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?

  • 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.
    – Joshua
    Commented Mar 19 at 17:53

1 Answer 1


Running some quick-and-dirty Python code, I find that there are 197,281 positions at 4 ply (which agrees with this).

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.


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 @Danya02'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

Sankey Diagram of Evals between -1 and 1 for the first 4 ply

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.

  • 4
    Perhaps this could be improved by using the evaluations from the Lichess evaluation database for the positions that were already deeply evaluated?
    – Danya02
    Commented Mar 18 at 20:04

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.