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My classmate says that you can't have another queen if one of your chess officials (knights, bishops and rooks) are captured and not yet replaced.

Is this true?

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You can promote a pawn to any piece (other than a Pawn or King), regardless of how many of that piece is on the board. In theory, you could have nine Queens by the end of the game (unlikely, of course).

Piece availability is not a concern, either. An upside-down rook (if available) is the recommended stand-in for a queen, though you may have to improvise due to limited resources (stacked checkers tiles also work well).

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    You can promote a pawn to any piece as long as the piece is of the same color and it isn't a pawn or a king ;-). – Toon Krijthe Jan 7 '16 at 15:36
  • Thanks for catching that, I've edited my answer accordingly. – aaron Jan 7 '16 at 15:40
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    Actually, an upside-down rook is still a rook, whether you want it or not. You may use it when you don't have ressources, but when you have (and competitions always have more than enough), use the queens. – Amaras Jan 8 '16 at 18:58
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    The upside down rook bit comes from U.S. Chess Federation's Official Rules of Chess (5th ed.). While having spare pieces available is obviously preferable, it frequently is not practical. – aaron Jan 8 '16 at 19:12
  • What if you play with Bauhaus chess set? – Deo Apr 26 '17 at 9:57
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Ok, going for official rules here :

When a player, having the move, plays a pawn to the rank furthest from its starting position, he must exchange that pawn as part of the same move for a new queen, rook, bishop or knight of the same colour on the intended square of arrival.

This is called the square of ‘promotion’. The player's choice is not restricted to pieces that have been captured previously. This exchange of a pawn for another piece is called promotion, and the effect of the new piece is immediate.

(source : FIDE Handbook E, Laws of chess, §3.7.e : https://www.fide.com/fide/handbook.html?id=171&view=article)

This doesn't state whether or not you can promote you pawn to a queen if one or more of the other pieces are gone. Therefore you can do whatever you want in promotion as long as you don't do an illegal move.

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