Comment by acjohnson55

I eventually won and went on to score 32420, eventually losing after getting a second 1024 on the board. I'm fairly certain a 4096 is achievable.

The cardinal rule, as many have said, is to keep one side filled, in descending order, with your largest piece in one corner. Once you have that side filled, you have to make sure that any time you have a duplicate on that row that you:

(1) only ever shift toward your largest number

(2) ideally have a parallel row that will not shift before you do (1)

Until you can refill your last row, circumstances may lead you to have to move in the forbidden direction, which could wreck the whole game. Point (2) ensures that you can fill your back row with another piece immediately, restoring 3 directions of moves as quickly as possible.

If you end up with any 2's on your back row, you must build them up to higher numbers ASAP. Last thing you want is buried 2's.

Once your numbers start getting high, I think it makes sense to use the front two rows exclusively for 2's, 4's, and the occasional 8, but to shift 8's to the third row as soon as possible.

I've found that to actually finish once you have all the pieces you need, it may make sense to break script, but if you want to go on to try to make 4096, you may want to carefully stay on script.

I've found that in tricky situations when I want to combine large value pieces that are just not in alignment, it makes sense to try to slide lower value pieces under one to "boost" one of the others into alignment. The ability to do this makes it valuable to keep your combining pieces in the middle of the board.

Lastly, when you have multiple possible moves, make the move that takes most advantage of the piece that's about to appear, either because you can quickly combine the new piece or because it can "boost" another piece into alignment.

Follow this advice, and you will be a star!