Suppose you are playing many 2048 games, all blindfolded. As usual you can press left, right, down, or up to move the tiles. When there are no more moves the game terminates and you are told your score. This is all the information you get. What should be your strategy to maximise your average score?
Swipe mainly in one vertical direction (ex. down) and one horizontal direction (ex. right). Since you can get stuck by doing this, occasionally, swipe left and down to free up some blocks. This way, the largest blocks appear in the bottom right (getting larger to the left).
Here is the board after using only down and right alternating. Numbers are building up toward 128 on the bottom row. No more down/right moves can be made, so the best option is to use left once then down to combine the 4's and 8's. Going once more down and continuing using only right and down will cause the numbers to continue to go up.
With this strategy, I normally get around 2000-3500 points and get a 256 or 512 tile as the max.
With a single random game, this was the outcome (3828 points):
Source: I played this game a lot while distracted and this seems to work pretty well.
[Sort of unrelated, but 2048 is one of the first C++ programs I wrote. Code is here: link to code.]