This is inspired by the question at Game about placing pennies on table
"Consider the following two player game. Each player takes turns placing a penny on the surface of a rectangular table. No penny can touch a penny which is already on the table. The table starts out with no pennies. The last player who makes a legal move wins. Does the first player have a winning strategy?"
The first player will win by placing a penny in the centre of the table, then can always symmetrically match the opponent's moves reflecting across the central point (assuming equivalent dexterity), until the second player has no remaining move.
However, suppose we are playing as the second player, and we observe that the first player does not know this strategy - it appears that the first player has played in a 'random' (edit: leaving a central play possible) position on the board.
Can the second player use this bad first move to create a winning strategy? Even if the first player then returns to playing 'perfectly'? How?
If not, what is the second player's best option for a chance to win?
Further to discussion: If the first player can return to play in the centre later on (or, even if the second player plays directly in the centre), the first player will take back their winning strategy.
Can the second player partially cover the centre enough in order to prevent this/gain the "central play" advantage? Can we be specific about what the second player should do in each case?