Alice and Bob’s card game
Two perfect logicians, Alice and Bob, play a game with 2n blank cards. The cards are numbered with random positive integers and laid out in a row. Alice goes first. She takes a card from either end of the row. The value of that card is added to her score. Bob then takes a card from either end of the remaining row and adds its value to his score. This continues until all the cards have been taken.
Show that Alice can always match or beat Bob’s score.