Largest tile possible in 1597 (2048 with Fibonacci numbers)

1597 or 2584 is a variation of the game 2048 where pairs of tiles numbered with consecutive values in the Fibonacci sequence are merged into a new tile with the next value in the sequence.

An important difference is that new tiles may only have a value of either 1 or 2 (whereas in 2048 new tiles have a value of 2 or 4).

What is the largest value for a single tile that can be achieved in this game?

Here are some playable links: 1597, 2048, FIB.

There are also a few variations which are not of relevance for this puzzle, like this one where new tiles may have a value of 1, 2 or 3.

• btw If there is any 2048 fan (like me) who wants to try 1597, don't bother about it. I just kept alternating between the down and left arrow keys for 90% of the game, and managed to win it in 3 attempts. Jan 2, 2016 at 10:08
• Well, that's because 1597 is way too low a goal. The "equivalent difficulty" of winning 2048 would be getting a 6765 tile. Making a 1597 tile is only as difficult as making a 512 and a 256 tile at the same time in 2048. Jan 3, 2016 at 0:42