Single Comment

How many games are there that can be *played* symmetrically? 
This would possibly be restricted to east-west symmetry, as the 2 players
are north-south, and, unless they move simultaneously, the N-S symmetry
would be lost at the end of the first player's turn. 
With different arrangements of board, pieces, and moves, however, I
imagine there could be more than 1 kind of symmetry preserved throughout a game, or could there?
Finally, could symmetries appear and disappear [more or less] regularly?