And as I mentioned in my original post, the goal for me to get 4096 or over 50,000 points. 2048 is easy, 50,000 points isn't.
House ruling is fine but shouldn't that level of challenge (either through an enforced time limit or some other means) exist in the vanilla game?
It may be, in effect, a customisable game but that feels accidental rather than anything the designer intended. I could make any game harder by drinking heavily before playing it but that external factor making the game more difficult hasn't really improved it as a game.
Worth saying, I'm not wild about either game. For me they're simply not rewarding and I found myself resenting rather than enjoying the time I spent on them.
I just tried it out again and I used a slightly modified version of the technique laid out in this article (Left-Down-Left-Down until I couldn't anymore then switched to Right-Down, rinse repeat only occasionally switching directions to setup long number chains ) and I got a 4096.
For you maybe, not me - not all the time anyway. Granted when I am bored and feeling lazy, or I have a quick subway ride, I'll spin up 2048, but if I want a challenge and some thinking, I'll spin up Threes. In some sense, 2048 for me now serves as a less twitchy, less exciting Tetris substitute.
Moving the goal posts back on behalf of a game makes the goal more difficult, sure, but it doesn't necessarily mean the difficulty of the actual gameplay increases at the same rate, i.e. it can lag behind the difficulty of the goal, which in my opinion is very much the case for 2048.
Nonetheless, hitting 8192 remains a challenge, and I feel like I've been tantalizingly close to 16384, but have never quite managed it. So as far as I'm concerned 2048 (or, I guess, 16384) remains quite challenging.
In Threes, 768 is the furthest I've gotten. I've found that when things get tight in Threes, you can easily be stymied not just by new tile placement (the only real wildcard in 2048), but also by the "+", "1", and "2"'s that can result in the position being unplayable, thus adding in my mind a greater degree of chance to the game.
Generally speaking the beginning doesn't really matter all that much so just start building up numbers however you see fit (some people go left right left right multiple times before crunching downwards). But start building and pinning your largest number on either the left or right corner. So, for example, try to make a 32, and pin it in the bottom right. Then start working on a 16 to its left, and an 8 to the 16's left, and a 4 to the 8's left. Generally, I try to make sure the entire workspace row is locked as often as possible by making sure it's always filled. This minimizes the chance that you'll need to unpin the largest number from its corner.
Once you've got your workspace row locked, there are a few things you can do. I haven't decided which I really prefer yet, but I basically just start creating another workspace row above the first workspace row. I'll usually try to focus on creating row #2's largest number on the opposite side of row #1's pinned corner number so that I can start crunching downwards as numbers begin to vertically match.
That's the very general gist of it. There are a few minor special case tactics you can use, but I'll leave that for you. Oh, and as faet said, don't swipe up (if your workspace is at the bottom). It's a recoverable mistake, but can make things much more difficult if you get a 2 stuck below your workspace (but it does kind of add some more spark to the game trying to recover from it). Personally, once you start using this strategy, the biggest thing you need to look out for is to not create a scenario where the game will generate 3 locked rows, because that will force you to swipe up. You'll see what I mean. Good luck.
Seems like a good math problem.
[EDIT] http://stackoverflow.com/a/22498940 won 100 out of 100 games using expectimax. 100 are not a lot of games, but hey.