To reach 2048 the game works by adding the numbers 2 or 4 at each play with probabilities 0.9 and 0.1, respectively. Then the expected average optimal number of steps to win is 2048/(.1 * 4 + .9 * 2) ~= 930.9. This optimal number of steps occur when 2048 is reached and is alone in the board. In the real case, the larger the board, the more scattered are going to be the numbers, and the number of step will increase accordingly. This result is valid for every board size.