I've been playing this for awhile now and I think I have found that the best method is to only use 3 directions. This forces your highest number into a corner and only spawns 2's and 4's in the opposite corner. You build up numbers that cascade down to the corner. It almost never gets stuck, but if you do I guess you'd have to push the 4th direction you haven't been using.
I got up to 16220 that way-- the thing you have to look out for though is as you build the cascading layers, when you get the row three, not to block yourself in (having all 3 rows full so that the only direction you can go, is the one you are avoiding).
Try to keep your cascading layers down to 2, and keep about 2 steps ahead when you get to the 3rd layer.
Many people have suggested keeping your highest number in the corner but I've found that doing so makes it easier to have 2's and 4's "invade" that fortress of high numbers you're building close to the wall.
The best position is for the highest number to be 2nd or 3rd in the row closest to the wall cushioned by the second highest numbers on either side so that you can build up the numbers to either side of them, and eventually add them in.
I won 4 times in a row using a variant of that strategy where I lined up biggest to smallest numbers in a snake like pattern across the bottom of the grid. I only used up if my largest number got moved from the corner and I only used left if my bottom row was completely filled or my choices were narrowed to up or left.
EDIT: 5 times in a row now. I think I'm addicted.
EDIT: lost on my attempt for 6 in a row. I had to press up right after the 1024 appeared and was scrambling the rest of the game. I managed to get the 512 and 2 256s to appear as well but couldn't get them together.
I was doing the same. I got up to 1024 before losing, so I wonder if the algorithm would be better if you changed it to do a minmax search on three directions, and always omit the fourth unless you're forced to move that way.
That way your large values tend to be clump together and you don't get a small value buried which burns up a square.
Likewise, I wouldn't say I only used the other direction only once, but I definitely keep the highest tile in the top right, and build up the top row, mostly moving up and right only
That's what I have been doing. It "feels" like a good strategy.
But I couldn't tell if it was really just for my own cognitive convenience. That is, it's easier for me to reason about moves if I constrain moves to keep my high tiles against an edge.
I watched the AI play once, and it of course does not constrain itself this way. To really rub it in, the AI won the game, which I have not.
