Answers.Body: <p>Running some quick-and-dirty Python code, I find that there are 197,281 positions at 4 ply (which agrees with <a href="https://www.chessprogramming.org/Perft_Results" rel="noreferrer">this</a>).</p>
  <p>Of those positions, I find 61,191 can be reached via moves that don't move the evaluation to worse than -0.5 for white or -0.78 for black (roughly symmetric around the initial position). This is ~31% of the positions. The engine runs on each position for 0.1s, so I wouldn't expect this to be especially robust.</p>
  <hr />
  <p>Edit:</p>
  <p>On reflection, the asymmetry in position at the start of the game is irrelevant; white just has slightly more &quot;playable&quot; moves than black for any given threshold of &quot;playable.&quot;</p>
  <p>Using @Danya02's suggestion from the comment, I am using the Lichess evaluations where they are available and then looking at a threshold of:</p>
  <ul>
  <li>0.30 - 21,581 valid positions ~10.9%</li>
  <li>0.50 - 54,186 valid positions ~27.4%</li>
  <li>0.60 - 75,796 valid positions ~38.4% (*roughly KID level &quot;playable&quot;)</li>
  <li>0.75 - 106,947 valid positions ~54.2%</li>
  <li>1.00 - 151,261 valid positions ~76.7%</li>
  </ul>
  <p><a href="https://i.sstatic.net/48Z1r.png" rel="noreferrer"><img src="https://i.sstatic.net/48Z1r.png" alt="Sankey Diagram of Evals between -0.5 and 0.5 for the first 4 ply" /></a></p>
  <p><a href="https://i.sstatic.net/2pUwT.png" rel="noreferrer"><img src="https://i.sstatic.net/2pUwT.png" alt="Sankey Diagram of Evals between -1 and 1 for the first 4 ply" /></a></p>
  <p>There's probably something more to &quot;playable&quot; than just compute eval. For example the Kings Indian Defence is roughly ~0.6, but I don't think there's much doubt that it's playable. The playability of a position also depends on the level of the players. I guess one measure might be &quot;positions where both sides score at least 0.3 for a given Elo&quot;, but that might be even harder to measure.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-03-18T20:04:50.520Z
Answers.Text: Perhaps this could be improved by using the evaluations from the [Lichess evaluation database](https://database.lichess.org/#evals) for the positions that were already deeply evaluated?
Answers.UserDisplayName: Danya02
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-03-18T15:01:25.630Z
Answers.LastActivityDate: 2024-03-19T11:28:01.487Z
Answers.LastEditDate: 2024-03-19T11:28:01.487Z
Answers.UserDisplayName: Simon M
Body: <p>Google says 197,742 positions are possible after 4 halfmoves. Let's call a position
  playable if it is not worse than 0.5 pawn units on the engine of your choice (I use Lichess Stockfish). By this definition, Grob is the worst (-1.7), even before Nh3 (and after f3, the only other unplayable move - if I didn't blunder).</p>
  <p>Which percentage of the possible 4 halfmoves &quot;openings&quot; is playable?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-03-19T17:53:25.297Z
Comments.Text: There are more plausibly playable variants of Hippopotamus than all the variants of all book openings combined. Note that analysis of Hippopotamus variants is hard for computers.
Comments.UserDisplayName: Joshua
Tags: <opening><statistics>
Title: Percentage of "playable" openings
ThreadText: # Percentage of "playable" openings
  
  (Asked by: username_0 on 2024-03-18)
  
  Google says 197,742 positions are possible after 4 halfmoves. Let's call a position
  playable if it is not worse than 0.5 pawn units on the engine of your choice (I use Lichess Stockfish). By this definition, Grob is the worst (-1.7), even before Nh3 (and after f3, the only other unplayable move - if I didn't blunder).
  
  Which percentage of the possible 4 halfmoves "openings" is playable?
  
  **Tags:** opening, statistics
  
  > **Comments:**
  > **username_1**: There are more plausibly playable variants of Hippopotamus than all the variants of all book openings combined. Note that analysis of Hippopotamus variants is hard for computers.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_2 on 2024-03-18. Score: 17 | Accepted answer
  
  Running some quick-and-dirty Python code, I find that there are 197,281 positions at 4 ply (which agrees with [this](https://www.chessprogramming.org/Perft_Results)).
  
  Of those positions, I find 61,191 can be reached via moves that don't move the evaluation to worse than -0.5 for white or -0.78 for black (roughly symmetric around the initial position). This is ~31% of the positions. The engine runs on each position for 0.1s, so I wouldn't expect this to be especially robust.
  
  ---
  
  Edit:
  
  On reflection, the asymmetry in position at the start of the game is irrelevant; white just has slightly more "playable" moves than black for any given threshold of "playable."
  
  Using @username_3's suggestion from the comment, I am using the Lichess evaluations where they are available and then looking at a threshold of:
  
  * 0.30 - 21,581 valid positions ~10.9%
  * 0.50 - 54,186 valid positions ~27.4%
  * 0.60 - 75,796 valid positions ~38.4% (\*roughly KID level "playable")
  * 0.75 - 106,947 valid positions ~54.2%
  * 1.00 - 151,261 valid positions ~76.7%
  
  [![Sankey Diagram of Evals between -0.5 and 0.5 for the first 4 ply](https://i.sstatic.net/48Z1r.png)](https://i.sstatic.net/48Z1r.png)
  
  [![Sankey Diagram of Evals between -1 and 1 for the first 4 ply](https://i.sstatic.net/2pUwT.png)](https://i.sstatic.net/2pUwT.png)
  
  There's probably something more to "playable" than just compute eval. For example the Kings Indian Defence is roughly ~0.6, but I don't think there's much doubt that it's playable. The playability of a position also depends on the level of the players. I guess one measure might be "positions where both sides score at least 0.3 for a given Elo", but that might be even harder to measure.
  
  > **Comments:**
  > **username_3**: Perhaps this could be improved by using the evaluations from the [Lichess evaluation database](https://database.lichess.org/#evals) for the positions that were already deeply evaluated?  
  
  ---
  
  