2048 is a very addictive game. It combines three classic games into one: (1) the fifteen puzzle (2) the Tower of Hanoi puzzle, and (3) Tetris.
It’s addictive like Tetris because every new bit of order is threatened with random chaos. It uses a 4×4 grid with tiles that move, like the fifteen puzzle. And moving up from one level to the next roughly doubles the playing time, like the Tower of Hanoi puzzle.
Starting with the Tower of Hanoi puzzle, the key is to first figure out how to move 3 disks. It takes 7 steps. Once you’ve figure that out, let’s call that sequence of 7 moves “A”. Now, how you do move 4 disks? Simple. You do the “A” move from the first peg to the second, then you move the #4 disk to the second peg, then you do the “A” move from the second peg to the third. That whole process takes 15 steps. Let’s call it “B”. So… how do you move 5 disks? First you do B from first to second then you move disk #5 from the first to the third, then you do the B move again from the second to the third. The process takes 31 steps.
The 2048 game has a similar structure to it. You try to combine 2’s and 4’s to make an 8. Then once you’ve got an 8, you make another 8, then you put them together. It takes at least 3 moves to get an 8, then at least 3 more moves to get another 8, then it takes at least 1 more move to put them together into a 16 tile, total of 7 moves. So… how do you get a 32 tile? Simple, first you get a 16 (7 moves) then you get another 16 (7 moves) then you put them together (1 more move, total of 15 moves). How do you get a 64 tile? First you get a 32 (15 moves) then another 32 (15 moves) then put them together (15+15+1=31 moves). See how much this resembles the Tower of Hanoi Puzzle?
Okay, down to strategy. This is my suggestion of how to play, which I worked out for myself. It’s by no means the only way to do it.
First, you need to play around with the game a little bit and get the feel for it. I assume you’ve already done that before you’re reading this. If not, go play around for a while and then come back.
Now suppose you have this on the bottom row of your board: [ 2 ][ 2 ][ 4 ][ 8 ] Don’t worry about what’s on the rows above that; it doesn’t matter right now. Imagine what would happen if you swiped Right 3 times. The two [ 2 ]’s would combine to make a [ 4 ], then the two [ 4 ]’s would combine to make an [ 8 ], then the two [ 8 ]’s would combine to make a [ 16 ]. Neat huh? Okay, see if you can figure out how to make that happen. Get [ 2 ][ 2 ][ 4 ][ 8 ] on the bottom row. I’ll give you some help: Rule #1: Don’t swipe Up. The time to break this rule is when that’s the only legal move. Otherwise, only swipe Down, or Left, or Right. Also, try to avoid putting a [ 4 ] in between two [ 2 ]’s. Okay, go and play around until you manage to get [ 2 ][ 2 ][ 4 ][ 8 ]. Then swipe Right three times.
Woohoo! You now have a [ 32 ] in the lower right corner. Now add Rule #2: Keep your highest numbered tile in the lower right corner. If you only swipe Down and Right, then you’ll be following Rule #2. But sometimes you can swipe Left without moving that tile. Here’s an example: Suppose you have [ 4 ][ 2 ][ 4 ][ 32 ]. Swiping Left won’t cause anything to combine on that row. So Left is a safe move here without breaking Rule #2. But if you had [ 2 ][ 4 ][ 4 ][ 32 ] then swiping Left would break Rule #2. Don’t do that unless Down and Right aren’t legal moves.
Remember what I said about not putting a [ 4 ] in between two [ 2 ]’s ? Generally, you want to avoid having isolated singles of any size. For example, if you get a [ 4 ] stuck between two [ 8 ]s then you’ll have a hard time combining the [ 4 ] with another [ 4 ]. That’s Rule #3, tiles need to be in pairs, so don’t isolate them. Keep swiping Down and Right (and throw in an occasional Left, breaking Rule #2 as little as possible). Hopefully, you’ll end up with another [ 32 ] right next to the [ 32 ] you already have in the lower right corner. Now combine them with a Right swipe and voila, you have a [ 64 ] in your lower right corner.
Suppose you could get this on your bottom row: [ 16 ][ 16 ][ 32 ][ 64 ]. Wouldn’t that be sweet? Try to do it by swiping Down and Right. You can also swipe Left, assuming it won’t dislodge the [ 64 ]. If swiping Left would move the [ 64 ] tile, don’t do it unless you have to. If there’s a moment where Down isn’t a legal move and Right isn’t either, then you have to swipe Left. But what if Down and Right and Left are all illegal moves at some point? What if Up is your only move? Then you have to break Rule #1. When that happens, all your carefully cultivated order will quickly descend into chaos. It’s difficult to regain control after that.
If you manage to get [ 16 ][ 16 ][ 32 ][ 64 ] on your bottom row, swipe Right three times and wham! you have a  in the lower right corner. Now keep on following those same three rules and try to get [ 32 ][ 32 ][ 64 ].
Maybe you see what I’m leading up to here. Your goal is that you want the bottom row to look like this: [ 256][ 256][ 512] and then you could swipe Right three times and boom! you win the game.