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Forums - Hard Drop - Tetris Community _ Strategy/Help _ Perfect Clear Study - Phase 1

Posted by: Shuey Dec 15 2011, 09:33 PM

Ever since seeing players build perfect clears, and seemingly with such ease, I've been fascinated with it. Since my strongest Tetris attribute is "pattern building", and since building perfect clears is essentially a 4x10 pattern, it wasn't long before I HAD to dedicate time to studying this skill in more detail.

When I first attempted to build a standard 4x10 perfect clear from a clean matrix, I was amazed at how difficult it was. I've cleared the playing field many times, but rarely when purposely setting out to build a 4x10 perfect clear from a clean matrix. I spent some time looking around in the forums and found some posts that talked about common methods and patterns to look for, and I also spent time watching videos of people building them on YouTube (this is something I'd actually like to add to this post soon)

Just before to diving into this study, I had discovered the "http://harddrop.com/wiki/Playing_forever" pattern a few weeks prior. The playing forever pattern was such a surprise to me because I never knew that the pieces spawned in a way that was a lot less random than most people are aware of. Knowing this led me to wonder if something similar could be discovered with regards to building perfect clears.

In order to start this study, I needed data. Since, at the time, I had just completed a game where I built two back-to-back playing forever patterns, I collected my piece sequences from there. I wanted to use a sequence that I knew had been used in an actual guideline game.

After a couple weeks or so of collecting and organizing the data, and with the help of several great people in the community, I am ready to "publish" part 1 of the study. I welcome anyone who is interested to please take the time to check it out, and post comments/feedback here. I'm hoping that this will be the beginning of something great!

https://sites.google.com/site/shuey187/tetris-perfect-clear-study-phase-1

*update 01 - 2011-12-16*
I updated the documentation with some info from Kitaru about the origins of perfect clears and which games rewarded players for completing them. Kitaru also said something that I hope will get other people excited as well: "I'm just starting to read your write-up, but I got to say this is probably one of the more important studies on Tetris in modern times, and I'm really excited to see if we can devise a way to 'solve' Tetris other than Playing Forever".

Posted by: Paul676 Dec 15 2011, 09:41 PM

Another interesting thing would be to ask whether PCs can be done infinitely without any twists, spins or slides given bag+10 previews+hold. Likewise without hold. Where does it break down and why?

Also, there's something about the imbalancing effect of zs and ss which necessitate Ls, Js or Ts to fix them to make a PC in 4 lines. I don't know exactly what mathematically does it, but it's something to do with the fact that they can't stack to form any shape which doesn't have a base where on one side, it is 1 block higher than the other, and the same goes for the top of that stack. Call it right and left if you stack the pieces horizontally.

Posted by: Barneey Dec 15 2011, 10:28 PM

Hey Shuey, I like what you're doing, it looks very interesting!
Let me know if there is anything I can do to help, I have too much spare time.

Posted by: Shuey Dec 15 2011, 11:10 PM

Something I forgot to mention previously, but I have since included it in the Preface: One of the most amazing things about this study is that we collectively completed 60+ perfect clears in a row using genuine piece sequences! The most I had seen prior to this was 20 by Noogy. Another amazing thing about this accomplishment is that we did it without using any 180 degree rotations.

It'll be awhile before I post the start of Phase 2, but I'm very anxious to keep pursuing this study! And I'm especially excited to have as many people as possible all participating Smile.png

Posted by: Shuey Dec 16 2011, 03:49 PM

I had a chat this morning with Kitaru and I'm hoping that our conversation will help spawn more interest in this topic. I'd be lying if I said I'm not a little bummed out that barely anyone has replied yet Frown.png. Below are all of Kitaru's initial thoughts, and my responses:

Kitaru:
I wonder if there is a nice way we can crowd source some of the work once we have a better idea about parts of it? Like a website where people can get assigned patterns and then input answers, and get points for finding solutions. Especially if the solutions improve upon an old one -- no hold solutions, no kick solutions, etc. Store all that stuff in a db and who knows... I think having a website to store a lot of this stuff would be big and then we need to think a bit about how to consolidate piece sequence info so we can minimize repeated effort. Like, where are we coming into this sequence from, has this PC been charted already? But yeah if it's just a game you play and you get credit for your unique PCs that'd be super fun. I think it'd be cool if there were a leaderboard and you'd get points for different things. Like, if previously there was a SRS twist only or 180 only or something solution and you improve upon it with a general one, you'd get more points than the restrictive solution. Solutions that require splits or trickiness might also be worth more for the leaderboards. Some day down the line I think it'd be sick if we had enough info to make an AI/screensaver that literally can play forever. Especially if we're clever enough to convert all of these into 20G-able solutions. I think the nice thing about PCs is it has a lot of vertical partitions. We might be able to figure out some property of moving these partitions about to double up solutions. Solutions that are valid for all partitions of the stack (i.e. don't require a left or right wall to execute) would probably be pretty valuable.

Shuey:
What would be the best way to go about having a website? To make it easy for users to contribute... and who and/or how should we manage it? Also, I like what you're saying there - this also makes me think that, if we see repeated patterns, saving info about that could also be helpful initially - also, with the "credit" concept for players, what could they use their credits for? There would need to be incentive. There's so much potential with this study, and I think one of my ultimate dream goals would be that we could eventually discover some kind of consistent, workable pattern, in the same way that someone discovered it with "playing forever". It's doubtful though that it exists, but if we can at least get to a point where we can recognize what to look for, I think players could have a very high success rate of building PCs, which could also lead to a "who can build the most back-to-back PCs?" The first challenge could be one where there's low gravity and pauses for thinking time (that's how Noogy did his 20 b2b pc's). Then eventually we could have a challenge where a player would have to try building as many b2b pc's as they could in a standard TF marathon game. Regarding an AI, that is one of the goals of this project! I was looking at Ryan Heise's study on "stacking" and I believe it will be possible for us to build an AI that analyzes pieces and builds PC's infinitely. This could also be used in the same way that Ryan used his AI: for humans to learn from it! And yeah, I'd like to get to the point where we can build PCs with more ingenuity where "awkward" placements aren't necessary in order to complete PCs.

Posted by: Paul676 Dec 16 2011, 04:03 PM

Should this be an inductive study rather than a deductive one? Because PCs are in effect mathematical entities, I'd think we should look at them deductively to see what is possible, rather than inductively.

e.g. why can't you PC with only S pieces. Why not with only S pieces and Z pieces? Why not with all S and Z pieces, and only one other piece? Why not with any number of S pieces and Z pieces and all O pieces? Then we might be able to obtain a proof of certain possibilities of PCs. If we do it inductively it might take a lot of time to sort out.

e.g. this seems to be the minimum number of other pieces than S and Z to use.

Using this, we might be able to find a pattern to solve tetris with all PCs given certain conditions, or at least know it's possible.

Posted by: Anonymous Dec 16 2011, 04:57 PM

Sounds interesting to me! Hot.png

Posted by: Shuey Dec 16 2011, 05:00 PM

Paul: Yes, one of the main intentions of this study is to dive into the mathematics of Tetris and use code to analyze all the data. We're going to find out a lot more by using computers to solve problems and give us more clues to things our mortal minds can't yet see.

