PC after 8 lines (was: C-Spin with first T placed vertically?) Options

[Okey_Dokey]

This is a follow up of my post about Single-Triple-Double or short STD Attacks. Last time I overlooked one thing: The overhang can also point away from the wall which can make a difference.



The STDs from last time are shown on top, the ones for this post on the bottom. First of all, this transformation only works if there was an O piece on the shown position. For example in Early Eye STD there wasn't, so there is no counterpart. The old way forced the usage of a J piece on a certain position, the new way forces the usage of an I piece on a certain position. The transformation also fails, if the red marked cell was filled but not the cell directly above. All in all, in the counterpart setup it's harder to complete lines 3, 4 and 5 with the second bag (T-Spin Triple) and if you do so, you will usually also fill the red cell.

The transformation can be advantageous though: in the old setup, the left side and right side were seperated completely by the overhang, so there was no interaction between them. Now, the overhang is on the wall and there can be interaction. An example where it works out is Mr. T-Spin's STD. Actually, it's the reason why I made this post. I claimed last time that Mr. T-Spin's STD cannot result in a Perfect Clear. While this is true for the reversed setup, it's not true for the real one as you can see below:



So, the overhang is stacked with an O piece here. Unfortunately, I don't have the tools available right now to calculate PC chances or make pictures showing all PC solutions. I expect the PC chance to be rather low but at least there's a chance.

Here are some ways how to place the T piece in the second row but still get a T-Spin Single. Sadly, neither of them will work properly. As a reminder, if you count the number of empty cells in the bottom line right before the T-Spin Single and right before the T-Spin Triple and if you add those 2 numbers, then the result should be odd (exactly one odd clear) or otherwise there will be no PC solution with a T-Spin in third bag. So, the setups in frames 5 and later should be useless.



Here's a way to stack the first bag which I forgot last time. It doesn't really make a difference, if you stack it in the old or new way. You cannot complete the T-Spin Triple in the second bag.



Here's an example where the old way was better: There you could complete the T-Spin Triple after 2 bags (one time with a small PC chance). While the empty gap on top is bigger in the new way, the stack still doesn't yield any new PC solutions (all new potential PC solutions would need a 4th I piece).



Here's an example where the new way is beneficial: The chance for PC is not increased but you have a further option how to stack the second bag (shown in last frame):



Actually, the first bag can always be stacked like that when starting with a J piece. Pokemino's STD and pwn's Hachispin variation have the same property. I consider this setup on par with them. Offtopic: I like that way of stacking the first L piece and J piece (it's like in pwn's Hachispin variation). Here's a good way to place a first bag; it's not involving STDs and PCs though (but an odd clear).



Well, since I am already at STDs, let's cover the weirder ones. Here's one where the left side is one column wider. You can even complete the T-Spin Triple with the second bag but sadly this doesn't result in a PC chance. Last time I had posted a STD involving a Fin T-Spin Single. There the left side was also one column wider.



And here's one where the bottom line is completed instead of the second line. The T-Spin Triple cannot be completed at the end of the second bag.



And last but not least, a comparison between standard STDs (on top) and Hachispin variations (on bottom). Hachispin variations have 2 less cells on top of the overhang. Hachispin and pwn's variation are the only good Hachispin variations (well, you could also mirror the OSZ part in Hachispin but that's not beneficial), and sadly in both of them you cannot reach a Perfect Clear and a third T-Spin at the same time.



Okay, the very last one and pretty much offtopic: A setup were you start with a T-Spin Double via the T-Spin Triple kick. It's followed up with an Imperial Cross. It's interesting that in case of a T-Spin Triple kick you can never complete the 2 bottom rows with just one bag - however it is possible to complete rows 2 and 3 as that Number One opener proves.

[Okey_Dokey]

Here are some ways how to stack the first 2 bags in C-Spin TKI signature, the setup mentioned in my very first post. I think only frames 1, 2, 3 and 7 are beneficial.



Actually, that setup is quite decent. It could be a good center 4-wide defense in Puyo Puyo Tetris. Here are some ways to achieve the Perfect Clear; there should be more (currently the PC tools are unavailable to me).



