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Consider this Chess960 game.

[FEN "rnkqbbnr/pppppppp/8/8/8/8/PPPPPPPP/RNKQBBNR w KQkq - 0 1"]

1. d4 Na6 2. e4 Nb8 3. Ba5 Na6 4. Bb5 Nb8
5. Qh5 Na6 6. Nh3 Nb8 7. Na3 Na6 8. O-O-O Nb8
9. Rd3 Na6

Can White's next move be to castle h-side? I can see an argument both ways: either yes, because the king never left c1, or no, because castling counts as a king move.

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    Side-note, but the board playback feature on this site evidently does not handle Chess960 and castling very well. If you scroll through the moves, and then scroll back, when you scroll back before the castle move, the King ends up in the standard starting position rather than the modified 960 position, and the Bishop ends up on top of him. Scrolling back forward causes the King to move like a Bishop. You have to refresh the page to fix it... – Darrel Hoffman Dec 28 '20 at 14:19
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    @DarrelHoffman don't forget the part where the bishop castles – user253751 Dec 28 '20 at 16:59
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    I put up a meta post about the glitch. – Darrel Hoffman Dec 28 '20 at 17:05
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Excellent question. The rules state that this is not possible. Castling can only be done once.

This is explicitly mentioned under Guidelines II. Chess960 Rules:

II.3.1 Chess960 allows each player to castle once per game, a move by potentially both the king and rook in a single move. [...]

Specifically, castling (even if the king doesn't move) should still be done by touching the king before moving the rook. You can do this several ways but the standard recommendation is to move the king off the board, move the rook to the new location, and move the king back to the new position (which can be the original c1 square).

II.3.2.5.1 When castling on a physical board with a human player, it is recommended that the king be moved outside the playing surface next to his final position, the rook then be moved from its starting position to its final position, and then the king be placed on his final square.
[...]
II.3.2.7.1 To avoid any misunderstanding, it may be useful to state "I am about to castle" before castling.

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