From Hard Drop - Tetris Wiki
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%.
Second Bag and later
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.
Second bag and later
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%.