I'm hoping to get Pineapple involved because I know this is exactly the kind of thing she likes most about Tetris.

Posted by: Ravendarksky Dec 16 2011, 05:17 PM

Don't stop posting fumens for me to try and solve just because computers can do it faster Frown.png

Posted by: Shuey Dec 16 2011, 07:43 PM

Hehe, I tell ya what: I think we still have a lot of "alternate" solutions we could come up with from our current data set. If you decide to come up with more non-180 rotation solutions, please don't hesitate to do so and to reply back so I can add the info into Phase 1's data set Smile.png. I was having fun building them too Wink.png.

Posted by: Ravendarksky Dec 16 2011, 09:37 PM

I'll do it myself then in a new thread =D

Posted by: myndzi Dec 17 2011, 10:44 PM

QUOTE(Shuey @ Dec 15 2011, 11:10 PM) *

The most I had seen prior to this was 20 by Noogy.

http://harddrop.com/forums/index.php?s=&showtopic=1186&view=findpost&p=39042
http://harddrop.com/forums/index.php?showtopic=3181&st=0 also has some good information.

If we say every perfect clear takes 4 lines, that's 10 pieces, but bags come in 7 pieces. 10 and 7 are relatively prime, so after 70 pieces (10 perfect clears) you will have a "new" bag from scratch. (Well, one of the pieces will have been used or be in hold).

Each bag loses three pieces, so your starting bags will be: 7, 4, 1, 5, 2, 6, 3, 7...
If you get a 2-line PC in there, you can shorten the cycle to five perfect clears - but this requires very specific pieces, so I don't think you can count on 5 PCs for an infinite cycle. (Though dealing with it wouldn't be a problem, since it can't give you any bag combination you couldn't already get).

Since it's obvious that this limit CAN be passed, the question you really need to answer is: is there any sequence of pieces that is a valid bag sequence but can NOT be made into a perfect clear?

In response to Paul's comment earlier, the reason S and Z unbalance things is because they force a 1-unit shift between rows/columns. It takes more pieces to make a 4-high block including a Z or an S than any other piece. t is included too, but since T is not balanced, it works better as a "fixer" piece; Z and S have the property that they are balanced AND offset.

Edit: in that vein, let's see somebody solve this one:
[o] iosz zsoitj

brackets are hold, osz is end of current bag, zsot is beginning of next bag. Also, if you can solve it with any other piece in hold, then it's not a solid counterexample; anyone else who feels like proposing fixes to the sequence is welcome Smile.png

Edit2: I realized that everybody's been assuming "optimal" perfect clears, but it may be possible to exploit the bag randomizer by stacking *taller* perfect clears. Not as impressive by a long shot, but I kind of doubt that every sequence is solvable. Easiest way to find out is to find an unsolvable sequence Smile.png

Posted by: Ravendarksky Dec 17 2011, 11:22 PM

QUOTE(myndzi @ Dec 17 2011, 10:44 PM) *

but I kind of doubt that every sequence is solvable. Easiest way to find out is to find an unsolvable sequence Smile.png


Bring it on!

Posted by: Paul676 Dec 18 2011, 12:10 AM

Yes myndzi, I think that's unsolvable, due to the lack of Js, Ls and Ts which are the only 'balancing' pieces to the S and Z. In fact, I think this is the only possible unsolvable sequence-type, where there is only 1 T, L or J in the 10 possible (i.e. 10 upcoming and 1 held). This (I think) means that every single starting sequence is PCable.

Posted by: myndzi Dec 18 2011, 12:13 AM

There's more to it than just the pieces that are present. I'm fairly certain there are plenty of un-PCable opening bags, but it depends on your available kicks. Anyway, if the point is to determine if it's possible to construct and endless PC loop, then this I think is the simplest way to find out Smile.png

vvv Nice! You are discovering my present it looks like Wink.png

Posted by: caffeine Dec 18 2011, 01:35 AM

QUOTE(myndzi @ Dec 17 2011, 04:44 PM) *
Edit: in that vein, let's see somebody solve this one:
[o] iosz zsoitj
I haven't found a solution yet, but this idea makes me think it could still be possible:


I'm pretty exhausted from a long day/week right now. I'm going to try some more maybe tomorrow.

Posted by: Shuey Dec 18 2011, 02:41 AM

I'm with caffeine in that I'm very exhausted from a long crazy day today, so I apologize that I don't have a lot to say at the moment. But I would like to say thanks to myndzi for the link to the 51 PC run; very cool!

One thing I will say is that it's hard for me to say at this moment that there is any sequence of pieces generated from the bag randomizer that can't be solved. I think the only way to to prove it would be to write a program that completes perfect clears - nobody has done this yet, and that's one of my goals with this project.

I'll reply back with more info in the next day or so - I gotta get some sleep. Thanks to everyone who is participating in this, I really appreciate it!

Posted by: Shuey Dec 18 2011, 05:30 AM

OK, I'm back for a minute, lol. I just looked at your sequence myndzi, and I don't mean to rain on your parade, but this sequence never happens from the bag randomizer. Pineapple sent me a text file with a sequence of 60 million pieces, generated from the bag randomizer. I searched the file and found no matches on your sequence.

Until someone can prove that there's an unsolvable sequence that comes from the bag randomizer, I believe it's possible to build perfect clears forever.

Posted by: perfectclear Dec 18 2011, 06:44 AM

QUOTE(Shuey @ Dec 17 2011, 10:30 PM) *

I just looked at your sequence myndzi, and I don't mean to rain on your parade, but this sequence never happens from the bag randomizer. Pineapple sent me a text file with a sequence of 60 million pieces, generated from the bag randomizer. I searched the file and found no matches on your sequence.


then your file is incomplete. you can tell because no two pieces are repeated before the space, and no two are repeated after the space, so they come from two bags. If I were you, I would inquire as to whether your file has sequences that start part of the way into the bag, as this one does.

Posted by: Kitaru Dec 18 2011, 01:50 PM

I generated a list of "bad bags" where LJ have already been consumed leading into normal ones if anyone is interested. It is around 9MB and has 604,800 entries. http://kitaru.1101b.com/hd/badbags.txt

Posted by: myndzi Dec 18 2011, 09:58 PM

QUOTE(Shuey @ Dec 18 2011, 05:30 AM) *

OK, I'm back for a minute, lol. I just looked at your sequence myndzi, and I don't mean to rain on your parade, but this sequence never happens from the bag randomizer. Pineapple sent me a text file with a sequence of 60 million pieces, generated from the bag randomizer. I searched the file and found no matches on your sequence.

Until someone can prove that there's an unsolvable sequence that comes from the bag randomizer, I believe it's possible to build perfect clears forever.


Computer random number generation isn't perfect, so it's quite possible that there are sequences that can't be generated by a particular random number generator. That doesn't make it an impossible sequence, and it is merely illustrative anyway. There are many pieces you could swap to have the same effect that might very well be in your incomplete sample.

I counted pieces wrong because of the first hold, so this isn't a 2nd turn sequence - but this bag is certainly possible. I mean, all you have to do is look at it: the first part is a valid bag, and the second part is a valid bag. Any piece is valid in hold. The full bags would be something like:

???o??? jtliosz zsoitjl
[o] iosz zsoitj

I don't mean to rain on your parade, but what are you doing with a "study" where you are counting incomplete data as complete and making arguments based on that without even moderate consideration?

