There are a lot of Stockfish Chess Games

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Stockfish is a top chess playing engine. We got to wondering how many possible Stockfish chess games are there if Stockfish plays against itself? Could it be that there are only a few stereotypical games? Or are there a lot of games?

To answer this we recorded Stockfish playing against itself a hundred times at different levels of “blur” of the White piece player’s move selections. By “blur” we mean that instead of playing Stockfish’s chosen move we played (uniformly at random) any move within k “centi-pawns” (1/100th of the value of a pawn) predicted board value of what Stockfish scored as the best move.

This gives us a set-up close to what we used Using the methodology of “How Many Chess Games are Possible?” allowing us to estimate the magnitude of the number of possible Stockfish versus Stockfish games.

Our estimate table is as follows.


Stockfish table

Some observations from the table:

  • A typical Stockfish versus Stockfish game without blur lasts about 203.7 ply, typically ends in a draw, and is consistent with the white pieces having a 6.6 Elo advantage.
  • There are easily 10310.1 Stockfish versus Stockfish games. These games are mostly long draw-out draws.
  • Even a 10 centi-pawn blurring of White’s move selection is reverse this advantage.
  • A 30 centi-pawn blurring of White’s moves is devastating.

Some details:

    Stockfish 17.1 was run on a 2025 Mac book air through the Pychess chess engine API with the following settings: 
    
    "Threads": 8,
    "Hash": 10240,   # MB
    "Skill Level": 20,
    "UCI_LimitStrength": False,
    chess.engine.Limit(time=1.0),
    multipv=10,

That is: we didn’t run long, and we at most looked at the top 10 engine moves.

Some caveats:

  • The variance check as described in How Many Chess Games are Possible? is too high, indicating the sample sizes are not large enough to pin down the estimated exponents precisely. However, these runs are strong evidence that the number of possible Stockfish games is indeed huge.
  • The lower-blur estimates are biased low, as the Stockfish reported move set scores are non-deterministic. So we are not always looking views of the same search tree each run. In fact at the lower blurs we tend to see subsets of the Stockfish acceptable moves.

Categories: Computer Science Mathematics

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John Mount