Here's one way how to stack the first bag and how it is continued in the second bag. Frames 3 and 5 show the standard way which is quite nice because the PC chance is decent and with the help of spins and softdrop it works for a whole bunch of first and second bags. However, the placement of the first S piece can be problematic if O and L piece come late in second bag. In this case it can prove better to place the first S piece differently.



Here's another way how to stack the first bag and how it is can be continued in the second bag. Here an early second Z piece can cause problems.



I have also updated my last post a little.

[Okey_Dokey]

A further STD attack. It was found by pwn's solution finder with the settings noted in a readme file. 72.6 % PC rate in third bag (50.9 % if TSS or TSD beforehand).



And kinda a counterpart by switching sides and mirroring certain parts. 64.7 % PC rate in third bag (only 27.7 % if TSS or TSD beforehand).



I've written a wiki article (DoubleYou) about those setups.

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How about substituting the initial T-Spin Single with a T-Spin Mini? I've seen a Japanese Puyo Puyo Tetris player actually using the following setup, although a non-b2b T-Mini doesn't send any lines. On the other hand, you get a much better PC chance after 8 lines. Note that in Tetris Battle or Tetris Online Poland, a T-Spin Mini sends only 1 line less than a T-Spin Single, so it actually works decently there (+ b2b TSTs sending more lines than usual in those 2 games).

There are 2 different ways to stack the second bag. The first one has a PC rate of astounding 96.5 % (that's by far the most I've seen for a stack where a T-Spin is already prepared), and it's still 76.7 % if you want to get a TSS or TSD beforehand. The second one has a PC rate of 85.1 % (you'll need to use a lot of different hard-to-spot paths though); 66.3 % if TSS or TSD beforehand.



And here's a similar setup which I've given the name Joystick. I haven't seen anybody using it but I am pretty sure Japanese folks must have documentated it before. Very simple setup. You only need O piece before I piece in first bag, and despite its look nothing can go wrong in second bag. With the right continuation in second bag (the one where you do the odd clear), you get a PC rate of 82.7 %, whereas it's 75.1 % if you do a TSS or TSD beforehand (that's almost as much as for the better case of the other setup).



I've written a wiki article (Mini Triple Double) about those setups.

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In the following months I will try to do a little research on setups with just a T-Spin Single (with odd clear) followed by a T-Spin Double (not necessarily a T-Spin in third bag). Trying to find setups with a PC rate of 100 % achieved by only using a few easy solutions (where you only have to make an easy case differentiation). I think that's possible, because of that one Double PC case where you only need 2 different solutions in third bag (the odd clear is done in the first 4 lines).



The interesting thing about this Double PC case is that only one of the first 2 T pieces is dropped vertically - you usually get better PC rates by dropping both vertically. So I assume you should try to drop the first T piece vertically in the TSS -> TSD case I am interested in (to get easier solutions).

[Okey_Dokey]

This post is about a setup that is listed first in pwn's setup finder when searching for TSD -> TSD -> 8 lines PC. This will send 19 or 20 lines in Puyo Puyo Tetris which is usually enough to top out a 4 wider. I like the fact that you can always stack the second bag in the following way if O piece comes after either I piece or T piece - you may have to use softdrop though.



Another nice thing is that you get a symmetric shape which you try to fill for the Perfect Clear. In fact, this setup has a 100 % PC rate. That means for every piece order in the third bag, there's at least one way to stack it that results in an empty board. However, you can only reach those 100 % by using a lot of different solutions. There are a little over 100 solutions and you'll need about 30 of them. Note, that if you place the T piece in the third bag, then you'll need to make an "odd clear" (usually clearing a single line with an odd number of empty cells below).

Here are all solutions. The number means how many piece orders will work for that solution (first number without hold, second number with hold; there are 5040 different piece orders in total).



You can stack the first 3 pieces (or 4 with hold) in one of the following 21 ways and maintain the 100 % success rate. At least one will be applicable in around 86.9 % of the cases (with the help of hold & maybe softdrops). I've tried to arrange them by the needed shapes:



You can stack the first 4 pieces (or 5 with hold) in one of the following around 100 ways and maintain the 100 % success rate. At least one will be applicable in around 99.5 % of the cases. If a way is marked with '?', then all for-this-way-working piece orders are covered by other same-pieces ways.



