it should also include d5 and e5 just to make things fair.
oh sorry i forgot to mention that.
The only method to the center would be if one can take a peace with it. For example if opponents knights are for your pawn your allowed to take it and so get in the center.
fun to play.
Limit a game by not getting pawns into E4 or D4 the first one who gets a pawn there will loose the game by agreement.