Infinite TST

The Infinite T-Spin Triple Setup, or in short Infinite TST, is a looping pattern invented by the player Massi4h. Each loop consists of 2 T-Spin Triple Towers and 4 T-Spin Triples in total. It will only work in guideline games (bag randomizer, hold feature, T-Spins) but there it is one of the most efficient methods to score points in singleplayer modes like Ultra or Marathon. It can also be powerful in certain multiplayer modes where back-to-back T-Spin Triples send a lot of lines (e.g. Tetris Battle).

Execution
The following steps are required to reach the desired location:


 * At the top, rotate the T piece into vertical orientation (counterclockwise if overhang on left side)
 * Softdrop the piece until it reaches the bottom. The T piece should be facing towards the overhang (the T's center lies on the opposite side).
 * T-Spin Mini kick: Rotate the piece in the opposite direction as in step #1 (clockwise if overhang on left side).
 * T-Spin Triple kick: Rotate the piece in the same direction as in the previous step (clockwise if overhang on left side).

Those steps work thanks to the Super Rotation System (SRS). When executing the T-Spin Mini kick, the center of the T piece is shifted 1 column to the side and 1 row downwards. When executing the T-Spin Triple kick, the center of the T piece is shifted 1 column to the side and 2 rows downwards. Note that a 2-rows-downwards shift is required in order to clear 3 lines at once with a T piece (same is true for S and Z pieces).

Mirrored and Reversed Setups
Usually, players stack the setup on the left side which means the 4 left-most columns are used for the pattern and the right side is filled with excess pieces. In that case, the pattern needs 3 L pieces, 2 I pieces, and 1 of S, Z and J. The player must either try to keep T in hold for the next T-Spin Triple, or to keep L and I in hold for building the next T-Spin Triple tower.

It is also possible to build the setup in other ways. For example, completely mirrored on the right side. In that case, the pattern needs 3 J pieces, 2 I pieces, and 1 of S, Z and L. This may actually work better under high gravity. It is also possible to just mirror the 4 columns of the pattern, and not the whole stack. We will call that "reversed" in the following. The reversed patterns actually work worse under high gravity - there is one placement (the J/L piece overhang) which cannot be done under 20G.

Efficiency
To compare the efficiency of line clears we use the metric "points per cleared line". Following scores apply to almost every guideline game, multiplied by the current level in modes like Marathon:


 * Single: 100 points per cleared line
 * 16 combo (consisting of Singles): 500 points per cleared line
 * b2b Tetris: 300 points per cleared line
 * b2b T-Spin Single: 1200 points per cleared line
 * b2b T-Spin Double: 900 points per cleared line
 * b2b T-Spin Triple: 800 points per cleared line

b2b stands for back-to-back: Tetrises and T-Spin line clears receive a +50 % score bonus, if the previous line clear was also either a Tetris or T-Spin. Regular T-Spins have a higher efficiency than any other line clear. Note that those numbers do not factor in the amount of specific pieces a player gets. Every bag consists of 7 pieces and contains exactly 1 T piece. A player clearing nothing but T-Spin Singles and Doubles will eventually run out of space: 7 pieces add 28 filled cells and a T-Spin Double removes only 20 of them. So, in the long run Tetrises must be added to the T-Spin mix, unless T-Spin Triples are used. Even when using every T piece, a Tetris must be made every 5 T-Spin Doubles (5 bags = 35 pieces = 140 filled cells = 14 cleared lines = 5 TSDs + 1 Tetris). So, a strategy based on T-Spin Doubles will score 729 points per cleared line at most. The popular ST Stacking loop uses 1 Tetris per 4 T-Spin Doubles and thus scores 700 points per cleared line. That's obviously less than the 800 points you can get with T-Spin Triples only - and Infinite TST is the way to do so. With other words: Infinite TST is rather the most score-efficient method in guideline Tetris games.

The Start
The following subsections list ways to start the Infinite TST looping pattern on the left side. In any case, the goal is to reach the following 2 shapes at the bottom:



Openers
When starting with an empty board, a player might use these:


 * Early Z piece: Just place a Z piece horizontally 2 columns away from the left wall. This method has the disadvantage that 2 T pieces must be wasted on the right side before the first T-Spin Triple can be made.