The remaining 0.5 % meanest cases will have the following pattern: the first 5 pieces will consist of T,I,L,O,J whereas O piece comes at the 4th position and L or J piece comes at the 5th position. Here you'll have to pay attention to the whole sequence (S comes before Z? or vice versa). At least one of the following 4 solutions will always work with the help of hold (or at least two of the following 10 solutions respectively):

[Okey_Dokey]

I went through all 4-rows high fields that have no overhangs/holes and are theoretical PCable by placing exactly 6 pieces. That's basically the scenario you get when starting with 2 T-Spin Doubles and trying to get a 8th row PC afterwards. I got ~32,500 fields in total after making the following assumptions:

• there are no empty cells below a filled cell (no overhangs/holes)
• exactly 24 empty cells (6 pieces to place)
• if a column is filled to row 4, then the amount of empty cells on the left side is divisible by 4 (otherwise not PCable)
• most left column isn't filled to height 4 (to avoid pretty much identical fields which are just shifted by 1 or 2 columns)
• excluding the mirrored field (to avoid pretty much identical fields)
• if you lay a checkered board over the field and count the amount of filled cells by color, then #white - #black is divisible by 4 (parity: 2 T pieces placed so far, no "odd" clear because of the 2 TSDs)
• if you count the amount of filled cells in odd-numbered columns and even-numbered columns, then #even - #odd is divisible by 4 (because the following sum of previous placements is even: #L + #J + #verticalT , no T piece was placed vertically because of the 2 TSDs)

Calculating the Perfect Clear rate can be done pretty quickly for those ~32,500 fields. It roughly takes about 15 minutes, if you use knewJade's solution finder in the right way. Maybe, it's even possible to calculate the same for 5-rows high fields (8th row PC in case of T-Spin Single followed by T-Spin Double), although I assume it takes at least 20 times as long. Anyway, there're 5040 possible bags you could place in those fields, and that's the amount of fields where at least the following amount of bags are PCable:

• 1 bag ( > 0 % PC rate ): 14060 fields
• 1008 bags ( >= 20 % PC rate): 9973 fields
• 2520 bags ( >= 50 % PC rate): 5256 fields
• 3780 bags ( >= 75 % PC rate): 1786 fields
• 4536 bags ( >= 90 % PC rate): 551 fields
• 4788 bags ( >= 95 % PC rate): 289 fields
• 4990 bags ( > 99 % PC rate): 80 fields
• 5040 bags ( 100 % PC rate): 22 fields

The following fumen lists the top fields by PC rate (number of bags where there's at least one way of placing the pieces ending in a PC). If fields have the same PC rate, then they are secondarily sorted by the first-3-placements-guaranteeing-success rate (amount of bags where you can place 3 out of the 4 first pieces (one piece is left on hold) in a way, that a PC is always possible for the remaining 4 pieces). First number is PC rate and second number is first-3-placements rate:



And here are the first-3-placements solutions listed for the top 5 fields. Some solutions just look weird. BTW the 6th best field is the one known from pwn's setup finder when looking for top setups for TSD -> TSD -> 8th row PC (see previous post).

#1:


#2:


#3:


#4:


#5:


I am not saying that there is any TSD -> TSD setup leading to one of those 5 fields. My project is currently on hold, will be continued in 2019.

edit: I forgot that you can also determine the quality by the amount of bags that are PCable without the use of hold. Here are the fields sorted primarly by no-hold PC rate (second number in Fumen) and secondarily by with-hold PC rate (first number in Fumen). The field known from pwn's setup finder conquered the third spot in this ranking:

[Okey_Dokey]

I guess I will leave it here: It's about a 14th row PC setup I once analized - no 8th row PC this time (the difference is that the PC is done with 7 pieces instead of 6). Setup was invented by Riviclia and it's a Pelican continuation. 14th row also means that it is loopable. However, for each of the first 4 bags, there's only about a 80 % chance to continue it in the shown way (and in third bag you may have to split TST into TSD + Single to achieve that chance). Setup clears a TSD, then wastes a T piece, followed by a TST and another TSD. The odd clear is done via a C-Spin (same as in BT Cannon loop). Like in the BT Cannon loop, there is a T-Spin prepared at the end of the fourth bag but the BT Cannon loop clears one more line on its way (2 TSTs).



