And it's all about the corner strategy. Although it's also worth bearing in mind that keeping an eye on the next tile is very important, often much more so than making matches. And take your time; use the ability to preview moves to see what's best. There's no time limit, so no rush.
Edit: the other thing is setting up chains. I play towards the bottom right corner, and try to stack my next biggest numbers to the left. When the bottom row starts filling up with big numbers, I start building towards the left trying to get a big number to match with my bottom line. Hopefully I end up in a position where I can make four or five matches in a row which ends up doubling my biggest number.
Bit of an office competition going on with Threes! at the moment, with me comfortably in the lead with 28,746. Not sure I'll ever see the 1,536 tile, despite being only a sliver away.
It's true. Similar thing jumping from around 20k to around 60. In fact, my score is entirely beatable as once I saw the chain that would give me the 1536 (and beat Mrs. Yoss's score in the process) I went for it without a second thought for the consequences. I think I managed less than half a dozen moves after that.
Hmmm... I'm not sure about the game lasting me "months if not years". I feel like I'm nearly done with it. It takes too much time in the later stages, and loses its appeal as a result. Plus, I'm afraid that to get the 3000 tile I'll need to invest more time than I have.
I see this as being a game I'll be coming back to in the years to come. Much like Tetris, I don't play it every day, but I do get back into it periodically every now and again.