So, it appears as though this has become predictable. I have been able, after some off-and-on playing, to not only get 2048, but to get the tile that is double that. The perfect score for getting the 4096 tile should be 45,056 points, and I got 44,360, and that’s close enough to perfection for me.
“Perfection” is a factor in this game, and I don’t feel that anyone can perfectly attain it, since if we let the highest tile on the board equal , the “perfect” score would equal . This is with the tile being the only tile left on the board. Getting that situation appears highly improbable due to the random placement of new tiles on the board.
I know that people have gotten beyond the 8192 tile, but I feel they have more time on their hands than I do. However, I think the real challenge in this game is efficiency: getting scores as close to the ideal as possible. Not that getting even an 8192 tile would be easy, even if it were inefficient.
By my reckoning, the highest tile one can get is 131,072; and that the ideal score for that would be . Good luck, whoever thinks they can do it.