... to all merging/matching/combining games like this is creating what's called immutable subsets. I'll explain what this means using 2048, but it really applies to most, if not all, of the games similar to it in nature.
An immutable subset is a collection of tiles that don't change (in this case move) within a specific set of rules. Usually this comes with a restriction on the input commands you can use and the immutable subsets with respect to the different input commands can be different. Let me give you an example:
In sum, the immutable subsets w.r.t. each input are:
Understanding immutable subsets is basically all you need. From there on, the trick is to use only such input commands that include your highest tile in an immutable subset. This way, the highest tile will remain in the same spot no matter what you do. Pick a corner, build a high tile there and make sure it's always part of an immutable subset from then on. The only exception is when you actually created another tile of same value next to it and merge them to get one step further. In this case, though, make sure the location of the new highest tile is the same as that of the old highest tile.
To actually do this, you will need a preference order of keys you use. One key will be the one you use most of the time, another one nearly as often. Those are the keys that point towards the corner you picked earlier. The key you use most often will result in the creation of an immutable subset along an entire border of the field w.r.t. the inputs perpendicular to the first one. For example, if you choose the bottom left corner and
Respecting this preference order, the second trick to solve the puzzle is to build consecutive chains, that is, tiles with values decreasing one step each, one next to the other. This chain can be along borders, usually in a snake formation, but can also go inside the field. What's important is that this chain or most of it should be part of your immutable subset. So basically, you're building a tile of one step less than your highest value tile next to it in such a way that they don't move around.
Sometimes it just happens that the entire field is immutable w.r.t. some direction and mutable to all others. An example of such a field would be this:
This is completely immutable w.r.t.
This could be a lucky result from going
While purely subjective and based solely on personal experience, I'll give you some things to look out for which I feel are done wrong often, even if you try to apply the strategy described here. Avoiding those can be the key to reaching the next level.
That's all I can give you, if you stick to this strategy and make sure you avoid the mistakes, winning should be a matter of time. Due to the random nature of the game and the occurence of situations where you must break the pattern, you just can't win sometimes. Keep trying and the strategy described here should help you win something between 10 and 60 percent of your games. It all comes with experience.
I have been following the instruction from the link below:
Managed to get to a 4096 tile and I think it is possible to do a 8192, see the screenshot.
My strategy is to make a number one before the current (eg if the current highest is 4096, make 2048). Then make the one before that, and repeat until you have an easy one to get 2 of. Make 2, then combine the 2 to make a higher one, repeat until you have 2 of the highest number, combine them, and you have a new highest number. Hope this helps. :D