Game idea:

You build/alter a level right before playing, but every edit is symmetrical.  

The resulting level is technically guaranteed to be "fair", but you can try to build it to what feels like your advantage in the moment, which may mean sabotaging what the other player is building, or adding an obstacle at the last second before the round starts.  

It could be called "Symmetree" if the level is a tree, and you edit it by extruding and cutting branches.  

It could be called "Fearful Symmetry", referencing a the poem The Tyger by William Blake. Or "Fearful SymmeTree" combining them. 

You could be tigers in a tree, why not.