I would highly suggest going for cards that make you draw cards. Ive found that if you play 2 back to back in the first round, the opponent will pass about 80% of the time regardless of how low his total strength is. 2nd round all you'll need to do is let him play every card. If you don't have enough str to defeat him that round, since his deck is empty, you could just pass and automatically win the 3rd round since he has 0 cards.
The only thing to watch out for with that strategy is that opponents that use N. Realms decks draw a card when they win. I've had a few times where all I had left was a something lower and the opponent drew something higher.