Edit: partially beaten, but not with a clear example...

Edit2: Interestingly, there should be only 25,401,600 possible combinations of two bags, so it should be possible to explicitly generate them all without all that much trouble. [Ah, but you said 60 million pieces, which means you only have ~8.5 million bags, or about 1/3 of the total possibilities in that file]

Posted by: Paradox Dec 18 2011, 09:59 PM

QUOTE(caffeine @ Dec 18 2011, 01:35 AM) *

I haven't found a solution yet, but this idea makes me think it could still be possible:


I'm pretty exhausted from a long day/week right now. I'm going to try some more maybe tomorrow.


howd you get the T on the 9th frame in there?

Posted by: myndzi Dec 18 2011, 10:02 PM

He's just fitting shapes. As he said, he doesn't have a solution; the fumen is just a work in progress with a possible arrangement of pieces.

Posted by: Pineapple Dec 18 2011, 10:17 PM

QUOTE(Shuey @ Dec 18 2011, 05:30 AM) *

OK, I'm back for a minute, lol. I just looked at your sequence myndzi, and I don't mean to rain on your parade, but this sequence never happens from the bag randomizer. Pineapple sent me a text file with a sequence of 60 million pieces, generated from the bag randomizer. I searched the file and found no matches on your sequence.

Until someone can prove that there's an unsolvable sequence that comes from the bag randomizer, I believe it's possible to build perfect clears forever.

QUOTE(perfectclear @ Dec 18 2011, 06:44 AM) *

then your file is incomplete. you can tell because no two pieces are repeated before the space, and no two are repeated after the space, so they come from two bags. If I were you, I would inquire as to whether your file has sequences that start part of the way into the bag, as this one does.

By your standards, the file is very definitely incomplete.

There are 5040 ways to arrange one of each piece into a bag. For a file to contain all possible seams between two bags, it would have to have 25401600 seams in it, which means 177811207 pieces. I also believe that such an extended sequence would never be generated by any official Tetris game, even if you could play it forever. (And here, I must note that it is not yet known if you actually can play forever, since the current proof assume low gravity, and stacking techniques that just aren't possible at 20g, even with a simple arrangement of the columns)

We believe that the Random Generator does not make any attempt to make sure that each bag order happens before repeating a bag order (an "overbag"). I can't say for sure that it doesn't, as I don't believe that anyone has tried to test the Birthday Paradox with bag orders (85 bags is enough to make the probability of having a bag order occur twice be above 50%). Does anyone know if there is a video online of someone playing more than 250 lines (preferably more) in a guideline game? I could transcribe it, and see if there's a repeated bag order, to prove this definitely.

Likewise, we also believe that it makes no attempt to make sure that each bag seam appears before repeating a bag seam, although this is somewhat harder to demonstrate for sure (something like 6000 bags would be needed, to get above 50%).

Given a long enough output (and we're talking longer thamn we could probably ever generate from an official game), it would possible to count the number of occurances of each bag or bag seam. If there is no overbag, the probability of these occurances being exactly evenly spread tends to 0 very quickly.

So no, I do not expect a 63 million piece sequence to look like it was generated with an overbag, when it wasn't. If it does, I need to play the lottery more often...

Edit: For myndzi:
CODE
$ time bzcat 63m.bz2 | sed -r 's/(.{14,14})/\1\n/g' | grep "ioszzsoi"
ltjioszzsoijtl
jtlioszzsoijtl
ljtioszzsoitjl
ljtioszzsoiljt

And that's only looking at half of the seams...

Edit 2:
CODE
$ time bzcat 63m.bz2 | tail -c +8 | sed -r 's/(.{14})/\1\n/g' | grep "ioszzsoi"
ljtioszzsoiljt
tljioszzsoijtl
ljtioszzsoijlt

Posted by: Shuey Dec 19 2011, 01:08 AM

myndzi: Thanks for the reply and all the extra info. And I apologize if I came off in a negative way. That was never my intention, and I clearly responded out of ignorance. I definitely want this study to be exhaustive, and I don't want to miss ANYTHING. So I very much appreciate your input and thank you for it Smile.png.

Pineapple: I am SO glad to see you found this thread AND have become a part of it. I believe you have A LOT to offer to this study and I look forward to having your help with it!

Posted by: myndzi Dec 19 2011, 03:30 AM

If I was to try and design a random bag generator that didn't repeat bags, I would use a linear shift feedback register. If you just want to generate every possible combination of bags, there are algorithms to generate the Nth permutation of a set; you would just loop every pair of A and B where A is the number of the first bag and B the number of the second. It should be fairly easy to fit in a file.

Posted by: Kitaru Dec 19 2011, 01:42 PM

I generated a file where each line was some bag followed by some other bag, but all permutations as such is (7!)^2 = 25,401,600 lines of 16 characters each (including space/newline), which is uh... 450MB or so. It was some really simple Python but I'll be damned if I'm uploading the output lol.

Posted by: Shuey Dec 19 2011, 02:01 PM

Bit Torrent?...

LOL

Posted by: caffeine Dec 19 2011, 02:03 PM

QUOTE(myndzi @ Dec 18 2011, 09:30 PM) *

If you just want to generate every possible combination of bags, there are algorithms to generate the Nth permutation of a set; you would just loop every pair of A and B where A is the number of the first bag and B the number of the second. It should be fairly easy to fit in a file.

Are you talking about generating a list of possible sequences used for a PC? (I'm having trouble following.) If so, don't forget http://harddrop.com/forums/index.php?s=&showtopic=1956&view=findpost&p=55126.

Posted by: Ravendarksky Dec 19 2011, 06:21 PM

Unsolvable bag? It's avoidable by changing the previous PC, but that's not really the point =D

From a larger fumen I'm working on:

Posted by: caffeine Dec 19 2011, 06:55 PM

QUOTE(Ravendarksky @ Dec 19 2011, 12:21 PM) *

Unsolvable bag? It's avoidable by changing the previous PC, but that's not really the point =D


Posted by: Ravendarksky Dec 19 2011, 07:52 PM

Nice Smile.png

Posted by: caffeine Dec 20 2011, 03:28 AM

QUOTE(myndzi @ Dec 17 2011, 04:44 PM) *

Edit: in that vein, let's see somebody solve this one:
[o] iosz zsoitj

Very nice job, myndzi. This is the first legal sequence I couldn't solve. I spent a good 3.5 hours on it tonight (before this, the longest I ever spent on a sequence before solving it might've been around 20 minutes). The Z/S's and O's are incredibly awkward, and they prevent the constructions required for a T/J ending. Good luck to whoever else gives it a shot.
QUOTE(myndzi @ Dec 17 2011, 04:44 PM) *

the question you really need to answer is: is there any sequence of pieces that is a valid bag sequence but can NOT be made into a perfect clear?

Even if some sequences are unsolvable, that is not enough to refute the possibility of being able to do 10-piece PCs indefinitely. This is because of 1) the existence of hold and 2) the ability to solve a PC in multiple ways. If it is known that certain sequences are impossible, the player may be able to ensure he has the right piece in hold beforehand in order to avoid it.

