Ok, I did go too far. But castling doesn't require all previous moves - only one bit of information carried over. So in practice that's board + 2 bits per player. (or 1 bit and 2 moves if you want to include a draw)
Castling requires no prior moves by either piece (King or Rook). Move the King once and back early on, and later, although the board looks set for castling, the King may not.
Yes, which means you carry one bit of extra information - "is castling still allowed". The specific moves that resulted in this bit being unset don't matter.
Ok, then for this you need minimum of two bits - one for kingside Rook and one for the queenside Rook, both would be set if you move the King. You also need to count moves since the last exchange or pawn move for the 50 move rule.
