'Value' isn't a concept that has any significance in the game rules. You might as well give the piece a longer name when it captures something.
Let's invent some crazy chess variants

The Anchor chess
On the rim of the board there are anchors, that immobilize pieces that land on the adjacent squares. Those pieces won't be able to move unless to capture, only after that they are free again. You can legally move your pawns and pieces into the anchor adjacent squares, but you may not want to. Once the king is forced into the anchor zone, it's easier to checkmate it.
Anchors can't move or capture like regular pieces, but they also are not capturable. However, apart from usual promotions pawns can promote to a piece called smasher, that moves like a king, knight, or alibaba, and caprures without moving (shoots) in a 2 square range. Only this piece can eliminate the anchors.
Other than all that, things are pretty much the same as in regular chess. Created in the android app Chesscraft.
The title explains everything, so I'll start with one:
Promotion Chess:
Same as regular chess, but pieces become a piece of larger value when it takes a piece. The piece is the piece that has the same (or approximate) value of the piece+the taken piece's values. If the piece does not directly correspond to a value, then you round down if original value-lower closest value piece is greater than original value-larger closest value piece, and vice versa. (exception: if the distance between the values when you round down and round up from the original value are equal, then round up).