Posted by: coolmaninsano Dec 20 2011, 05:21 AM

IPB Image

Posted by: arbanz Dec 20 2011, 05:33 AM

http://i39.tinypic.com/vdefys.png

Posted by: myndzi Dec 27 2011, 07:01 AM

QUOTE(caffeine @ Dec 20 2011, 03:28 AM) *

Very nice job, myndzi. This is the first legal sequence I couldn't solve. I spent a good 3.5 hours on it tonight (before this, the longest I ever spent on a sequence before solving it might've been around 20 minutes). The Z/S's and O's are incredibly awkward, and they prevent the constructions required for a T/J ending. Good luck to whoever else gives it a shot.

Even if some sequences are unsolvable, that is not enough to refute the possibility of being able to do 10-piece PCs indefinitely. This is because of 1) the existence of hold and 2) the ability to solve a PC in multiple ways. If it is known that certain sequences are impossible, the player may be able to ensure he has the right piece in hold beforehand in order to avoid it.


Lost this thread too. See what searching your name gets you?! Grin.png

You are allowed to change the hold piece to anything you want. This is a valid sequence that you could encounter in an actual game; if it (or another sequence) can't be solved even with whatever piece you want in hold, then that's a pretty solid counterexample towards being able to always perfect clear. There are some other cases that may affect it but not in a way you can predict, such as opting for a 4-line PC instead of a 2-line PC. Anyway, the point was simply that the easiest way to determine if it's possible is to define the boundaries first.

I do believe that many sequences can be perfect cleared, and I believe that certain sequence rules could be described to help with the process, too (things to do when pieces come before other pieces, or late/early; it all depends what stacks on top of what).

Anyway, I encourage you to have a go with any piece you want in hold; it'll be much harder to prove unsolvable, but 'caffeine couldn't find it' is pretty close to solid Smile.png

P.S. on a similar note, the rules for "continuous PC" should be defined. Are you allowed to make 2-line PCs? How about 6 or 8 lines? How about stacking two on top of each other? Etc.

Posted by: caffeine Dec 27 2011, 01:50 PM

QUOTE(myndzi @ Dec 27 2011, 01:01 AM) *

You are allowed to change the hold piece to anything you want. This is a valid sequence that you could encounter in an actual game; if it (or another sequence) can't be solved even with whatever piece you want in hold, then that's a pretty solid counterexample towards being able to always perfect clear.

In that case, it's pretty straightforward.

I'm still kind of bummed out about not finding a solution for the [O] case. Now that I'm looking at it again, I'm still not 100% convinced it's unsolvable. Maybe I should give it another go. Raven or Perfectclear: neither of you could find a solution for it?

Solution for deep drop:

Solution for recursive gravity:

Posted by: myndzi Dec 27 2011, 06:31 PM

Ha, nice. Any ideas how to modify it so that doesn't work out?

Posted by: caffeine Dec 27 2011, 06:36 PM

It would seem to me to be pretty unlikely that there would be a legal case that wouldn't work with any piece in hold.

Posted by: Ravendarksky Dec 28 2011, 11:29 AM

QUOTE(caffeine @ Dec 27 2011, 01:50 PM) *

I'm still kind of bummed out about not finding a solution for the [O] case. Now that I'm looking at it again, I'm still not 100% convinced it's unsolvable. Maybe I should give it another go. Raven or Perfectclear: neither of you could find a solution for it?


I managed to get it to a similar solution to yours..... Where only the T and J were needed to be placed.... BUT it wasn't the same way you did it.

I also got it to a I finish (no I piece though) and I think perhaps I got it to an L finish too but I'm not sure. I don't have any fumens saved.

Posted by: Paul676 Dec 28 2011, 11:55 AM

If you did get it to an L finish then you can just reverse it to give you the J finish.

Posted by: Ravendarksky Dec 28 2011, 12:00 PM

QUOTE(Paul676 @ Dec 28 2011, 11:55 AM) *

If you did get it to an L finish then you can just reverse it to give you the J finish.

No... from my memory reversing it required a box - I piece combination which couldn't be reversed due the piece order... I don't really remember sorry Frown.png

Posted by: perfectclear Dec 28 2011, 06:41 PM

I got 3 or 4 or 5 solutions that were close to right, but I do believe that the O, I, S, or Z holds should be impossible as it meets the conditions to my postulate that aaron quoted.

another thought occured to me. you guys are discussing "continuous clears" with the idea of any piece in hold. this is silly, as you can be forced to use a specific piece in the hold. say in the bag we are using as an example, we need a T, L, or J in hold. so if we get the sequence repeatedly we would consume whatever is in the hold and render one of the bags eventually impossible (im not saying necessarily the same 10 piece sequence over and over- thats stupid and impossible- Im saying sequences that all can only be solved with an L, J, or T in hold).

Still, nearly any sequence would be solvable for infinite pcs.

Posted by: Shuey Jun 7 2012, 01:44 PM

Rather than create a new "interim" thread, I'd like to use this one as a continuation of what we accomplished previously

I have new bags/sequences I'm trying to figure out and had a lot of great feedback and help last time. I look forward to seeing who takes part and what kinds of cool solutions we can come up with!

First up:


Posted by: caffeine Jun 7 2012, 01:55 PM


Posted by: Shuey Jun 7 2012, 02:04 PM

LOL, awesome!! Caff is back baby! Dude, every time you kill a PC that I don't know how to solve, I get so pumped Grin.png. You've always been a PC beast. Hopefully as I continue to work on these with you and others, I'll get closer to your level with them Smile.png.

Posted by: StevieSmiley Jun 7 2012, 07:16 PM

QUOTE(caffeine @ Dec 20 2011, 03:28 AM) *

Very nice job, myndzi. This is the first legal sequence I couldn't solve. I spent a good 3.5 hours on it tonight (before this, the longest I ever spent on a sequence before solving it might've been around 20 minutes). The Z/S's and O's are incredibly awkward, and they prevent the constructions required for a T/J ending. Good luck to whoever else gives it a shot.

Even if some sequences are unsolvable, that is not enough to refute the possibility of being able to do 10-piece PCs indefinitely. This is because of 1) the existence of hold and 2) the ability to solve a PC in multiple ways. If it is known that certain sequences are impossible, the player may be able to ensure he has the right piece in hold beforehand in order to avoid it.



i found a way but it was not in the same order, the s/z order block off possible solutions.
Im unsure how to add a fumen.. so from left to right iioottzzsj and you will see how the z/s blocks it off from being solvable. ( at least from the found pattern )

Posted by: caffeine Jun 7 2012, 07:40 PM

To add a fumen diagram to a forum post type the following:

Here's how to use the fumen quiz feature:

Posted by: Shuey Jun 8 2012, 12:02 AM

Dammit, I messed with this one for nearly 30 minutes and can't come up with a solution. And as much as I want caff to dominate this one, I'm also jealous that he's so damn good at these! LOL



Yes, got this one!!

Posted by: caffeine Jun 8 2012, 12:30 AM

Nice. Took me a while too.

Posted by: Shuey Jun 8 2012, 12:38 AM

Ah cool caff! I tried the same thing as you before I got my solution, but I was lost at step 7 and couldn't figure it out. Cool alternate!

