2048 Masters / Lessons (Advanced) / PDF

Introduction

This lesson is for advanced players who have completed 16,384 but have a problem completing 32,768. This is the last hurdle. If you are proficient with Perimeter Defense Formation (PDF) and its companion Double Perimeter Defense Formation (DPDF), your odds of completing 32,768 jumps from 5% to 30%.

We have given a detailed explanation of how to do the PDF. To make it easier, we have also videotaped all the different variations that you will encounter while trying to complete 64.

Once you have mastered PDF, it is critical that you master DPDF. We have not provided videos for this but if players are frustrated and there is a clamor for it, we are happy to show how it is done.

The PDF and DPDF can also be used as recovery tools.

Later on we will give you drills that came from actual games. This will sharpen your skills further.

Perimeter Defense Formation



Perimeter Defense Formation (PDF) appears to be extremely difficult to master but once you understand a few points, it is as easy as making a 64 in the 2X4 space. We call it PDF because all the squares we are playing with are at the perimeter.

Here are the things you need to consider:

1) How the tiles combine:

If you have:
4 4 2 2

and press left, it does not merge like this:
8 2 2 x

Rather it merges like this:
8 4 x x

The x's is where either 2 or a 4 may spawn. Once we understand this property associated with merging, we can use it to our advantage. Double merging like the example above is dangerous because you lose control of the empty square. In PDF, you are more deliberate in how you are creating an empty square. You have one row and one column. Therefore, if you create one more empty square than what is required, it destroys the balance between the row and the column and you may be forced to press in the wrong direction.

2) Retractable squares:

If you don't know how to manipulate, create and retain retractable square(s), you cannot solve PDF. We call it retractable because you can either push forward or back to create a favorable situation. It is like a retractable awning.

Taking our example from above, if you want to build a 16 by pushing left, you will end up more than half the time with:
8 4 2 x

The success ratio for building a 16 is 47%. How do we raise the success ratio to 95%?

In a PDF, there are three ways to do them.

a) Build it like this:

8 4 2 x
x x x 4
x x x 4
x x x 8
The 4, 4 squares are retractable. You press down thereby creating a space in the top right corner so that you get a 2 there. This gives you a chance to make your 16 in the top row. This theme recurs all the time in PDF.

b)

8 4 2 x
x x x 8
x x x 4
x x x 2
In this situation the bottom right corner with a 2 acts as a retractable square. You press up and a 2 should spawn 90% of the time. You then press down, combining the two but it leaves the top right corner open for a 2 to spawn. This is another way to make a 16 95% of the time.

c)

8 4 2 x
x x x 2
x x x 8
x x x 4
You know you may end up with 8,4,2,x in the top row. So you position a 2 just below the top right corner. You then push the 2 up and this allows you to make your 16 in the top row.

d) Because retractable squares give you optionality, it must be used judiciously. Do not merge unless you have to or you have a purpose in mind.

3) You need to know your math:

There are 3 ways to build a 64 in PDF.

a)

32 16 8 2
x x x 2
x x x 2
x x x 2
This is the easiest. The tiles spawn favorably. You make 32 in the top left corner. then you make a 16 and then an 8. In the column, you need to an 8. You then combine the whole thing to make a 16. This only occurs 10% of the time.

b)

2 32 16 2
x x x 2
x x x 4
x x x 8
This occurs most of the time. And this is one where you really need to understand the merging properties, and creation, retention and utilization of retractable squares. There are 3 or 4 variations and we will show you how they are done.

c)

2 4 32 16
x x x 8
x x x 4
x x x 4
This one is very difficult. The odds of success is less than 1%. You are just hoping for the tiles to spawn favorably at just the right moment.


In conclusion, the success ratio of making a 64 is about 55%. We played 1,000 times and we were successful 550 times. When we first started and did not understand the merging properties and how to make use of the retractable squares, our success ratio was between 15% and 20%.

Try it: Make 64 then merge it to make 128 and then merge the 3rd row to make 512 - the ultimate goal of DPDF

Reset

Stuck? Watch how to do it here:

1) Make 32 and 16

2) Make 32 in the corner

3) Don't Panic!

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