 * T-Spin Single: There are few methods to build the desired shape on the left side with the help of a T-Spin Single. This method has the advantage that usually only the second T piece must be wasted without doing a T-Spin (that said sometimes the third T piece must be wasted as well). The first listed way always works when starting with a J piece whereas the second way already builds a part of the T-Spin Triple Tower in the first bag.


 * TKI 3 variant: The desired shape on the left side is created with the help of a T-Spin Double. Always works when starting with an I piece and receiving L before O.


 * Another TKI 3 variant: This time 2 T-Spin Doubles are used to create the desired shape. Always works when starting with an I piece.


 * 2 x T-Spin Double (again): This method always works when starting with both L and J (maybe need an I-Spin). Note that in the second bag the Z piece can be placed after J (yet another spin).


 * Albatross: This method results in a platform T-Spin Double followed by a T-Spin Triple. Always works when starting with O and L. Note that in the second bag the S piece can be placed after Z (provided I has not been placed yet).


 * DT Cannon LS/JZ base: DT Cannon is by far the most commonly used way to start an Infinite TST. It results in a T-Spin Double followed by a T-Spin Triple. This way always works when starting with L and J or L and S, or just J (maybe Z spin needed).


 * DT Cannon TZ base: Another DT Cannon. It will always work when starting with T and Z or T and S. The stack usually looks the same way after 2 bags.


 * Pseudo DT Cannon: The following ways result in a T-Spin Double followed by a T-Spin Triple. One of them will always work for all first bags where the two DT Cannons mentioned above are not applicable. In the second bag J piece must be kept on hold until the first T-Spin is made.

Three Residuals
Usually, the 4 left-most columns do not interact with the other columns in Infinite TST, that means pieces are placed entirely in the left section or outside of it. In this case there will be 4*n + 3 filled cells in the left section with an arbitrary integer number n because each left-placed piece adds 4 filled cells and each cleared line removes 4 filled cells. For this reason Infinite TST can be started easily, if there are 3 leftovers in the 4 left-most columns. Here are some ways to do so; some of them use certain T-Spin techniques. Note that in any case the left section can be mirrored resulting in the "reversed" build.


 * Direct Starts: A T-Spin Triple Tower can be stacked immediately.


 * T-Spin Triple: A T-Spin Triple can be stacked directly.


 * 3 x T-Spin Triples: 3 T-Spin Triples can be stacked directly. Note that you most certainly have to waste some T pieces in the right stack until you have built up the tower.


 * Super T-Spin Double: This way uses an STSD which is a technique that usually results in 2 T-Spin Doubles, a T-Spin Triple Tower is stacked instead of executing the second T-Spin Double.


 * King Crimson: This way uses a King Crimson which is a T-Spin Triple above an STSD. Again, a T-Spin Triple Tower is stacked instead of executing the second T-Spin Double of the STSD.


 * King Crimson lvl.2: Similar like before but with another T-Spin Triple on top. It is as high as the 3 x TST tower, so most likely you will have to waste at least one T piece.


 * Crimson lvl.3, 4 x TST: We have gone too far. Now we will have to burn a lot of lines to still convert this into the Infinite TST loop.


 * T-Spin Triple Skim: Here one line is burned in order to stack a T-Spin Triple.


 * Skim until Setup: For other combinations of 3 left-overs, you can usually burn 1 or 2 lines until one of those left sides from above shows up.


 * Tetris: If the leftmost column is empty, one can also build a Tetris with the typical L piece overhang on top of it.

Other Residuals
The situation is more complicated for amount of residuals different from 3, 7, 11 and so on. In that case it is necessary to make a placement with blocks inside as well as outside of the 4 left-most columns. In the following we assume that the stack resembles a 3 wide where the fourth column is not too high, and try to apply the setups from above that make an I piece placement in the fourth column (or first column for the reversed build). When we speak about residuals in this section, we may mean the amount of filled cells in the 3 left-most columns.