Since there are so many people looking at the thread right now, I'll post the sequence I'm currently working on:


Posted by: Barneey Jun 8 2012, 12:38 AM

Is there a way to make specific bags playable in Nullpomino, so I won't have to fiddle around in Fumen?

Posted by: Shuey Jun 8 2012, 01:58 AM

QUOTE(Barneey @ Jun 8 2012, 12:38 AM) *

Is there a way to make specific bags playable in Nullpomino, so I won't have to fiddle around in Fumen?


You can use the sequencer I think, but I'm not familiar enough with how to use it Frown.png

Dang, I'm on a roll!
Solution to previous fumen:


caff, I'm gonna keep learning this technique until the world thinks of caff and Shuey as the PC kings Grin.png

Next sequence:


Aw snap, you got some competition caff! Grin.png
Solution to previous fumen:


Next sequence:


WTF is going on here! This is crazy Grin.png
Solution to previous fumen:


Next sequence:


O_o...
Solution already!?


Next sequence:


Got this one too, but I'm nervous that this point here may be a fork I'll have to return to later in order to generate an alternate, more solvable path.
Solution to previous fumen:


Next sequence:

Posted by: Paul676 Jun 8 2012, 02:05 AM

is there a methodology as to which fumens you give? Are you working towards a general definition of what is pc-able and what is not?

Posted by: Shuey Jun 8 2012, 02:19 AM

Solution to previous fumen:


QUOTE(Paul676 @ Jun 8 2012, 02:05 AM) *

is there a methodology as to which fumens you give? Are you working towards a general definition of what is pc-able and what is not?

The fumens are being generated from an actual piece sequence that was generated by the bag randomizer (the one TF uses), and I'm trying to create a PC from 10 consecutive pieces (or 11 using one hold), over and over again. I hope I explained that properly Grin.png.

Next sequence:

Posted by: carl256 Jun 8 2012, 03:17 AM

anything i can do to help?

Posted by: Shuey Jun 8 2012, 03:18 AM

QUOTE(carl256 @ Jun 8 2012, 03:17 AM) *

anything i can do to help?


Definitely Smile.png. Are you able to come up with a solution for the current fumen?

Posted by: carl256 Jun 8 2012, 03:22 AM

no, but i'll try.

Posted by: caffeine Jun 8 2012, 03:29 AM


Posted by: Shuey Jun 8 2012, 03:35 AM

Finally got it!
Solution to previous fumen:


Ah nice, caff got it too! Grin.png
But, uh oh, another possible fork in the road...

Since this is growing in complexity again, and since I REALLY need to stop "playing" and get ready to move to Florida, I think I'll put this "on hold" for at least the next week or so and come back and pick up where we left off. I'll also start documenting it on my end in more detail so I can keep track of the forks in case we need to consider going back to one or more of them.

Thanks to caff for participating again and see you all soon Smile.png

Posted by: XaeL Jun 8 2012, 05:39 AM

Did you know for just the beginning setup (7-3) there are
7! * 7C3 * 3! possible permutations?

thats 1 058 400

followed by
(4-6)
7C4 * 4! * 7C6 * 6!

followed by
(1-7-2)
7C1 * 7! * 7C2 * 2

followed by
(5-5)
7C5 * 5! * 7C5 * 5!

followed by
(2-7-1)
7C1 * 7! * 7C2 * 2

followed by
(6-4)
7C4 * 4! * 7C6 * 6!

followed by
(3-7)
7! * 7C3 * 3!

followed by
(7-3)
again.


I wrote a program that systematically creates the first 10 pieces of a game (i.e. 7-3):
http://users.tpg.com.au/onged/perms.zip


Usage: unzip
Run command prompt in admin mode.
run using

CODE

java -jar perms.jar > output.txt

then open output.txt. It's 26 megabytes.


To prove that you can play forever using perfect clears, you must:
prove that you can complete all (7-3), (4-6), (1-7-2), (5-5), (2-7-1),(6-4),(3-7) arrangements of bags
By solving each of these 6 unrelated subproblems we can prove whether or not we can play forever using PC.

Proving the first (7-3) involves proving or finding a way to solve each of the 1058400 starting entries...

Posted by: Paul676 Jun 8 2012, 01:45 PM

Yes, that's the point I'm trying to get at - we need to close off, say, all ones beginning with X pieces, or ending with X pieces, if we know somehow that all of them make a PC possible, and work on the harder ones. Then repeat the steps of exclusion until we find methods of PCing with harder bags, or bag-types which are impossible, rather than aimlessly doing PCs.

Posted by: Shuey Jun 8 2012, 01:49 PM

Paul, I totally agree. But I'm not knowledgeable or technical enough to know how to go about that. Also, all of the PCs I've been working on recently are not all being done "aimlessly". I'm actually working on creating a PC run consisting of 200 b2b PCs. Once it's completed, I'm going to upload it to YouTube and credit everyone who helped in the description.

Posted by: StevieSmiley Jun 10 2012, 03:03 AM


hope i did this right Sticking Out Tongue.png
it's the last one that was posted by shuey
guess I copyed the wrong one , but was still fun solving it Grin.png

Posted by: myndzi Jun 10 2012, 03:47 AM

QUOTE(Paul676 @ Jun 8 2012, 01:45 PM) *

Yes, that's the point I'm trying to get at - we need to close off, say, all ones beginning with X pieces, or ending with X pieces


How do you plan to approach that without an exhaustive search?

Edit: one approach might be to work with bigger pieces. If you know you can PC with a certain set of shapes, and you know that you can make those shapes with certain sets of pieces, then...

Here's a few:



(These apply to the "usual" setup and many of them can be flipped, etc. What needs to be done is to catalog which pieces MUST come before which other pieces, and then a number of permutations can be struck from the list. For something like this, hold usage should be ignored; the fringe scenario is carrying a piece through an entire bag, which is too many pieces for a perfect clear. First held piece and not unholding it gives a 6-piece bag which is covered in the bag combos. Any sequence you can make with hold you can also encounter naturally for these purposes.)

Posted by: Paul676 Jun 10 2012, 01:41 PM

myndzi: yes, that's what I was thinking about.

Posted by: Alucard Jul 1 2012, 11:12 PM

Still Reading all the comments for the study here, but myndzi, aren't you working on a new engine for KoS?
Tell me if I'm talking non sense, but wouldn't be a system like that one EXCLUSIVELY for PC counting and evaluation a good thing? something like the aforementioned site, but with an automatic DB entry recognition hmm

Well, I'll try my best to be with you guys soon, this is an extremely exciting iniciative! ^^
Congrats!

Posted by: Paul676 Feb 25 2013, 02:59 AM

I know it's a necro, but this is interesting: http://waka.nu/tetris/template/paf-table.html

Posted by: Shuey Feb 25 2013, 11:59 PM

That's pretty cool Paul! Too bad I don't have the patience to try to read and understand it all Grin.png.

Posted by: Panda Feb 26 2013, 02:38 PM

QUOTE(Alucard @ Jul 1 2012, 11:12 PM) *

Still Reading all the comments for the study here, but myndzi, aren't you working on a new engine for KoS?
Tell me if I'm talking non sense, but wouldn't be a system like that one EXCLUSIVELY for PC counting and evaluation a good thing? something like the aforementioned site, but with an automatic DB entry recognition hmm

Well, I'll try my best to be with you guys soon, this is an extremely exciting iniciative! ^^
Congrats!



