Comment by Hbthegreat

Once you know the basic strategy/naive algorithm behind winning it becomes easy to get to much higher than 2048.

1) Swipe left until nothing else moves

2) Swipe down until nothing else moves

3) (If an empty space) Swipe up once

4) Repeat from 1.

There will only be a few times that you have to stop this process to get "unstuck".