercrisis - It's more in effect than ever. The rule has been tightened in 2017. However, what was discarded a hundred years ago, is a rule that if the piece touched had no legal moves, then the player had to move their king. – Jirka Hanika Nov 19 '21 at 07:12
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1Note, though, that it is at least "bad style" to touch a piece that can't move. Assuming I'm the arbiter, I let it go if it is a non-knight officer in the starting position (usually then a "jadoube" gets mumbled into the beard at most if at all), but if I see this frequently, this probably will earn the player a "you, you!", preferrably after the game, since it might be construed as a distraction of the opponent. Hands belong under your posterior while not moving :-) – Hauke Reddmann Nov 19 '21 at 09:37
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I think it was in the 2019 World Fisher Random semi final between Nakamura and So, where Nakamura wanted to castle, and the rook had started on g1. He moved the rook first, then the king to g1, and So called the arbiter because you can't castle if you touch the rook first. If I recall, the final rule decision was, Nakamura should've touched the king first, and ideally placed it outside the board, then moved the rook, then placed the king. So it's definitely in effect. – Arthur Nov 19 '21 at 13:11
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1@theonlygusti - It was more complicated than that, and the practice was neither uniform nor abandoned uniformly worldwide. It's worth googling up and/or a standalone question. The opponent had a choice of punishments for an invalid move out of which to request a move by the king was by far the most common one. – Jirka Hanika Nov 19 '21 at 13:23
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@HaukeReddmann I'd think the etiquette or even rule that forbids distracting or annoying your opponent is distinct from the touch rule. After all, instead of actually frequently touching pieces you can't move you could as well stop a millimeter short; the distraction would be the same, and the distraction is the reason it's frowned upon. But if a player once or twice touches a piece they cannot move in error or for adjusting its position without announcing that, it's only about the touch/move rule (and no infraction of it, as has been stated). – Peter - Reinstate Monica Nov 20 '21 at 10:26
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@Peter Yes, the touch-rule is separate. It is more specific in when it applies at all, and what the consequences are. Doesn't mean the other rule is irrelevant, especially if the touch-rule has no effect. Even if OP only asked after that rule, I would expect a good answer to touch on it. (pun appreciated) – Deduplicator Nov 20 '21 at 11:06