YES you have the best forum username in existence!! I just finished watching both the regular and Ultimate seasons, Alucard is so effing badass lol Hot.png


Back on topic, is there currently a Perfect Clear tutorial on Harddrop? I've been stumped by this concept for a while and am only aware of the most generic perfect clear method, found all over the net on Youtube. If anyone could provide me a more in-depth guide that covers more tactics and PC solving methods, that would be very much appreciated.

Posted by: Paul676 Feb 26 2013, 10:23 PM

Strategy --> Guides --> http://harddrop.com/forums/index.php?showtopic=4143 --> http://harddrop.com/forums/index.php?showtopic=1985 Wink.png

Posted by: Panda Feb 26 2013, 11:35 PM

QUOTE(Paul676 @ Feb 26 2013, 10:23 PM) *

Strategy --> Guides --> http://harddrop.com/forums/index.php?showtopic=4143 --> http://harddrop.com/forums/index.php?showtopic=1985 Wink.png


Yes, I've read through the entire thread but once again I find only the most generic PC pattern and nothing new or useful besides Noogy's fumen which introduces a new PC pattern. What I'm looking for is a bigger more comprehensive list of all possible PC patterns so I can be flexible in my PC creation. Or at least some in-depth tips and techniques to creatively solve PC without resorting to these basic patterns. I am positive people are aware of such knowledge, as shown by professional KoS players, but I've yet to come across a guide that can teach me the same. It's so frustrating :/

Posted by: Pineapple Mar 15 2013, 07:31 AM

QUOTE(Paul676 @ Feb 25 2013, 02:59 AM) *
I know it's a necro, but this is interesting: http://waka.nu/tetris/template/paf-table.html

The page takes the initial opening setup, and talks about the probability of the next bag cooperating. The long table at the bottom enumerates all 840 possible sequences of the next 4 pieces. The smaller table above summarizes this table, grouping by the first piece of the second bag.

The key to failure after the 8th piece being a T seems to be an O that you are forced to place...

Posted by: Paul676 Mar 15 2013, 10:37 AM

exactly, and that's why it's so interesting - someone's done a full scale study into PC's! (almost...I bet they've decided that they may as well stick with the normal PC setup as you can't do anything else without knowledge of the next 4 pieces, and then seen how it goes from there.)

Posted by: Shuey Mar 15 2013, 11:24 PM

Well, I hope that this will somehow get people interested in this study again Grin.png.

Posted by: myndzi Mar 16 2013, 10:02 PM

One thing you can do situationally is build the left or right side only of the 'standard' opener; this will burn 3 pieces and with hold you'll be able to see all the necessary pieces to make alternate solutions with your remaining space. Due to 'parity' you're going to need to have a flat block and a jagged block anyway, so this isn't all that big of an impediment.

Posted by: Ravendarksky Mar 16 2013, 11:23 PM

I vaguely remember someone posting lots of bags of PCS and we found one which was unsolvable eventually didn't we?

Posted by: Paul676 Mar 17 2013, 12:04 AM

I recall something but I don't think it was a true bag. Also this was crying out for someone to give a rule like "no 180 twists".

Posted by: Xdarkshadow8 Mar 20 2013, 04:40 AM

QUOTE(Shuey @ Mar 15 2013, 11:24 PM) *

Well, I hope that this will somehow get people interested in this study again Grin.png.


Well, just found this (new tetris player, got into the game originally in puzzle pirates (suedo tetris game), then found tetris battle later. now trying to get better). So if you want help solving PCs I definitely can help. I'm a math major so I know a thing or two about this kind of thing. Honestly I'm not all too familiar with how tetris systems work (tetris battle isn't exactly very well documented.... >.<)....


Posted by: Panda Mar 23 2013, 06:42 PM





6 PC's in less than a minute against 101 in TB. Most of her PC's, such as the first one, follow the standard PC method. But some of them, such as the second one, seem improvisational and yet structured/methodical.

So what exactly is the unspoken method to follow here? Surely there must be some sort of guideline or trained intuition that allows her to solve these PC's in non-standard ways. Many of you here are capable of performing such improvisational PC's, could any of you carefully explain this PC solving method? Any particular tips or hints?

Posted by: zaphod77 Apr 2 2013, 03:44 AM

One thing.

if you find an unsolveable 10+1 sequence, then it's worthwhile to see if said sequence can be made into a 5+1 to avoid it. a 5 piece perfect clear is still a perfect clear.

also, infinite PC is a way to play forever. like the standard PC loop, it uses 10 bags, unless you get a 2 liner in there, in which case it will use five bags.

Posted by: Shuey Apr 14 2013, 05:43 PM

Ravendarksky: We never found a bag that was unsolvable during my two phases of study.

Paul: I don't recall a bag that wasn't "true", and the rule IS "no 180 twists" because my study was based on the guildeline games, which do not allow 180 twists.

Xdarkshadow8: By all means, I would love to have someone help get this study going again!

zaphod77: PCs can certainly be done as 2-line and 3-line clears as well. And the studies I was working on DID involve using them. If you look into the details of my studies, you'll see that we completed many 2-line clears while continually testing the theory of "infinite PCs".

Posted by: caffeine Apr 14 2013, 08:37 PM

QUOTE(Shuey @ Apr 14 2013, 12:43 PM) *

Ravendarksky: We never found a bag that was unsolvable during my two phases of study.


He's referring to the one myndzi posted (#Q=[O](I)OSZZSOITJ):


No one's really shown it to be "unsolvable" yet, but then again no one's figured out a method to solve it either.

Posted by: Shuey Apr 18 2013, 10:55 PM

I've built the playing forever pattern hundreds of times in the last year or so, and I've NEVER experienced a bag sequence where 8 pieces spawn before a T, L or J piece.

If someone is able to solve this sequence that myndzi posted, great. But I don't believe ANY of us will EVER see a sequence like this when playing a guideline game...

I really wish we could get some programmers involved in this study (Zirc, Kitaru, Pineapple, XaeL, etc) because their skills could crunch out all of details that still seem to be debatable... This would enable us to either narrow our efforts, or possibly even eliminate a lot of them; giving us a sooner chance to come up with something definitive.

Side note (mostly off-topic Grin.png): I believe that another playing forever pattern DOES exist, that has not yet been discovered.

Posted by: UJS3 Apr 19 2013, 07:05 AM

QUOTE(Shuey @ Apr 18 2013, 10:55 PM) *

I've built the playing forever pattern hundreds of times in the last year or so, and I've NEVER experienced a bag sequence where 8 pieces spawn before a T, L or J piece.

If someone is able to solve this sequence that myndzi posted, great. But I don't believe ANY of us will EVER see a sequence like this when playing a guideline game...

The probability of getting a sequence like that under bag randomizer is (3!4! / 7!)^2 = 1/1225

I've thought of writing a program that does an exhaustive perfect clear search given a specific piece sequence, but I'm too noob to do it. If you're given 10 pieces, you know that all pieces have to fit in a 10*4 rectangle, otherwise a PC is clearly impossible. This rectangle grows smaller as lines are cleared. Given that, there aren't very many legal piece placements for any one piece, and I think the search can be done quickly. Is there a way to get all legal piece placements from nullpo, given a piece and a field?

