Think of it this way. Every move is from 1 position on a 64 location board to another (therefore most moves could be stored in about 12 total bits). There might

Think of it this way. Every move is from 1 position on a 64 location board to another (therefore most moves could be stored in about 12 total bits). There might be a couple more bits to represent enpassant and promotion, and my simple representation could easily be compressed, but for a regular game (generally less than 100 moves), you can store it < 1kb. (You still need the names of the participants, and maybe some other metadata, but my point is that the game compresses easily without too much thinking at all.) The game gets even more compact in that not all source and destination squares are possible at every move, etc. But, you're dead on in your estimate.