Player A and Player B play a game. On the middle of the table there is a pot full of $N$ apples of different weights. Player A starts first and chooses an apple and starts eating it. Losing no time Player B does the same. When a player eats a whole apple, without losing time repeat the same procedure. In case both players have eaten their apple at the same time, Player A still has the advantage of choosing first. Note that both players eat with the same speed.
What apple should Player A choose at first to ensure that with right tactics he'll eat as much grams of apples as possible if Player B plays optimally?
I wasn't able to achieve much progress. I thought that if Player A chose the lightest apple then he'll choose first in the "second round", but it's not the solution when we have 4 apples that weigh: $300, 400, 500$ and $600$ grams. But also choosing the biggest apple isn't a solution. Example: Apples with $300, 400, 500$ grams, because choosing the smallest apple is the optimal solution.
Any help?