Posted by: Shuey Apr 19 2013, 11:26 PM

I came up with a similar solution to caff's, but still no cigar Frown.png. I don't see how 1. This is even possible to solve, and 2. Anyone would EVER get stuck with a piece sequence this ridiculous...


Posted by: Kitaru Apr 20 2013, 01:57 AM

I think these near-solutions are still important, even if they don't directly solve the problem initially proposed. Consider also http://harddrop.com/wiki/Playing_Forever#The_Final_Bag -- it's possible that the procedure will result in a one piece leave, but this can be worked into the first step of the next iteration. It's possible to leverage that Z in Hold for a "mini PC" TST -- a complete tiling still occurs, albeit beneath the fold and with the aid of a placement in the one proceeding it. Moreover, it might be that it's OK to have a partial solution if it can be interleaved into the next sequence for a deferred full solution. Then, I suppose, the next question to ponder would be if any particular forced leave would inhibit a Perfect Clear given a particular sequence of pieces to follow.

Posted by: myndzi Apr 21 2013, 04:13 AM

The point isn't whether you are likely to get it or not -- the question was if ALL SEQUENCES could be solved. It only takes one (improbable) counterexample to answer that question Wink.png

QUOTE(Kitaru @ Apr 20 2013, 01:57 AM) *

I think these near-solutions are still important, even if they don't directly solve the problem initially proposed. Consider also http://harddrop.com/wiki/Playing_Forever#The_Final_Bag -- it's possible that the procedure will result in a one piece leave, but this can be worked into the first step of the next iteration. It's possible to leverage that Z in Hold for a "mini PC" TST -- a complete tiling still occurs, albeit beneath the fold and with the aid of a placement in the one proceeding it. Moreover, it might be that it's OK to have a partial solution if it can be interleaved into the next sequence for a deferred full solution. Then, I suppose, the next question to ponder would be if any particular forced leave would inhibit a Perfect Clear given a particular sequence of pieces to follow.


Air 2 shows this to be quite useful. I get lots of "full tiles" if I am able to defer pieces. Air provides a bit more flexibility though, since you can "defer" them to another new stack, instead of on top of the existing one. It's greatly reduced in effectiveness, however.

Posted by: Shuey Apr 21 2013, 01:32 PM

I don't know why I never thought of this before, but I just looked at the original collective again and started wondering, "should we run through it again and try to limit ourselves to ONLY using each set of 10 consecutive pieces, without allowing ourselves to use a piece from the next set of 10 in each current set we're working on?". If we could run through the original 28 sets again like this, and still "solve" each set, it would not only provide more patterns/possibilities, but it would also lend itself to proving the theory even more (especially since nobody has yet come up with a way to use programming to prove it)...

Posted by: Kitaru Apr 21 2013, 02:48 PM

I think one of the things we would want to do to prune the problem is to figure out a method for proving sequences share an equivalent solution. Mobility and line clearing rules make this difficult, but we can try to scan sequences forward to ensure that certain key piece orderings are satisfied if we're able to properly identify what those rules should be.

As for automated verification, you'd want to be able to bot the solution given any of the resultant sequences that should be able to reach an equivalent solution based on proposed ordering rules. I'd imagine some problem sequences might slip through the gaps, but human verification of all sequences produced is obviously too much. However, reviewing just the ones that stand out from the pack would help us refine the rules or create new solution classes.

Or, I suppose, if you were to implement the rules of Tetris in reverse, you could produce a list of possible orderings from a drawn tiling by iterating over all possible ways to remove piece from the playfield?

Posted by: Shuey Apr 21 2013, 02:59 PM

I think it's also very safe to say that, when considering the limitation of only being able to focus on a maximum of 7 pieces at a time, it would pretty much be impossible for a human to recognize a solution (or planning for a solution) to ANY 10 piece sequence. But this obviously and ultimately wouldn't matter for all intensive purposes of what we're trying to determine. And I'm totally fine with that. Part of the joy of figuring out solutions to the patterns in the first phase of the study was simply in the fun of trying to figure out a solution and then finding one (without the limitation of only knowing 7 pieces at a time of course). But it would definitely be cool to find a "final" solution to the entire range of possibilities, even if it would never be humanly possible to actually do it 100% of the time. One could at least become better at the process, and increase his/her level of enjoyment/reward by learning how to see and complete more PCs than he/she was able to previously.

It's definitely going to take a lot more involvement than the few of us who have continued to revisit this study and its ultimate goal.

Thanks for continually being involved in this Kitaru! Smile.png

Posted by: Pineapple Apr 25 2013, 03:42 AM

QUOTE(Shuey @ Apr 21 2013, 02:32 PM) *
should we run through it again and try to limit ourselves to ONLY using each set of 10 consecutive pieces, without allowing ourselves to use a piece from the next set of 10 in each current set we're working on?

So, you can still use hold, but any piece that goes into hold has to be played as the 10th piece? That seems like a worthwhile idea. But I still think that looking into a leftovers-based system isn't a bad thing.

Also, while 10 pieces may seem to be the most obvious thing to do, it may be best to look at shorter and longer clears. 15, and 20 both have potential, and the occasional quick 5 may also be possible...

Posted by: Shuey Apr 25 2013, 11:35 PM

Thanks for replying Pineapple! I'm open to pretty much anything at this point because I can't do this study myself. If we're going to get anywhere, some solid coders (like you Smile.png ) are going to need to step in and crunch the numbers/data. Otherwise, mere man is extremely limited with what he/she/we can accomplish.

P.S. I realize there are ways that a PC could be built with 5 pieces (if a bag randomizer wasn't used), but I'm trying to understand how it could be possible using a bag randomizer?....

Posted by: MarioThePhenom Apr 26 2013, 01:34 AM

QUOTE(Shuey @ Apr 25 2013, 11:35 PM) *

P.S. I realize there are ways that a PC could be built with 5 pieces (if a bag randomizer wasn't used), but I'm trying to understand how it could be possible using a bag randomizer?....

the legendary myndzi does it with a 7 bag Sticking Out Tongue.png
you can see it on his second turn in http://kingofstackers.com/replay.php?gid=7113#game game

Posted by: Pineapple Apr 29 2013, 01:36 AM

QUOTE(Shuey @ Apr 26 2013, 12:35 AM) *
If we're going to get anywhere, some solid coders (like you Smile.png ) are going to need to step in and crunch the numbers/data.

I'm not sure how I feel about you calling me a "solid coder". What exactly would need to be crunched?

QUOTE
P.S. I realize there are ways that a PC could be built with 5 pieces (if a bag randomizer wasn't used), but I'm trying to understand how it could be possible using a bag randomizer?....

Across a bag seam is the only way. Although unlikely, as 3 pieces (S, T, Z) can't be used in a 5, and the other 4 are too useful elsewhere to hold on to.

Posted by: Shuey Apr 29 2013, 02:02 AM

I guess I should've elaborated more since I thought my message would've been understood correctly. First of all, myndzi is not legendary for doing a 2-line perfect clear. Building 2-line perfect clears is easy. My point was that, I don't understand how it could be possible from a clear playfield to get the exact pieces needed to complete it. You'd have to get two L's, two I's and an O, or two J's, two I's and an O, or two J's, two L's, and an O. When have you ever seen the bag randomizer produce this? I have played thousands of guideline games and never seen this happen. And I'm sure plenty of people on hard drop have played as many as hundreds of thousands of games and never seen this happen.

