One way Fog of War

no matter how much material advantage you would give the player with the fog, it would mean nothing if the other player can see and avoid all attacks, leaving the player with fog grasping for something he can not get,
unless that is if you give the player with fog like 8 queens or equivalent points advantage, but then it would just be somewhat stupid technically,

I'd happly take the visibility and give you my queen in exchange.
For it to work you'd have to have a series of games changing sides i.e. which one has the material advantage, not just colour of pieces.
After a pair of games, if the score is level, the material advantage increases or decreases depending which way the games went, until you have a winner.

I think an interesting variant would be one, in which one player would have the same visibility as in Fog of War, but the other player can see the entire board. I think this might work provided that the player who has the same visibility as in Fog of War has more material at the start than the player who can see the entire board.
Orrr: one player has fog of war, the other cannot move a piece backwards (I thought that is what you meant by one way).
I think an interesting variant would be one, in which one player would have the same visibility as in Fog of War, but the other player can see the entire board. I think this might work provided that the player who has the same visibility as in Fog of War has more material at the start than the player who can see the entire board.