The latest stats show no "game-win" events :P It might just be a matter of time though.
EDIT: oops, there was a bug in the win/lose tracking so I probably missed out on a few wins. I fixed it now, so it should hopefully track it if someone else wins!
Each turn, one 2 tile is added, and other tiles may be combined. So you can derive the move count by adding together the numbers on all the visible tiles and dividing by 2.
This is inaccurate, because you have a 10% chance of getting a 4 tile added instead of a 2. That part makes the game tricky, because otherwise you could optimize every solution like an algorithm without ever losing.
Oh, huh, I didn't even realize it was doing that. Even so, the move count will still be roughly proportional to the sum of the board (plus or minus some random variation), won't it?
This would be cool. I think winning in the fewest moves would be the most impressive. i.e. how few tiles you 'waste'. Though winning with the lowest score may approximate this.
There's actually a semi-optimal strategy that nearly guarantees winning if you're diligent about it. Just build a stairstep pattern with the highest numbers in the bottom corner of the stairs. Then basically combine sideways and downward and "always" resist the temptation to push up. Its kind of how some tri-diagonal matrix algorithms work. The only problem is you have to be fastidious about never using the one direction you've reserved as your excluded case (Up in my example) as that can screw your staircase by putting a [2] right underneath your wonderful [1024]. Just move blocks back and forth, waiting for the right blocks to create combo patterns, while generally storing lower cost blocks on the outside of the stairs, and then snake them through the stairs when you get a chain set up.
I found one not-completely-horrible strategy was just blindly running round the curser keys.. eg. up - right - down - left, repeatedly. Got near 4000 points with that..
Great game though - wasted waaay too much time last night playing.
It's a good start but you will get stuck at higher level. in your case focus on increasing the value on the bottom left. When possible, shift the last line to the right. Never go up.
I was surprised at how well that worked. I was basically blindly cycling between left,down,right (with one accidental up) and got to 1024 on my first try.
With enough tries anything is possible. There is probably even a person who ascended nethack on his first try (using the wiki of course, we're still talking things with p > 0) and didn't play it again because it's too easy and boring.