I was fascinated with this game when I first saw it. I don't have an iphone to play it on, but I've just played it online. Over a period of like a week I played every day and at the end I got a score of about 65300. That was a 4096 and 2048 tile on the same board. My strategy is to:
- Designate one edge as your home edge, with your highest tile in the corner, with the next biggest afterwards, and so forth.
- If left is your home edge, never press right. Also, if the left edge is not totally filled up, then don't press down.
- Other than that, you just have to slowly build up with the goal of adding to your left edge.
- Practice to learn nifty tricks.
One kid at my school somehow got a 32768 tile. I didn't see it myself, but he had witnesses. I'm assuming he just used the same strategies I just listed, but he was much better at them. :O