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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?

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  • 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

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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.


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 @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.

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  • 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

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