https://en.wikipedia.org/wiki/Branching_factor https://en.wikipedia.org/wiki/Branching_factor: “For example, in chess, if a "node" is considered to be a legal

https://en.wikipedia.org/wiki/Branching_factor https://en.wikipedia.org/wiki/Branching_factor: “For example, in chess, if a "node" is considered to be a legal position, the average branching factor has been said to be about 35, and a statistical analysis of over 2.5 million games revealed an average of 31.” So, if (all) you can assume is that the receiver can write down all legal moves and order them in some way, it seems ≈5 bits are sufficient (so, one letter or digit is more than enough). You should vary code length depending on the number of legal moves (That is less than the 6 bits you need to indicate a single field on the board) I think ease of understanding of the message and robustness of transmission may be more important than message length, though.