Tried 3 games, and the scores were 2700, 1200, 5000. So maybe. But then I wrote a function to play it for me:

    var manager = new GameManager(4, KeyboardInputManager, HTMLActuator);
    
    function play() {
      manager.restart();
      var m = 0;
      while (!manager.over) {
        manager.move(m);
        m = (m+1)%4;
      }
      return manager.score;
    }

... and that gets scores between 500 and 3000.

(Edit) Histogram of 500 runs:

  0k: ***
  1k: *******************
  2k: ****************
  3k: *********
  4k: *
  5k: *
  6k: *

Which is about the same score you get if you concentrate and really try hard to get a high score.

I think this might be a "hacker" version of the slot machine - the player feels as if he's in control while in fact the outcome is pretty random.

I don't buy it. I got monotonically increasing scores, with my last play around 10k.

Hmmm, that wasn't my experience. I got a score of 7540 on my first try. Although I do suspect that the skill component might be less than we think.

Yeah, when I tried a systematic approach, I was getting better results than when I tried thinking about it. Left Down Right Down repeat.

This is actually a good method: by using this method (avoiding up and favouring down), you tend to cluster 2s and 4s towards the top while larger numbers percolate downwards (and towards the middle). If you encourage this natural tendency, you can do even better.

When you're nearly stuck, you can often pick left or right so that a new tile can access both 2 and 4 and save yourself.

I got comfortably to 1024 with one go of this method, scoring 16744.

Nah, if I concentrate I can get to 14k. I haven't actually won yet, though; I keep making a mistake.

I don't know, but I can confirm.