You are correct good sir, in the analysis above I eliminated luck whatsoever and set all numbers appearing to 2 make an argument. My analysis still holds with that restriction.

I've seen numbers as large as 128 appearing, so if we go that route greatest winnable version would be even higher. I suspect that maximum number appearing is based on max number on the board now, so while we are speculating, it could be possible to make endless game by dynamically adjusting window of appearing numbers.

  // Adds a tile in a random position
  GameManager.prototype.addRandomTile = function () {
    if (this.grid.cellsAvailable()) {
      var value = Math.random() < 0.9 ? 2 : 4;
      var tile = new Tile(this.grid.randomAvailableCell(), value);
  
     this.grid.insertTile(tile);
    }
  };