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    <p>[edited after reading the question properly] If you assume every legal position can be reached from the initial position (which is a possible definition of "legal"), then any position can be expressed as the sequence of moves from the start. A snippet of play starting from a non-standard position can be expressed as the sequence of moves needed to reach the start, a switch to turn the camera on, followed by subsequent moves. </p> <p>So let's call the initial board state the single bit "0".</p> <p>Moves from any position can be enumerated by numbering the squares and ordering the moves by (start, end), with the conventional 2 square jump indicating castling. There is no need to encode illegal moves, because the board position and the rules are always already known. The flag to turn the camera on could either be expressed as a special in-band move, or more sensibly as an out-of-band move number.</p> <p>There are 24 opening moves for either side, which can fit in 5 bits each. Subsequent moves might require more or less bits, but the legal moves are always enumerable, so the width of each move can happily grow or expand. I have not calculated, but I imagine 7 bit positions would be rare.</p> <p>Using this system, a 100 half-move game could be encoded in approximately 500 bits. However, it might be wise to use an opening book. Suppose it contains a million sequences. Let then, an initial 0 indicate a start from the standard board, and a 1 followed by a 20 bit number indicate a start from that opening sequence. Games with somewhat conventional openings might be shortened by say 20 half-moves, or 100 bits.</p> <p>This is not the greatest possible compression, but (without the opening book) it would be very easy to implement if you already have a chess model, which the question assumes.</p> <p>To further compress, you'd want to order the moves according to likelihood rather than in an arbitrary order, and encode the likely sequences in fewer bits (using e.g. Huffman tokens as people have mentioned).</p>
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    1. POProgrammer Puzzle: Encoding a chess board state throughout a game
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    1. USDouglas Bagnall
    1. USDouglas Bagnall
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    1. COInitial position isn't necessarily known. It could be a game fragment.
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      1. USAndrew Rollings
    2. CO@Andrew: yes. my mistake. I have edited to allow for game fragments.
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