If someone wants to cure his addiction, here is my variant of the game - 2048 with AI autoplay and taking back moves:

http://www.kongregate.com/games/random_strangers/2048-analyz...

Also, 511 is a variant of 2048 on a 3x3 grid, completely solved:

http://www.kongregate.com/games/random_strangers/511-game