[jcranmer]

Just encoding algebraic chess notation gets you to 9 bits without much skill: 3 bits for the 6 pieces, 3 bits for rank and 3 bits for file, with the edge cases shoved in the extra encoding space given that you have 3 bits to encode 6 pieces.

On average, chess has a branching factor of 30-40, so you need a touch more than 5 bits on average even with clever Huffman coding. Just Huffman coding regular algebraic chess notation for movement would probably get you down to 6 bits on average.

Of course, the other issue is that the tighter you compress the data, the harder it is to actually manipulate that data, and it's not clear that the space saving for denser encodings is worth it.

[jiggawatts]

That’s a lot of extra wasted bits! There are only 32 pieces in total, and only one of 16 can move each turn. So a mere 4 bits is sufficient to select the moved piece.

The assumption here is that this is an encoding “at rest” and isn’t used directly, except perhaps for equality comparisons. The decoder would have to track the game state and expand this into a much larger format for programmatic manipulation.