I'm with TacticalStache, I beat it almost every time now and have gotten to 4096 twice, my best score being about 50,000. The trick I use is to keep stuff in the bottom right corner, snaking from there. I always keep 4 different numbers in the bottom row so that I can move down, left, right without "dislodging" the bottom row, which can create unfixable gaps in the snake. If my bottom row ever compacts into something less than 4 across, my first goal is to fill it again so that I can get the down, left, right movements back.