Counting up to 2048 is hard

I came across a fun game last week and it's so fun I can't stop playing. All the action takes place on a four by four grid system. Here's an image of it just below.

The idea is to merge tiles having identical numbers to form their sum. Number tiles are moved around using the keyboard arrow keys. When you hit the Up key, all tiles slide upward as if gravity were pulling them in that direction. When they halt at their new position, if a 4-tile were to knock against another 4-tile, those two tiles combine into a single 8-tile. After each move, a new 2-tile is added to the board at a random location. The primary objective of the game is to repeatedly manipulate the tiles such that you create a 2048-tile.

So far the single largest tile I have created is a 256-tile. I have a lot of work ahead of me still...