For example in the first turn there are 20 possible legal moves (16 pawn moves and 4 knights moves). This number increases in the middlegame and then decreases in the Endgame.

Are there some calculations on the average? Google search seem to be focused only on "average number of moves per game". Would appreciate if somebody have some links to some scientific researches or also blog posts.

  • If I understand your question correctly, you would have to average over the number of all possible chess positions, which is an extremely large number. Besides, I am not sure how meaningful this average is (might depend on what you need it for). – user1583209 Dec 4 '18 at 17:36

What you are looking for is called the branching factor, and I've always seen the number 35 mentioned, but I don't know what the original source is. I guess someone estimated it some 50 years ago by counting the number of moves in a number of random positions from games, and then it became "common knowledge". The number 35 is reasonable enough in practice, but of course is not exact.

In today's age of big data, it should be easy to take a game database and answer the question of what is the exact average number of moves per position in the database. I'm sure someone must have tried that already, but I haven't seen it.

  • 2
    Correct. Not a very hard exercise but pointless. – SmallChess Dec 5 '18 at 4:11
  • Are those 35 for a typical game of chess or an average over all possible positions of chess? A game database would not contain all positions, but only a fraction of possible positions which could affect the value. – user1583209 Dec 5 '18 at 15:15
  • @user1583209 I think it is the average of the played games. – Predicate Dec 6 '18 at 15:46

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