I think Steve and I are saying the same thing. For a simple move one square forward the compensating transaction would just be the prior position. (Compensating transaction is just way too big a
word for that
.) If I took a piece, it might be that plus the piece that should go where I just came from. So is the state stored for every move: prior position, current position, zero or one pieces removed by my move?
Just firing random neurons now ... for checkers a move could have several hops and take several pieces. You might need a chain of these things.