Double Perimeter Defense Formation(4x4)

A DPDF drill to practice the final 1024 before 65536

Double Perimeter Defense Formation, or DPDF, is one of the oldest non-snake formations that is played. Traditionally, it is played with 3 small tiles forming one "perimeter", with a 2x3 block of larger tiles under, and the tiles on the outside forming the second perimeter.

General Principles

[TODO]

Traditional DPDF (Minsker Formation)

Named after ptminsker, the Minsker Formation starts immediately before a merge to two main tiles in the DPDF space. An example for a 32k endgame is:

4   2   2   _
256 64  32  8
2k  1k  512 8
16k 8k  4k  16

From here (assuming all 2 spawns), the player can go LLRL UUUL UDU LURD to set up a very clean formation for the final 128:

4   4   2   _
256 64  32  8
2k  1k  512 8
16k 8k  4k  16

8   2   2   _
256 64  32  8
2k  1k  512 8
16k 8k  4k  16

2   _   8   4
256 64  32  8
2k  1k  512 8
16k 8k  4k  16

2   8   4   2
256 64  32  8
2k  1k  512 8
16k 8k  4k  16

2   8   4   2
256 64  32  16
2k  1k  512 16
16k 8k  4k  2

2   8   4   2
256 64  32  32
2k  1k  512 2
16k 8k  4k  2

2   8   4   2
256 64  32  32
2k  1k  512 4
16k 8k  4k  2

2   8   4   2
256 64  64  2
2k  1k  512 4
16k 8k  4k  2

2   8   4   4
256 64  64  4
2k  1k  512 2
16k 8k  4k  2

2   8   4   2
256 64  64  _
2k  1k  512 8
16k 8k  4k  4

2   8   4   2
256 64  64  8
2k  1k  512 4
16k 8k  4k  2

2   8   4   2
256 128 8   2
2k  1k  512 4
16k 8k  4k  2

2   8   4   4
256 128 8   4
2k  1k  512 2
16k 8k  4k  2

2   2   8   8
256 128 8   4
2k  1k  512 2
16k 8k  4k  2

2   2   2   _
256 128 16  8
2k  1k  512 4
16k 8k  4k  4

Some key variations with 4 spawns include:

2   8   4   4
256 64  32  8
2k  1k  512 8
16k 8k  4k  16 |  RRDLL

2   8   4   4
256 64  64  4
2k  1k  512 2
16k 8k  4k  4  |  LULD

2   8   4   4
256 128 8   4
2k  1k  512 2
16k 8k  4k  4  |  LLRRDLD

Minsker formation loses about 1.5% accuracy over optimal play. However, it is a very straightforward and intuitive setup without loads of different variations that the player must learn, so it is still often taught to players who are new to learning DPDF.

Modern DPDF (Eners Merge and Super Pepsi)

The Eners Merge, named after eners49, is the optimal setup for 16k DPDF endgames. When done correctly, it leads to a formation that has been (somewhat jokingly) named "Super Pepsi", the optimal setup for 32k DPDF endgames.

There are many initial setups for the Eners merge, but the most common way to do it begins with this position:

4   2   2   _
256 32  16  8
2k  1k  512 8
16k 8k  4k  2

Assuming all 2 spawns, the player should now go left thrice, resulting in one of the following formations:

8   4   2   _
256 32  16  8
2k  1k  512 8
16k 8k  4k  2  |  DUL

8   4   _   2
256 32  16  8
2k  1k  512 8
16k 8k  4k  2  |  LUL (side note - tables actually want LL immediately here, there are about 40 different lines though and this move offers only about 0.07% advantage so it isn't strongly recommended for humans)

This results in the following formation, from which the player should go up four times:

8   4   4   _
256 32  32  2
2k  1k  512 2
16k 8k  4k  2

This will result in one of two formations:

8   4   4   8
256 32  32  4
2k  1k  512 2
16k 8k  4k  _  |  LDUDULDDUDULDDD

8   4   4   8
256 32  32  4
2k  1k  512 _
16k 8k  4k  2  |  ULDULDUDDDULDDD

This results in either of the following:

16  8   8   2
256 64  16  _
2k  1k  512 2
16k 8k  4k  8  |  UDRLRDRUULDL

16  8   8   _
256 64  16  2
2k  1k  512 2
16k 8k  4k  8  |  RL; then LRUDRUULDL if D4 spawn, DURDRUULDL if C4 spawn

Finally, the result is one of the two forms of the Super Pepsi formation:

2   4   2   _
256 128 4   2
2k  1k  512 4
16k 8k  4k  2  |  R

2   4   2   2
256 128 4   _
2k  1k  512 4
16k 8k  4k  2  |  U

DPDF in variants

2x4 DPDF:

2x4 DPDF normally looks like:

128 64 32 2
16  8  4  2 | DLRRULL (side note - 2x4 DPDF isn't optimal until 256+128)

The main line for merging into final 64 for 512 is:

256 128 32 2
16  8   4  2 | D; then LLRU If only 2's. If 4 spawn after D go LRRU then L until either:
8 2 2 x | In the bottom 1x4 or
8 2 x 2 | If 8 2 2 then go D and the normal DPDF line. If 8 2 x 2 then you are most likely going to lose unless you win many 50/50's and a 4 gamble. Both of these lines assume no 2 spawns. If you get any 4's you will have to take many 50/50's and 2 gambles UNLESS you get in the 1x4 space:
4 4 4 x | Then go L and get:

8 4 4 x | If that happens you can go D and play the normal DPDF line.

Main DPDF line:

256 128 16 8
4   2   2  x | RRUL if 4 spawn after first R go RU and if:
2 2 4 x in the 1x4 space play L and continue and go U after a 2 spawns in:
x x x 2 then continue main line. From here you would play mainly D and L moves.
L until you cant then D unless something like:
x x x 2
8 4 4 2  | here you would go D and if 4 spawn go D again. After if you get the 2 spawn LD if 4 go L if 2 go D if 4 go L.
More to be done.

3x3 DPDF:

[TODO]

See also

Gap, a superior, snake-like formation where the player builds into the 1x2 gap next to the main DPDF block.