 * Direct Conversion: We apply the 3-residuals setups that make an I placement in the fourth column.


 * Skim until Conversion: Since we have a 3 wide, placing pieces in it will change the amount of residuals (plus 4 per placement but minus 3 per cleared line). So, all 3 stacks shown above are eventually reachable.


 * TST beneath DT Cannon: This might be needed if the fourth column is too high for that 1-residual stack.


 * Reversed Conversion: We apply the 3-residuals setups that make an I placement in the first column and stack them reversed.


 * Reversed STSD: We apply the Super T-Spin Double and King Crimson setups and stack them reversed.


 * Reversed Burn: We burn lines until we reach the reversed version of that one T-Spin Triple Tower.


 * Double Triple: If the fourth column is very low, we may use one of the T-Spin Double into T-Spin Triple Openers, namely DT Cannon and Albatross (latter also resembles Pseudo DT Cannon).


 * T-Spin Mini into ...: If the first column is empty, one may make a T-Spin Mini and try to use one of the other mentioned techniques afterwards.

Keeping Stable
Once you have started the Infinite TST loop, you want to stay in it as long as possible, doing just T-Spin Triples. This section lists some aspects which could help to achieve that.

Useful Spins
Spins can help to keep the stack in the 6 right-most columns stable. In the following, the dotted pieces can be spun under the other shown pieces, basically changing the order in which the pieces are placed normally.



Non-4 Wide
Usually, we have a predefined pattern in the 4 left-most columns and a random stack in the 6 right-most columns whereas pieces are placed entirely in one of those 2 sections. Sometimes, it is better to break out of the pre-defined pattern by letting the sections interact with each other. For example, here are some different ways to create that one overhang without the usual L or I piece placement.



And here are some ways to complete the part above it depending on the overhang shape:


 * ZS Overhang: This overhang is unique and can be completed easily using 3 wide patterns.


 * ZJ Overhang: This overhang is also unique but usually a bad choice because of the lack of decent continuations.


 * OL Overhang: The usual SL continuation works here as well as some 3-wide patterns.


 * SJ Overhang: The usual SL continuation works here as well as a bunch of 3-wide patterns. The OL Overhang patterns may also work from time to time.

Height Increasement
The player will usually clear 2 T-Spin Triples after building each T-Spin Triple Tower. In case of the tower with the L piece overhang, it is possible to only clear one T-Spin Triple before building the next tower. This technique might be used when the second T piece shows up very late because otherwise there is the danger that the next tower is not ready yet when the following T pieces appear. The main use is in Ultra mode where a player will spend less time softdropping this way.

Note that this technique is relatively hard to pull off and may backfire. The stack in the 6 right-most columns must be relatively high and the player must pay attention to the previews in order to not waste a T piece. After the loop is completed one time, there will be 3 T-Spin Triples ready below an L piece overhang: The player can decide to only clear 2 of them to use this technique yet another time.



Temporary height increasement is also possible in case of the tower with the Z piece overhang. Here you can place a S piece instead of the Z piece and use it to make a T-Spin Double. Eventually, the height of the tower is increased by one T-Spin Triple by some further L and I placements.



Burning Lines
In order to use only T-Spin Triples over a long period, the player is allowed to waste only one T piece every 15 bags: 15 bags are 15*7*4 = 420 filled cells or 42 completed lines which corresponds to 14 T-Spin Triples. Usually in practice however, more T pieces than that must be put in the 6 right-most columns, either to stabilize the stack on the right side or because the T-Spin Triple tower is not ready yet when a T piece arrives. If 2 T pieces are wasted in a relatively short period of time, then it is best to burn some lines. Rule of thumb is to burn 2 lines for every wasted T piece.

