Answers.Body: <p>Sorry for the late answer, but here’s “my” suggestion of a total mobility <strong>215</strong> in a legal configuration. White has 216 total moves, minus away one for Black’s only legal move for total.</p>
  
  <pre><code>[FEN "1Q5R/4Q1K1/B1Q5/B4Q2/N2Q4/pQ4Q1/pn2Q3/krQ4R w - - 0 1"]
  </code></pre>
  
  <p>This position was originally created by <a href="https://pdb.dieschwalbe.de/search.jsp?expression=probid=%27P1182014%27" rel="nofollow noreferrer">William Shinkman</a> as the record for the most mates in two. This position’s mobility will be very hard to beat, as it has no checkmate/stalemates in one, in addition to how the known maximum for any move is <a href="https://chess.stackexchange.com/questions/4490/maximum-possible-movement-in-a-turn/8392#8392">218</a> contains so many checkmating/stalemating move that it won’t work here.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-01-08T00:39:34.127Z
Answers.LastActivityDate: 2020-01-08T00:39:34.127Z
Answers.UserDisplayName: Rewan Demontay
Body: <p>I consider the mobility score of a board to be the number of legal moves one player could make less the number of legal moves the other player could make.</p>
  
  <pre><code>8/7k/2Q2K2/8/6b1/8/8/8 w - - 0 1
  </code></pre>
  
  <p>Using the board above, white king has 3 legal moves, white bishop has 9 legal moves, black king has 4 legal moves, and black queen has 11 legal moves. According to white, the mobility score of this board is <code>(3 + 9) - (4 + 11) = 12 - 15 = -3</code>.</p>
  
  <p>What is the maximum mobility score possible of a board which is not a terminal case (checkmate, stalemate, draw) keeping consideration for a legal number of pieces (ie. maximum of 9 queens, 2 rooks, 2 bishops, 2 knights, 1 king of each color)?</p>
  
  <p>I don't really care if the board configuration is impossible to get to (it's probably possible to have 9 queens on the board and not be a checkmate/stalemate, but not possible to get to that state without a checkmate/stalemate), I only care that the configuration is legal.</p>
  
  <p>I've written a chess engine which uses a heuristic which considers the mobility score of a board. I want to know the maximum possible mobility score so I can better define the value of a checkmate, check, etc. There's no point in setting a checkmate to, say, 200, if the mobility score of a board can exceed this, yet I don't want to define a checkmate as an arbitrary number: it need only be the highest mobility score plus one.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-12-27T16:56:22.350Z
Comments.Text: Adding the moves would make more sense than subtracting them.
Comments.UserDisplayName: yobamamama
Tags: <engines><problems><evaluation><mathematics>
Title: What is the highest mobility score of a board without a checkmate, stalemate, or draw?
ThreadText: # What is the highest mobility score of a board without a checkmate, stalemate, or draw?
  
  (Asked by: username_0 on 2019-12-27)
  
  I consider the mobility score of a board to be the number of legal moves one player could make less the number of legal moves the other player could make.
  
  ```
  8/7k/2Q2K2/8/6b1/8/8/8 w - - 0 1
  
  ```
  
  Using the board above, white king has 3 legal moves, white bishop has 9 legal moves, black king has 4 legal moves, and black queen has 11 legal moves. According to white, the mobility score of this board is `(3 + 9) - (4 + 11) = 12 - 15 = -3`.
  
  What is the maximum mobility score possible of a board which is not a terminal case (checkmate, stalemate, draw) keeping consideration for a legal number of pieces (ie. maximum of 9 queens, 2 rooks, 2 bishops, 2 knights, 1 king of each color)?
  
  I don't really care if the board configuration is impossible to get to (it's probably possible to have 9 queens on the board and not be a checkmate/stalemate, but not possible to get to that state without a checkmate/stalemate), I only care that the configuration is legal.
  
  I've written a chess engine which uses a heuristic which considers the mobility score of a board. I want to know the maximum possible mobility score so I can better define the value of a checkmate, check, etc. There's no point in setting a checkmate to, say, 200, if the mobility score of a board can exceed this, yet I don't want to define a checkmate as an arbitrary number: it need only be the highest mobility score plus one.
  
  **Tags:** engines, problems, evaluation, mathematics
  
  > **Comments:**
  > **username_1**: Adding the moves would make more sense than subtracting them.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_2 on 2020-01-08. Score: 2 | Accepted answer
  
  Sorry for the late answer, but here’s “my” suggestion of a total mobility **215** in a legal configuration. White has 216 total moves, minus away one for Black’s only legal move for total.
  
  ```
  [FEN "1Q5R/4Q1K1/B1Q5/B4Q2/N2Q4/pQ4Q1/pn2Q3/krQ4R w - - 0 1"]
  
  ```
  
  This position was originally created by [William Shinkman](https://pdb.dieschwalbe.de/search.jsp?expression=probid=%27P1182014%27) as the record for the most mates in two. This position’s mobility will be very hard to beat, as it has no checkmate/stalemates in one, in addition to how the known maximum for any move is [218](https://chess.stackexchange.com/questions/4490/maximum-possible-movement-in-a-turn/8392#8392) contains so many checkmating/stalemating move that it won’t work here.
  
  
  ---
  
  