Herlock Sholmes: But there's the classical strategy stealing argument. If there's a winning strategy for the second player, the first player can just pretend to be the second - he plays a random first move, as getting numbers is never a disadvantage.

Saying "if the first player plays an attacking strategy, there are chances for the second player if he plays defensive" doesn't mean the first player doesn't have an advantage. After all, if playing defensive is a winning strategy, there's nothing that prohibits the first player to play defensive.