Mountainous Stacking

Mountainous Stacking (also known as Mountain Stacking or ITO Cannon) is a Triple Double opener that results in a T-Spin Triple in the second bag, then a Perfect Clear chance in the third, as well as a chance to get a T-Spin Double and Perfect Clear within the third bag.

First Bag
For early I and L/J starts in the first bag, one can use this Triple Double opener. Also, the J piece (L piece in the mirrored setup) would be on hold since that will be used in different places, especially setup B in the second bag. This opener has the same piece depenencies as ITO Cannon and Syrup Stacking, except without the J piece.

The overall setup rate with Hold and softdrops when the mirrored setup is also counted is 53.33%, or if the only the regular setup, it would be 33.33%.

Perfect Clear after 6 lines
For these methods, you must keep a certain piece on hold so that you can try achieving a Perfect Clear after 3 further lines. The first method would give more firepower, but it is also hard to assemble because you must place the L piece after the T-Spin Triple.

Triple Double Perfect Clear
The first method involves placing the L piece after the T-Spin Triple. This method is hard to assemble because you must get the L and S pieces late, place the L piece after the T-Spin Triple and also keep the S piece on hold entirely. The overall Perfect Clear rate is 7.14%, ideally with a T-Spin Double first.

If you cannot make a Perfect Clear after 6 lines, you would still have a 68.19% success rate (3437 bags out of 5040) to achieve one after 8 total lines. The first 5 out of the 14 minimal solutions are shown below.

Triple Single Perfect Clear
The second method is less powerful than the first, but it is however a bit easier to assemble, if the O piece comes before S and J and also be able to hold the L piece. The Perfect Clear rate is 21.43%. The final 2 solutions may result in a T-Spin Single.

If you cannot make a Perfect Clear after 6 lines, you would still have a 96.55% success rate to achieve one after 8 total lines. The first 5 out of the 35 minimal solutions are shown below.

Perfect Clear after 8 lines
Ideally, you should be able to stack one of these 4 cases for a Perfect Clear chance. You have a 99.44% chance to stack one of these cases. If that is impossible, the compromise can always be stacked.


 * Setup A (65.71% setup rate, 98.85% PC rate, 65 minimal solutions): For the first diagram, the first J piece can be placed on the left if the I piece comes early, or the right if L comes early. It is the most ideal way.


 * Setup B (43.33% setup rate, 98.57% PC rate, 40 minimal solutions)


 * Setup C (64.29% setup rate, 96.87% PC rate, 15 minimal solutions): For the first diagram, the first J should placed on the very right and therefore the second J is used for the overhang.


 * Setup D (59.01% setup rate, 95.91% PC rate, 29 minimal solutions): For the first diagram, the first J piece can be placed the on the left if the I piece comes early, or the right if the L and S pieces come early.

Compromise
There is a 0.56% chance that all the setups above will not be possible because of the bag order. In that case, one can always stack the compromise below, which has a 44.80% PC rate (one solution).

If you cannot achieve a Perfect Clear with the compromise, in most cases you will be able to stack the third bag depending on the order of the I, Z, J and L pieces, even if the O piece comes after S. In this case, you have a 35.71% chance to achieve a Perfect Clear after 10 lines.

Mountainous Stacking 2
Mountainous Stacking 2 is the successor to Mountainous Stacking. This opener is fully developed in early May 2021. Like its predecessor, it is a Triple Double opener that is mainly intended for a Perfect Clear in the third bag. The L piece (J in the mirrored opener) is on hold until the second bag.

There is a 100% chance to stack this opener, when Hold and softdrops are allowed and also coonsidering the mirrored setup, or 66.67%, if only the regular setup.

Perfect Clear after 8 lines
Ideally, you should be able to stack one of these four cases. Perfect Clear setup C is complemented with the compromise setup (setup E). There also exists a setup where the I piece is on hold and will be used with the third bag.


 * Setup A (50% setup rate, 99.09% PC rate, 22 minimal solutions): If the O comes early but not if it comes after I, which otherwise forces one to stack the compromise, this is the case to stack.


 * Setup B (56.79% setup rate, 98.57% PC rate, 24 minimal solutions): The L piece should come before I or J. It will create the same shape as setup B in Mountainous Stacking.


 * Setup C (66.67% setup rate, 97.94% PC rate, 14 minimal solutions): This setup is complemented with the compromise setup.


 * Setup D (59.48% setup rate, 96.90% PC rate, 8 minimal solutions): If OL or LI are already placed, the extra setup may be used instead the compromise. It is the same shape as the ideal way in Pancake Stacking.


 * Bonus setup 1 (19.05% setup rate, 99.76% PC rate, 20 minimal solutions): Ideally, the I piece should be on hold and this will give you a very high chance of getting a Perfect Clear. If you must place the I piece, use setup A or B, provided the O piece comes before S.

Compromise
There is a 0.75% chance you must stack the compromise setup, if all the setups above fails. However, there is a decent continuation if you stack the compromise, that is, the third bag can always be stacked depending on the order of the Z and J pieces as the O piece will be placed after the L is placed, and the fourth bag can always be placed as so, and this will lead to a 100% Perfect Clear chance. The compromise is complemented with Perfect Clear setup C. (1.19% if you only consider shooting TST at the end of the bag, but 0.75% if you also consider shooting it in the middle of the bag.)

Setup 2C loop
Since setup 2C is complemented with 2E (compromise), there also exists a loop where if you have placed the S piece before O (setup 2C). In the third bag, you can always place the pieces and then place the held I piece on SZO. The fourth bag can always be placed when you use an L-Spin to place the L piece after the O and J were placed. There is a 100% chance to get a Perfect Clear after six more lines (14 lines in total).

Mountainous Stacking 3
Mountainous Stacking 3 is the successor to Mountainous Stacking 2. This setup released alongside Ruby Stacking. This opener is similar to Bacon's Maple Stacking, except the O piece is kept on hold as this will be used in different situations. You can use this opener if you have a J/L start.

There is a 86.67% chance to stack this opener, when the mirrored setup is also considered, or if only the setup shown on the left, then it would be 66.67%.

Perfect Clear after 8 lines
Ideally, you should be able to stack one of these five cases. You have a 93.33% chance to stack one of these cases. Perfect Clear setup D should be complemented with the compromise setup.


 * Setup A (21.43% setup rate, 99.90% PC rate, 12 minimal solutions): Ideally, the O piece from the second bag is held altogether and will be used within the Perfect Clear, as well as a very high chance of making a PC. If you must place the O piece, use setup D.


 * Setup B (50% setup rate, 99.09% PC rate, 22 minimal solutions)


 * Setup C (43.89% setup rate, 96.87% PC rate, 14 minimal solutions): For this setup, the first O piece will be placed after a piece from the second bag is placed.


 * Setup D (75% setup rate, 95.91% PC rate, 18 minimal solutions): If you must place the O piece, which means you cannot use setup A or C, use this setup. It is complemented with the compromise below.


 * Setup E (50% setup rate, 90.40% PC rate, 12 minimal solutions): Aside from a possibility of making a Perfect Clear with a T-Spin Double, there is also a chance to achieve this with a TSS and a Tetris line clear. The shape is originally seen in Kisaragi Stacking.

Compromise
If any of the Perfect Clear setups above are not possible, the setup below will cover all bags that would not allow one to stack a PC setup. Unlike all the setups above, this will only result in a T-Spin Double in the T-Spin Triple form. The whole setup would last until the 5th bag. The compromise is complemented with Perfect Clear setup D.

Source

 * ITO Cannon