Comment by Dave_Rosenthal

I wrote a version myself in python and have been playing with strategies. It seems fairly resistant to simple greedy strategies (maximize highest score/maximize empty squares/etc).

In terms of "blind" strategies [up, right, down, left]* works pretty well, but [up, right, up, left]* is by far the best I've found. It gets to 512 about 30% of the time (!), with about 0.2% hitting 1024. Still haven't seen a "win" using the blind strategy in several 10,000s of runs.