Best BT Cannon loop continuation has a 99.9 % PC rate. Here, it's 100 %. Most frequent ways to achieve a PC (only 13 solutions required when knowing the whole bag):



99.40 % of all bags can be PCed with a T-Spin beforehand. And that's astounding in my opinion. There's about a 14.3 % chance that the T piece comes last in the bag, but in this case you can almost always reach the T piece with an I or O piece in hold, do a T-Spin Double and then a I-Single or O-Double afterwards.



98.06 % of all bags can be PCed without softdrop, not counting the optional T-Spin:



And there's a 98.10 % first-3-placements PC rate (see my last post - don't want to explain it again).



Here again first-3-placements where I tried to delete redundant ones and added some useful solutions on the top (some solutions are redundant but I included them because I thought they would result in less softdrops in certain cases; I did all this per hand - too much wasted time).

[Aitch]

I recently read this thread and thought I might try my hand at making an 8 line C-Spin PC.

Here's the first bag.

Almost always possible with an early I.

And the second bag options with PC percentages.

You can usually get one of these. There are other options, but these have the highest PC%.
Note the second has a low probability to be set up, as the Z blocks the T from being spun in. This also prevents a full TST, so it's a TSS unless the I has been placed.
I wonder if there's a tool for determining the percent chance of setting these up...

And going in more detail in each of the options. (In order of appearance in the above fumen.)






Note you may not get the TSD, as you you need to fill in the block beside with a J.

[Okey_Dokey]

Thank you for the reply. I tried to list some possible C-Spin setups with vertical T placements in this post in case you missed it. I gave up on C-Spins after some practice. Didn't work out too well for me. From the ones you listed, the one with the I + L overhang looks the most interesting to me. BTW there's also a 4-lines PC opener called Grace System that stacks the IOSZ pieces the same way in the first bag.

I have a tool for determining the percent chance of setting one bag up but it is too messed up to share. These should be the chances, if you assume softdrop and demand a T-Spin Triple. The 3 listed first bag setups have a chance of 68.13 % together. The 7 (or rather 6) listed second bag setups have a 74.40 % together (i.e. at least one of them is stackable for 74% of all 5040 bags; and whenever the one with the horizontal I piece is stackable, then another one is also stackable).

[Aitch]

I guess my post was kinda pointless, then, other than the I + L overhang.

You're right, I did miss that fumen. My bad.

Unfortunately, I'm a lot less smart than you, so I'll keep trying different setups bags to see if I can get high probability bags. If I find anything that works almost every time, I'll post it.

Forcing the TST limits the second bag, I believe. The probability of getting the second bag is quite a bit higher if you allow a TSS or a TSD. But you may not be able to offset garbage without the TST. I don't know how your program works, either, so maybe enforcing the TST was enforced .

[Okey_Dokey]

Your post wasn't useless. For example, you listed the percentages (and sorted the 2nd bag setups by them) and the PC solutions. I didn't even know that you can make a Fumen (listing all solutions and their stacking percentages) with knewJade's solution finder - must be a newer version. And sorry I should have updated the first post (but editing posts messes up the layout for posts with images, so I didn't bother).

If you just demand 1 line clear with the T piece, then you get the following working rates for the 2nd bag setups. All setups together should work for 82.66 % (4166/5040) of all bags. I am not 100 % sure that my tool is working correctly (I haven't even implemented T-Spin Triple detection, also note that I inserted a T piece placement in the corresponding location to calculate the chances and that the tool just works for 1 bag and not beyond).



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very late edit after the forums were closed down:

Aitch had posted a C-Spin with the first T piece placed vertically in another thread:

Sends between 24 and 16 garbage rows, depending on combos, and TSS or TSD or neither. Here's a write up for the opener and how to PC.

I saw a tweet with a similar build. Just the LOI placements are different in the first bag. The Perfect Clear rate is 99 % (or 61.3 % with a T-Spin beforehand).



And here are some placements that guarantee the PC no matter in which order the other pieces show up. The chance to make those placements is 21.9 % for 2 pieces, 56.3 % for 3 pieces and 92.5 % for 4 pieces.



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And here's a DT Cannon with the first T piece placed vertically. DT Cannons don't have a parity-changing line clear, so the Perfect Clear rate is not that high. It's still 51.9 % in the best case - much better than what you can achieve with a horizontal T placement in the first bag (horizontal = leave L or J on hold if PC + T-Spin, vertical = leave S, Z, O or I on hold if PC + T-Spin). While this DT Cannon requires an early I piece, the corresponding pseudo DT Cannons are usable for most bags (pseudo = S takes the place of O).

