that's a very complicated one; but what's more complicated is that it was very unclear what you meant. For the longest time I thought it was the 'cross out the dots game' but I assume you place 1 penny per turn. So the winning strategy is held by player 1. Player 1 places his penny in the center of the table. Whereever player 2, the devil apparently, places his penny, player 1 places his penny in a straight line across from the penny player 1 placed so that the pennies would have a midpoint at the center penny. This strategy ensures that whenever your opponent has room to play a penny, so do you.
edit: basically, mirror your opponent.
edit: basically, mirror your opponent.