I had some luck (winning the game, that is) by following this general heuristic:
- Default to placing tiles in one corner, so, for example, using Up & Left primarily so that high numbers will accumulate in the upper left corner.
- Don't automatically consolidate tiles, but rather, maximally fill out the diagonal half-matrix with 2-4-8-etc... before moving to force a consolidation. Example:
- When no Up or Left move is available, move right. Sometimes, this allows for a general consolidation chain reaction to occur, which generally radically empties the board.
- repeat - sometimes you'll need to switch corners to the upper right.
What's important to realize that after being forced to go right you will occasionally get a small tile trapped either in the corner or directly below it. You need to focus all your energy into merging other tiles into this small corner until it is the largest tile on the top row. Learning how to deal with these small tiles correctly was the key to my victory.
Right/Down/right/Down with an Up/Right/Down thrown in when stuck has worked well for me. My first 1024 block came that way.
When I began playing I was moving around the board in an unorganized fashion, but am now finding that moving the larger numbers to one corner (bottom-right for me) is the best method. By having your block consolidation take place in one particular area, the odds that you'll have matching large numbers goes up dramatically.
I've tried a few games where I do those exact moves with no human judgement and the score ends up quite a bit lower than when I 'generally' follow those moves and consolidate using my best judgement.
Another interesting test was to always play a clockwise or counter-clockwise pattern. The consolidation happens in the middle of the board. This method seemed to result in higher scores than the right/down/right/down pattern.
Easy to implement in an AI as well. Could try various permutations and see which works best fairly trivially then too, eg up down left right / up left down right / up left right down etc...
- Default to placing tiles in one corner, so, for example, using Up & Left primarily so that high numbers will accumulate in the upper left corner.
- Don't automatically consolidate tiles, but rather, maximally fill out the diagonal half-matrix with 2-4-8-etc... before moving to force a consolidation. Example:
https://www.dropbox.com/s/aargiwvoyg1shdp/Screen%20Shot%2020...
- When no Up or Left move is available, move right. Sometimes, this allows for a general consolidation chain reaction to occur, which generally radically empties the board.
- repeat - sometimes you'll need to switch corners to the upper right.