Answers.Body: <p>A very rough approximation you can use is to multiply by 30 for each half move. Since in an average chess position, the number of possible moves tends to be in the ballpark of around 30 (of course, not for the starting position, but for chess positions in general). This should give you the answer within an order of magnitude or two. For an exact solution though, see Miguel's answer.</p>
  
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Answers.CreationDate: 2022-06-10T23:33:38.000Z
Answers.LastActivityDate: 2022-06-10T23:33:38.000Z
Answers.UserDisplayName: Inertial Ignorance
Answers.Body: <p>Such counting of moves is called perft and it is used for testing move generation of chess engines.</p>
  <p>You can find a table with your answer up to n = 15 here:
  <a href="https://www.chessprogramming.org/Perft_Results" rel="noreferrer">https://www.chessprogramming.org/Perft_Results</a></p>
  
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Answers.CreationDate: 2022-06-10T21:16:03.903Z
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Answers.UserDisplayName: Miguel Ambrona
Body: <p>What is the number of legal positions after n plies for n=1 through 5? I know that for n=1 it is 20.</p>
  
Tags: <opening><mathematics>
Title: The number of legal positions after n plies
ThreadText: # The number of legal positions after n plies
  
  (Asked by: username_0 on 2022-06-10)
  
  What is the number of legal positions after n plies for n=1 through 5? I know that for n=1 it is 20.
  
  **Tags:** opening, mathematics
  
  
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  ## 2 answers
  
  ### Answer by username_2 on 2022-06-10. Score: 12 | Accepted answer
  
  Such counting of moves is called perft and it is used for testing move generation of chess engines.
  
  You can find a table with your answer up to n = 15 here:
  <https://www.chessprogramming.org/Perft_Results>
  
  
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  ### Answer by username_1 on 2022-06-10. Score: 3
  
  A very rough approximation you can use is to multiply by 30 for each half move. Since in an average chess position, the number of possible moves tends to be in the ballpark of around 30 (of course, not for the starting position, but for chess positions in general). This should give you the answer within an order of magnitude or two. For an exact solution though, see Miguel's answer.
  
  
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