Answers.Body: <p>Chess is a game in two dimensions. The game is made to be played in two dimensions. Pieces move horizontally, vertically, and diagonally very naturally on a chess board. It's purely visual and the sort of thing our brain does very well. Other depictions of the position sacrifice the two dimensional nature of the game. When this information is lost, we have to calculate to reconstruct the spacial relationships in the game. Consider the difficulty of spotting a pin or discovered check when using FEN.</p>
  
  <p>In the other notations other than the standard diagram, you'll spend a lot of time doing mechanical sorts of math.</p>
  
  <p>The different representations (diagram, moves, and FEN) exist because they fill different needs.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-05-19T13:27:24.730Z
Answers.Text: I have wondered if there is some sort of transform that could be done to a 2D board (for instance, into higher dimensions) which would make looking ahead multiple moves easier.  For instance, one representation might represent forced mates as a kind of corridor would could easily be recognized.
Answers.UserDisplayName: Michael
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2015-03-20T11:48:41.883Z
Answers.LastActivityDate: 2015-03-20T12:29:00.563Z
Answers.LastEditDate: 2015-03-20T12:29:00.563Z
Answers.UserDisplayName: Tony Ennis
Body: <p>Consider <em>the classical representation</em> of the state of a chess game. I'll draw the board:</p>
  
  <pre><code>R BK BNR
  PPPP  PP
    N Q
      PP
      p
    np p
  ppp   pp
  r bkqbnr    
  </code></pre>
  
  <p>Here is its move list:</p>
  
  <pre><code>d5 d5
  c4 c6
  Nf3 e6
  Qd3 Nf6
  ...        
  </code></pre>
  
  <p>Here is its FEN notation:</p>
  
  <pre><code>rnbqkb1r/pp3ppp/2p1pn2/3p4/2PP4/3Q1N2/PP2PPPP/RNB1KB1R w KQkq -
  </code></pre>
  
  <p>These three ways to describe the game state are isomorphic and contain exactly the same information represented differently. A computer would have no problem converting from one representation to the other (kind of, the castling flag isn't available in the first representation and the second one encodes all the game states). Computers uses even stranger representations like bit boards which I won't go into here.</p>
  
  <p>In fact, there is an almost endless amount of ways to represent the state of a chess game. For example, here is one I just came up with:</p>
  
  <pre><code>R.BK.BNRPPPP. PP..N.Q.......PP......p.....np.p..ppp...ppr.bkqbnr    
  </code></pre>
  
  <p>But if I asked you to "find the best move for white" the first representation would be much easier for you than the others. </p>
  
  <p>Why? Is it just because the classical representation is what most players are used to or does it have some inherent advantage? Could you train your skill at playing chess using only FEN notation and over time come to prefer that? Has any research been done into this area? Maybe there is a better way to represent a chess game than the classical one which gives you a huge advantage when calculating lines deeply but just no one has found it?</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-03-20T11:27:54.627Z
Comments.Text: The board diagrams above are not equal. Only FEN includes the player on move, that a pawn be taken en passant, and which sides can castle which way.
Comments.UserDisplayName: Tony Ennis
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-03-20T11:53:25.363Z
Comments.Text: You might improve the question so the various representations of the position match one another.
Comments.UserDisplayName: Tony Ennis
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-03-20T16:31:58.733Z
Comments.Text: You're right about that and there are other details about the game state that isn't encoded either like the 50 move rule, repetition count and so on. I hope what I*m asking about gets across anyway.
Comments.UserDisplayName: Gaslight Deceive Subvert
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-03-20T18:58:45.470Z
Comments.Text: How do you convert from FEN to the move list? How do you get around the fact that the move list is not uniquely determined by the position?
Comments.UserDisplayName: bof
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-03-21T13:56:56.070Z
Comments.Text: My point is that you can play a chess game by only looking at the FEN instead of the board. I know that the move list contains more info in total but it's irrelevant for what I'm asking about.
Comments.UserDisplayName: Gaslight Deceive Subvert
Tags: <engines><psychology><fen><computer-chess>
Title: Do better board representations than the standard one exist?
ThreadText: # Do better board representations than the standard one exist?
  
  (Asked by: username_0 on 2015-03-20)
  
  Consider the classical representation of the state of a chess game. I'll draw the board:
  R BK BNR
  PPPP  PP
    N Q
      PP
      p
    np p
  ppp   pp
  r bkqbnr    
  
  Here is its move list:
  d5 d5
  c4 c6
  Nf3 e6
  Qd3 Nf6
  ...        
  
  Here is its FEN notation:
  rnbqkb1r/pp3ppp/2p1pn2/3p4/2PP4/3Q1N2/PP2PPPP/RNB1KB1R w KQkq -
  
  These three ways to describe the game state are isomorphic and contain exactly the same information represented differently. A computer would have no problem converting from one representation to the other (kind of, the castling flag isn't available in the first representation and the second one encodes all the game states). Computers uses even stranger representations like bit boards which I won't go into here.
  In fact, there is an almost endless amount of ways to represent the state of a chess game. For example, here is one I just came up with:
  R.BK.BNRPPPP. PP..N.Q.......PP......p.....np.p..ppp...ppr.bkqbnr    
  
  But if I asked you to "find the best move for white" the first representation would be much easier for you than the others. 
  Why? Is it just because the classical representation is what most players are used to or does it have some inherent advantage? Could you train your skill at playing chess using only FEN notation and over time come to prefer that? Has any research been done into this area? Maybe there is a better way to represent a chess game than the classical one which gives you a huge advantage when calculating lines deeply but just no one has found it?
  
  **Tags:** engines, psychology, fen, computer-chess
  
  > **Comments:**
  > **username_1**: The board diagrams above are not equal. Only FEN includes the player on move, that a pawn be taken en passant, and which sides can castle which way.  
  > **username_1**: You might improve the question so the various representations of the position match one another.  
  > **username_0**: You're right about that and there are other details about the game state that isn't encoded either like the 50 move rule, repetition count and so on. I hope what I*m asking about gets across anyway.  
  > **username_2**: How do you convert from FEN to the move list? How do you get around the fact that the move list is not uniquely determined by the position?  
  > **username_0**: My point is that you can play a chess game by only looking at the FEN instead of the board. I know that the move list contains more info in total but it's irrelevant for what I'm asking about.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2015-03-20. Score: 6
  
  Chess is a game in two dimensions. The game is made to be played in two dimensions. Pieces move horizontally, vertically, and diagonally very naturally on a chess board. It's purely visual and the sort of thing our brain does very well. Other depictions of the position sacrifice the two dimensional nature of the game. When this information is lost, we have to calculate to reconstruct the spacial relationships in the game. Consider the difficulty of spotting a pin or discovered check when using FEN.
  
  In the other notations other than the standard diagram, you'll spend a lot of time doing mechanical sorts of math.
  
  The different representations (diagram, moves, and FEN) exist because they fill different needs.
  
  > **Comments:**
  > **username_3**: I have wondered if there is some sort of transform that could be done to a 2D board (for instance, into higher dimensions) which would make looking ahead multiple moves easier.  For instance, one representation might represent forced mates as a kind of corridor would could easily be recognized.  
  
  ---
  
  