Nicholas' Solution:

For the cards that have been slid, the weight overhanging the deck must equal the weight still resting on the deck. So when you slide 3 cards, there must be 1/2 of that weight, 1 1/2 cards, overhanging the deck and 1 1/2 cards on the deck. To the weight of 1 card which you already have overhanging the deck from the previous slide, you must add the weight of 1/2 card. You must distribute that 1/2 card weight among all 3 cards which are being moved. 1/2 X 1/3 = 1/6, so you must slide the third card 1/6 of a card length to be perfectly balanced.