[pzs]

If you have only a single 2048 tile in the end, and arrived to that by only combining the minimum number of required tiles, then your score will be 10*2048. If you think backwards, you'll get 2048 for the last tile, before that you need to get twice 1024 for the previous two, and so on until the level of 4's, which is the first one at which you get scores. This assumes only twos appear on the board.

[seventytwo]

Initially, I had arrived at this conclusion as well, but I've seen solutions (both from other people posting and from running this script) that have gotten to 2048 with 14000 or less. I'm not entirely sure where the discrepancy is coming from, though... Obviously with a certain number of "4"s being generated each turn, the 10x2048 value will be reduced, but not to the degree we see. For example, I have logged a win with a score of 13404 points, and other people in here have screenshots of wins with significantly less than 20480 pts.

Intuitively, I want to say that the optimal score is more like 10x2048/2, but I haven't been able to prove that yet (at least not in between work today :) )

[ljf]

It seems there is a bug where only the higher or two cascades trigger at once, will be scored. So some of the points seem to being lost.