The game is arbitrarily winnable now. Press down until you get rows of 2-4-8-16, then collapse all the way to the left. Repeat this procedure until you get to 256/512.
That doesn't work, you get to 128 with some nice patterns and then the algorithm fills the screen. Maybe some clever play from then on would work, but the random pieces always mess with your strategy.
If you have a static solution, please show it.