Skimming above the Pattern
In order to burn some lines above the pattern, we have to fill the 4 leftmost columns in rows that are already filled on the right side. The best chance to do so is in the following 2 situations:



In the first situation, the Z piece overhang is still missing. Sometimes, the Z piece can be placed before the lines are completed. Example:



The following pictures show some ways to fill the 4 left-most columns, sorted by the amount of cleared lines. The easiest way is placing an I piece horizontally - this can be done at any time, provided the I piece is not needed somewhere else. However, this means that you just reduce the height of the stack by one row but give up the back-to-back bonus for the next T-Spin Triple in return. The most score-efficient way is a Tetris which keeps the back-to-back chain going. Tetrises are not that easy to set up though. If a piece is displayed dotted and split into 2 halves, it means that a line clear must happen before that placement.


 * Single


 * Double


 * Triple


 * Quadruple


 * Quintuple


 * Tetris

Skimming amid the Pattern
S, Z and O pieces are barely used in the 4 left-most columns. If there is a bunch of them coming and there is no space for them in the 6 right-most columns, then the player may still insert them in the pattern which will result in 2 burned lines eventually:


 * Bottom right O


 * Double S


 * Top right O


 * Bottom left O


 * Double Z


 * Top left O

Switching Directions
At one point during the loop, there is just in the 4 left-most columns the overhang left from a previous T-Spin Triple Tower (plus maybe S and L already placed on it). In this case one single line can be skimmed at the very bottom of the playfield with the help of an O piece or a J piece. In case of the O piece, nothing really happens: the previously built tower is build once again (skipping the tower facing in the other direction). In case of the J piece however, the Infinite TST setup is converted to the reversed build. Likewise, the reversed build can be converted to the normal build with the help of a L piece skim at the very bottom (not shown). Note that the skim with the O piece is not possible if S and L were already placed on the overhang of the previous tower (but the I piece can be placed before the skim).



T-Spin Double Skim
At one point during the loop, there is a T-Spin Double at the bottom of the playfield but an I piece is used instead to build a T-Spin Triple Tower. However, when receiving a T piece at the wrong time, it might be better to take that T-Spin Double instead of placing the T piece in the 6 right-most columns. A Single must be done additionally to the T-Spin Double, thus one T-Spin line clear will have no back-to-back bonus. The combination T-Spin Single plus Double is also possible. The patterns shown in the left pictures are usually the best choices, if an I piece is needed somewhere else.



At another point during the loop, there is just the remains of an overhang at the bottom of the playfield. These remains can be eliminated with a T-Spin Mini or Z-Spin, just to stack up for a Tetris and to create that overhang again (following pictures in top row). This does not sacrifice the back-to-back bonus in case of the T-Spin Mini. Instead of the S- / T-Spin into Tetris, one can also make a J-Spin followed by a T-Spin Double and 2 further burned lines (left pictures at the bottom). This will give up the back-to-back bonus twice though. One can also follow the J-Spin by the previously mentioned T-Spin Double Skim - but this time applied to the reversed build (right pictures at the bottom).



Other Stuff
This section is about further information regarding the Infinite T-Spin loop.

Follow-Ups
At a certain point, a player may want to stop using the Infinite TST pattern, either voluntarily or forced: The stack in the 6 right-most might be too high, too unstable or there might be holes in it. Here are some possible continuations:


 * 4 Wide: That is usually the best choice. Infinite TST is related to side-stacked 4 wide with 3 residuals because at any time there are a multiple of 4 plus 3 filled cells in the 4 left-most columns. The best chance to get a good combo going is when there is the L piece overhang with no piece placed on it yet. Under circumstances, the Infinite TST pattern can be started again immediately after the 4 wide.


 * C-Spin: C-Spin is a technique that results in a T-Spin Triple followed by a T-Spin Double. It is a good way to get rid of the T-Spin Triple overhang. You need to place a Z piece horizontally on the overhang which cannot be done if the stack in the 6 right-most columns is too high - unless there is a hole exactly in that spot.


 * Trinity: Trinity is an STSD with a T-Spin Double below it, so it results in 3 T-Spin Doubles in total. While the STSD overhang can be stacked in several ways, this continuation has a significant flaw: one T-Spin Double per bag means that you further upstack (additional 8 filled cells per bag) while you most likely want to downstack when abandoning the Infinite TST loop.

