Managed to get a 256 tile, and then got bored. Clever game but I always seemed to get all the valuable tiles in a checkerboard pattern.
As much as I enjoy this kind of puzzle, 16384 is just taking things a little too far. 2048 is a nice challenge, 4098 in the same format (or board size) is an endurance test, beyond that you really ought to have an auto-save or something, for the time involved.
It's actually really easy, oscilate left-down-left-up, and just move randomly. With the large board size, you're guaranteed a combine almost every move.
New challenge: try to lose. I just spent the last fifteen minutes literally doing nothing except cycling Up / Left / Down / Right / (repeat) like a numeric washing machine, and won. You can button-mash your way through this blind and eventually the numbers will come together for you.
So I did some math, because I have literally nothing better to do. Found out some random statistics about the game. Max Moves 36,892,925,197,465,681,919 Max Number 36,893,488,147,419,103,232 Max Points 4,759,259,971,017,064,316,928 What these mean, respectively: The absolute maximum number of moves possible in a 16384 game before you are forced to lose. The value of the highest tile achievable, given a very specific set of circumstances. The score you would achieve if you had only 2s, aside from the single 4 necessary to hit 2^65. These values would take an absurd amount of time, luck and skill to achieve. I've only got to 2^21 (2,097,152) while spamming an up->right->down->left macro at such speeds that my computer stalls entirely. Unfortunately, I got a game over before hitting 2^22, and I can't get past 2^20 anymore.