[Okey_Dokey]

I wrote some code that basically creates all setups that start with 2 T-Spin Doubles and lead into a decent PC chance immediately afterwards (6 & 8 lines PCs).

Download for the output

According to the data, what "ajanba TKI" seems to be among the best (at least that's how I called it on the wiki Opener page). Not sure why people barely use it.

Here's roughly how the output looks like (I tried to replicate the output of the setup-finder):

TSD -> TSD -> 8-th row PC

38 setups found

Setup 0



Best continuation: 100.00% PC success rate - 122 continuations with at least 60.95% PC success rate


(I had to shorten the Fumen/URL)

That finishes my TSD -> TSD -> PC study. In a few months from now, I will have a look at TSS -> TSD -> PC, provided the algorithm is fast enough to also handle that case.

[Cosine]

I liked that a lot. I really appreciate your work.

However, I can see some possible ones are missing because of the condition "no softdrop is used, no holes are made" and fumen below is an example.



Not a really big problem but just saying that some things are missing due to some conditions.

[Okey_Dokey]

Thanks. The setup with a hole after 2 bags is interesting because you can place O, S & Z pieces in any order, thus it will work for a high amount of bags (you just need a rather late J or T). 99 % may sound like a big number but it doesn't necessarily mean that the PC is easy to achieve. I don't think setups with holes can be on par with the best setups without holes. Maybe, I will try to implement that (holes after 2 bags) in 2 months. This would be rather easy to implement although I don't know if the program would finish then in a reasonable amount of time. Implementing softdrop is harder but doesn't extent the runtime too much (after examing all harddrops I could check for every hole, if there's a placement that can be inserted there - I have programmed something similar before)

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Here's a more complete download of the setup listing. This time it also mentions the chances to get a PC without hold and the chances to place the first 3 or 4 pieces in a way that guarantees a setup. This way I hope to illustrate better the quality of a playfield (among the 100 % PC rate ones).

Download

The one setup known from pwn's setup finder is among the best in every category (I think #2 at worst). The following playfield has the best chances (88 %) to guarantee a PC after placing 3 pieces. It can be reached after ajanba tki and also sometimes after a normal TKI setup:

[Okey_Dokey]

Thanks. This setup with a hole after 2 bags is interesting because you can place O, S & Z pieces in any order, thus it will work for a high amount of bags (you just need a rather late J or T). 99 % may sound like a big number but it doesn't necessarily mean that the PC is easy to achieve. I don't think setups with holes can be on par with the best setups without holes. Maybe, I will try to implement that (holes after 2 bags) in 2 months. This would be rather easy to implement although I don't know if the program would finish in a reasonable amount of time then. Implementing softdrop is harder but doesn't extend the runtime too much (after examing all harddrops I could check for every hole, if there's a placement that can be inserted there - I have programmed something similar before)

-----------------------

Here's a more complete download of the setup list. This time it also mentions the chances to get a PC without hold and the chances to place the first 3 or 4 pieces in a way that guarantees a PC. I hope this is a more sophisticated way to illustrate the quality of a playfield (i.e. rank the 100 % PC playfields).

Download

The one setup known from pwn's setup finder is among the best in every category (I think #2 at worst). The following playfield has the best chances (88 %) to guarantee a PC after placing 3 pieces. It can be reached after ajanba tki and also sometimes after a normal TKI setup:

[Aitch]

Cool stuff. Perhaps you could sort them by the least amount of solutions they have? A setup with a 90% PC and 10 solutions is arguably better than a 100% PC and 100 solutions. I know the more redundant solutions they have the better chance you can PC impromptu, but knowing what solution you should go for from the start is faster.

I've been thinking about TSD PCs lately too, but instead of 2 TSD 8/6 row PCs, I've been doing TSD 6 row PCs. 6 row PCs are usually hard, as you have to change your solution based on the first 2 pieces of the next bag, but not requiring a TSD in that bag allows you to PC somewhat consistently.

Here's the setup.


I can PC with around 80% consistency with this method. Also I should note Albatross has a theoretical 100% PC rate. ...But its not actually 100%. 6 bags don't work.