Non-reversible moves

In the Orion sector, a traveller showed me a book of games concerning reversible and non-reversible moves. In most of these games, pieces were judged by the notion of piece gradient. For example, a stone could move thru a friend if it was moving forward, but it could not jump again backwards. Transparent in one side, opaque in the other.

Earth has games with piece gradient (like Chess and its pawns) and games without gradient (like Go). I personally like games without gradient but it was fascinating to find a complete family of games using this specific concept. [T.Sagme, Travels]