New answers tagged mathematics
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For unique pawn structures I would not recommend going by any formula where you will have 10 to the power of n or any indices calculation. The best way to understand pawn structures is to know multiple openings in. There are more than 2000+ opening variations where the middlegame differs in many aspects along with the piece placement. It is always good to ...
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To classify pawn formations, a good source is chess master books that explore that topic. The book by Boris Persits comes to mind, for example.
I add that it seems impractical as you have been told, to make an exhaustive index of all the combinations that pawn chains can take.
However, it is useful to connect families of openings (classified by ECO, or by ...
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One way to do it is think about what the smallest computer encoding of a chess position (in bits). The maximum size for a given encoding provides an upper-bound on the number of chess positions. For some really tight upper bounds check out https://codegolf.stackexchange.com/questions/19397/smallest-chess-board-compression/19446#19446. This gives an upper ...
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More general answers:
OEIS A172532: Number of ways to place 5 nonattacking knights on an n X n toroidal board.
my book Non-attacking chess pieces (6ed, 2013), page 308, chapter "k Knights on an n x n toroidal chessboard".
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We can easily get a reasonably good upper bound on the number of positions. At any point in time, each player has 16 pieces of which the 8 pawns can perhaps be promoted to a knight / bishop / rook / queen. Consider all captured pieces to be off the board but part of the position (this would increase the number of positions but that is fine because we only ...
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