fix a determinstic chess engine and play a game against itself as follows. set it to do MultiPV, and, for each move, use an entropy source to choose a move from the top set of moves, the moves that are within 0.5 pawns of the best move.
the entropy source need not be random: it can be information to be encoded as a chess game. the moves are a mixed radix encoding of the information, because the number of moves within 50 centipawns differs from move to move. or, arithmetic coding.
because the moves are selected from among the best, it is (hopefully) a reasonable chess game. the moves tell a story, one that (hopefully) will not be difficult to memorize for someone experienced at chess. hopefully not too many weird "computer" moves. in this way, we can encode arbitrary information in a memorable way.
the exact parameters of the chess engine also need to be recorded and possibly memorized. it is important to record the MultiPV number of lines, because that affects the evaluation and relative ordering of moves.
the game ends when the evaluation exceeds +/-5. there are probably many ways to win from such positions, and, if left to its own devices, the computer might choose an unnatural way not easy for a human to memorize, perhaps made worse by losing up to 0.5 pawns per move.
also, let the game end when an endgame is reached. define endgame at some threshold of weighted sum of material on the board. we avoid endgames because they are different: computers tend to play endgames extremely well (including tablebase where they play perfectly), playing moves that far exceed what humans can understand and easily memorize.
if you have more information to encode than fits in a single game, then encode it in a sequence of games.
instead of doing MultiPV straight out of the start position, fix an opening book of popular openings and use the entropy source to select moves from it. this again helps the story take place in a familiar easily memorizable setting.
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