High Gravity
Infinite TST is a very score-efficient strategy, thus people may also use it in Marathon. In theory, the loop can also work under high gravity but in practise, players have to waste many T pieces (and thus burn many lines) to keep the loop going. In the following we will assume 20G gravity, that means the piece spawns at the ground and is immediately pulled towards it after each successful rotation or sidewards movement. In this case, there are some unusual placement restrictions:


 * I piece: At one point, an L piece is placed in the bottom left corner. The I piece can only fit on top of it, if the S piece to the right is placed beforehand. Additionally, clockwise rotation must be used to get the I piece into place.
 * Z piece: The Z piece will only fit on top of the previously mentioned I piece, if the L piece to the right is placed beforehand. Additionally, clockwise rotation must be used three times in a row to get the S piece into place.
 * L piece (overhang): At one point, an L piece forms an overhang of a T-Spin Triple Tower. There are no restrictions to the placement order but the L piece must be rotated before it is moved to the 4 left-most columns.



There are also some restrictions for the reversed build but most importantly, it is not possible to create that one overhang with a J piece - at least not without burning 2 lines as shown below. This makes the reversed build less efficient under high gravity. Players may also try to stack the looping pattern in the 4 right-most columns (not shown). This is different from the left side because L, J, T, S and Z pieces do not spawn perfectly centered (there is no center for 3 wide pieces in a 10 wide matrix). The right side seems to even work a little better under high gravity.



Parity
Imagine laying a checkerboard over the playfield. In that case, every cell has a color: white or black. Now you could count the amount of filled cells that lie on a white cell (#white); and you could do the same for black (#black). Parity describes the difference between these 2 numbers: difference = |#white - #black| (sign does not matter). Theoretically, you could do the same only considering the highest filled cells in each column (that's 10 cells in total). In a stack without holes, those 2 differences correspond to each other: difference_surface = 2 x difference_stack. It is important that the difference on the surface does not become too big because the only placements that can be done in columns, where the surface cells have the same color, are: vertical S, Z and I placements as well as most T placements. In fact, T pieces are the only pieces that change this difference. Line clears can change the difference as well but not in the following case because we will assume no holes and line clears done at the very bottom or below the lowest surface cell.

Now we apply the concept of Parity to the 6 right-most columns of the standard Infinite TST loop (we do not care for the other 4 columns because we will stack a looping pattern there). We do not want to have any holes in the 6 right-most columns because this will break the Infinite TST loop in the long run. As mentioned before, we have an odd number of filled cells in the 4 left-most columns (more precisely it is 3 more filled cells than a multiple of 4) which also means that we have an odd number of filled cells in the 6 right-most columns (assuming we start with an empty field and no garbage is inserted). And each of the mentioned openers will keep the difference as minimal as possible: difference_stack = 1, difference_surface = 2. That means we will have 4 white and 2 black cells on the surface or vice versa (2 white, 4 black).For example, take a look on those 2 T-Spin Single Openers:



From time to time, we will have to place a T piece in the 6 right-most columns. Let us say we have 4 white and 2 black cells on the surface. A T piece will change that to either 2 white and 4 black OR 6 white and 0 black - depending on the color of the T piece's center. 6 white and 0 black would be a bad placement but luckily it is almost impossible to actually make such a placement. So, in Infinite TST Stacking, we will switch back and fourth between 2 black and 4 white AND 4 black and 2 white cells on the surface in the 6 right-most columns. Thus, the difference on the surface will be 2 the whole time which means the stack stays pretty stable throughout the game (if kept relatively flat). The following picture shows a bad placement (6 white) and a normal placement (4 white -> 2 white).



Long story short: Thanks to the odd number of filled cells in the 6 right-most columns, we do not have to worry about T placements in that section: A normal T placement will have no effect on Parity. Similar argumentation can be used for 4 wide Combos (with 3 residuals). The opposite applies to ST stacking: There we have an even number of filled cells in the right-most columns; and as a result every T placement will change Parity: In fact, once a T piece is put in the right stack, another T piece must be placed there as soon as possible.