Ideas to try
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Sopel97 commented
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Try using an index into an ordered list of legal or pseudo legal moves. Could save 0.5-1 bits per move. This is a questionable change because it would make move encoding much slower.
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Try to reduce the magnitude of encoded score differences when encoding subsequent positions by using some form of prediction.
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Adaptive block size for variable length encoding of scores
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Reintroduce compression on top? Could reduce the size by further 5-10%