Answers.Body: <p>In Chess960, after castling, the kings and rooks end up in the same place as they do in standard chess.  That is, if white castles kingside, the king will always be on g1 and the rook will always be on f1.</p>
  <p>In Chess480, my understanding from your quote is that if the white king starts on e1, f1, or g1, then after castling kingside, it will end on g1 and the rook will be on f1.  However, if the king instead starts on b1, c1, or d1, then castling kingside is castling &quot;long&quot;, and the king will end up on the f1 square, and the rook will end on the e1 square.</p>
  
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Answers.Text: In chess480, The king moves two squares toward the rook if possible. So the king on e1 would move to g1 and the rook to f1.  The king on f1 would move to h1 and the rook to g1. In the case of the king on g1 (and the rook on h1), the king and rook just swap positions, so the king again winds up on h1.
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Answers.Body: <p>Consider two starting position that are each other's horizontal mirror images. Say, the normal chess starting position, and the one with king and queen reversed.</p>
  <p>In chess 480, those two are essentially the same game, normal chess: in normal chess you can castle long with the king ending on c1, and short with the king ending on g1. In the reversed position you can castle long with the king ending on f1 and short with the king ending on b1; as a result, any position resulting from the chess starting position is equivalent to a position from the reversed chess position, every possible move and strategy has a direct reversed equivalent. They're the same.</p>
  <p>In chess 960, in the reversed starting position, long castling still ends up with the king on c1 and short with the king on g1, and that is different from normal chess position because the queen started on e1 instead of d1.</p>
  <p>So chess 480 has half the positions of 960 because they are pairwise equivalent due to symmetry.</p>
  
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Body: <p>From <a href="https://en.wikipedia.org/wiki/Fischer_random_chess#Chess480" rel="noreferrer">wiki</a>:</p>
  <blockquote>
  <p>Lewis has named this chess variation &quot;Chess480&quot;; it follows the rules of Chess960 with the exception of the castling rules. Although a Chess480 game can start with any of 960 starting positions, the castling rules are symmetrical (whereas the Chess960 castling rules are not), so that mirror-image positions have identical strategies; thus there are only 480 effectively different positions. The number of starting positions could be reduced to 480 without losing any possibilities, for example by requiring the white king to start on a light (or dark) square.</p>
  </blockquote>
  <p>Ok someone tell me the maths here please. Why do the castling rules make this 480 from 960?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-04-20T08:23:27.303Z
Comments.Text: Mirror images are different positions in chess960 due to queenside and kingside castling being different. But they are effectively the same in chess480, thus there are only half as many "different" positions
Comments.UserDisplayName: David
Tags: <chess-variants><castling><mathematics><chess960>
Title: Chess480: Why 480?
ThreadText: # Chess480: Why 480?
  
  (Asked by: username_0 on 2021-04-20)
  
  From [wiki](https://en.wikipedia.org/wiki/Fischer_random_chess#Chess480):
  
  > Lewis has named this chess variation "Chess480"; it follows the rules of Chess960 with the exception of the castling rules. Although a Chess480 game can start with any of 960 starting positions, the castling rules are symmetrical (whereas the Chess960 castling rules are not), so that mirror-image positions have identical strategies; thus there are only 480 effectively different positions. The number of starting positions could be reduced to 480 without losing any possibilities, for example by requiring the white king to start on a light (or dark) square.
  
  Ok someone tell me the maths here please. Why do the castling rules make this 480 from 960?
  
  **Tags:** chess-variants, castling, mathematics, chess960
  
  > **Comments:**
  > **username_1**: Mirror images are different positions in chess960 due to queenside and kingside castling being different. But they are effectively the same in chess480, thus there are only half as many "different" positions  
  
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  ## 2 answers
  
  ### Answer by username_4 on 2021-04-20. Score: 10 | Accepted answer
  
  Consider two starting position that are each other's horizontal mirror images. Say, the normal chess starting position, and the one with king and queen reversed.
  
  In chess 480, those two are essentially the same game, normal chess: in normal chess you can castle long with the king ending on c1, and short with the king ending on g1. In the reversed position you can castle long with the king ending on f1 and short with the king ending on b1; as a result, any position resulting from the chess starting position is equivalent to a position from the reversed chess position, every possible move and strategy has a direct reversed equivalent. They're the same.
  
  In chess 960, in the reversed starting position, long castling still ends up with the king on c1 and short with the king on g1, and that is different from normal chess position because the queen started on e1 instead of d1.
  
  So chess 480 has half the positions of 960 because they are pairwise equivalent due to symmetry.
  
  
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  ### Answer by username_2 on 2021-04-20. Score: 5
  
  In Chess960, after castling, the kings and rooks end up in the same place as they do in standard chess. That is, if white castles kingside, the king will always be on g1 and the rook will always be on f1.
  
  In Chess480, my understanding from your quote is that if the white king starts on e1, f1, or g1, then after castling kingside, it will end on g1 and the rook will be on f1. However, if the king instead starts on b1, c1, or d1, then castling kingside is castling "long", and the king will end up on the f1 square, and the rook will end on the e1 square.
  
  > **Comments:**
  > **username_3**: In chess480, The king moves two squares toward the rook if possible. So the king on e1 would move to g1 and the rook to f1.  The king on f1 would move to h1 and the rook to g1. In the case of the king on g1 (and the rook on h1), the king and rook just swap positions, so the king again winds up on h1.  
  
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