Pineapple: It's hard for me to even answer that question because I don't have a programming background. But I think if we could get everyone involved in this again, we could all help determine exactly what would need to be crunched.

Posted by: Pineapple Apr 30 2013, 01:49 AM

QUOTE(Shuey @ Apr 29 2013, 03:02 AM) *
My point was that, I don't understand how it could be possible from a clear playfield to get the exact pieces needed to complete it. You'd have to get two L's, two I's and an O, or two J's, two I's and an O, or two J's, two L's, and an O. When have you ever seen the bag randomizer produce this? I have played thousands of guideline games and never seen this happen. And I'm sure plenty of people on hard drop have played as many as hundreds of thousands of games and never seen this happen.

Ok. Time for a lesson in probability, combinatorics, and psychology, ELI5 edition.

First of all, read this: http://harddrop.com/wiki/Random_Generator#Snake_sequences

Now, I'm going to use the same method that the code uses there to show that not only is it possible for such sequences to be generated with bag, but that it actually happens. Throughout, | will indicate a bag seam, and (pieces) will mean all of the listed pieces in any order.

Let's take your first case, (LLIIO). This will happen as either (LI)|(LIO) or (LIO)|(LI). Because of symmetry, we need to compute just one of these, and then double it, so we'll use the first. A bag ending (LI) has a 1 in 21 chance of occuring (usually specified as a fraction, so 1/21). There are 7 possible pieces for the last piece, 6 remaining for the penultimate piece, and 2 possible orders for the pieces to appear in (either LI or IL). This is more often refered to as the http://en.wikipedia.org/wiki/Combination function. If you're using Google Calculator, use the syntax 7 choose 2. Similarly, a bag beginning (LIO) has a 1/35 chance of occuring.

For (LI)|(LIO) to happen, we need both a bag ending in (LI) and a bag beginning in (LIO), which means 1/21 * 1/35, which equals 1/735. It's also 1/735 for (LIO)|(LI), and another 2/735 for each of (JJIIO) and (JJLLO), which brings our total to 6/735 (1/122.5). This means that 0.82% of all bag seams contain one of these sequences. Given that there are 14 seams in each sprint (just over 100 pieces, which is 15 bags), you'll see the sequence roughly once every 9 sprints.

So why are you not noticing this? Well... that's because there's nothing really noticable about it. Plus there are 3 quite different groups (I+J, I+L, J+L), and a number of a ways that each group can appear (20 in all; not 24, because O appearing third can be either side of the seam), so it doesn't stick in the mind nearly as well as something like II (1/49, 2.5 times as likely, and a lot more memorable), TT (exactly the same as II), or the dreaded four snakes in a row (1/441, 3.6 times less likely, but a lot more memorable).

Plus, you've missed out on a way of clearing with 5 pieces:


Working out how likely (IJLOO) is is left as an exercise to the reader.

Posted by: Ethereal_Intellect Jun 24 2013, 12:03 AM

Hey guys, nice to see this thread is still somewhat active. I stumbled upon it last summer, and have been thinking about it on and off since.

QUOTE(UJS3 @ Apr 19 2013, 07:05 AM) *

I've thought of writing a program that does an exhaustive perfect clear search given a specific piece sequence, but I'm too noob to do it. If you're given 10 pieces, you know that all pieces have to fit in a 10*4 rectangle, otherwise a PC is clearly impossible. This rectangle grows smaller as lines are cleared. Given that, there aren't very many legal piece placements for any one piece, and I think the search can be done quickly. Is there a way to get all legal piece placements from nullpo, given a piece and a field?

I've pretty much done this.

I'm a student for Machine Intelligence and Robotics, and was able to pass it off as a project for university. We learned quite a bit in our classes, one big point was the idea of breaking down a problem into a simpler versions to find more solutions than possible in the original one to wind up with a smaller search set for next time. My code doesn't consider gravity, doesn't consider piece order, and winds up with a lot of duplicate solutions afterwards. But it works really quick, and it can run through all possible sequences (not just bag 7) in about 3-4 hours, giving 316 134 400 possible solutions. Obviously this is a way too big number, but it's still orders of magnitude smaller than the ways to place 10 pieces on the board, giving a good starting point for later.

It's also pretty pretty ridiculous that it would end so quickly, computers today are just crazy fast. Relevant:
http://art.penny-arcade.com/photos/i-vLsqnmM/0/950x10000/i-vLsqnmM-950x10000.jpg


To clean this up I would need to find a way of figuring out if a given solution is actually "build-able", given that I know which 10 pieces make it up and in which locations.

I'm planning to continue the project, though I'm a little busy the next few weeks. If anybody wants me to, I will make an effort to clean up the code a little, create an interface, and post a document describing the algorithm (I am good at designing quick algorithms, but horrible at coding readable, clear, or object orientated for now. The code is an absolute C++ mess and I will probably need to refactor it before continuing). Also, a cool thing is that I might be able to get access to a 50 PC computer cluster for heavy calculations if we get far enough Smile.png .

I apologize for not giving any proof for now, as I'm still cleaning the code up, I am just checking if anybody is still here. I'll get something together ASAP in the next few weeks. Feel free to ask for a specific sequence (or to put it better a set of 10 pieces) you'd like to see solved.

Posted by: insatiate Jun 24 2013, 12:35 AM

Really cool! Good work.

I think the most useful determination of 'buildable' would be without twists. This means that each piece would be dropped from the top, lines cleared, and that's it. This would be easy to calculate too. Depending on how you filter down your results, and since you say there are duplicates I'm hoping that means that you essentially try every piece/rotation/position... the straightforward way would be to try *dropping* every piece in every position, game-style, rather than create the tesselations and work backwards.

Twists are trickier, but in a 10x4 area not too bad and could be done with some simple shape templates or something rather than the full SRS kick system.

Finally, it is easy to filter a full set of data down to sequences possible with 7-bag, so I'd say keep going at it from the "all piece combinations" perspective, the results will be more useful.

As for a piece sequence to test, how about:

iosz zsoitj



Posted by: Ethereal_Intellect Jun 24 2013, 01:19 AM

^Dropping from the top would be simpler to calculate, but it would eliminate possible solutions, and that's not ideal. I'd rather keep all the wall-kicks because they would allow for more solutions. I'll try to figure out a way that's not too computationally intensive. What do you mean by shape templates?

It says it found 682 solutions (13 seconds). Here are a few of them
http://img841.imageshack.us/img841/4969/nbi.png

Reading them may be a little tough, but here's how.
They are ordered from top to bottom, left to right.
They are ASCII graphics, so they are a bit taller than wide, stretched out.
If a piece is broken, find the line that breaks it, and check if it's made of full pieces. That's the line that needs to be cleared first. (This uses the same drawing style as the mhtml document in the first post of the thread, the second example has a broken Z piece. Just keep in mind that the line without broken pieces is cleared first.)

Posted by: insatiate Jun 24 2013, 02:34 AM

Tesselations won't get all solutions. Some solutions will require that you clear lines first (skim) - that's why drop from the top. The only solutions you may miss out on are twists, but that's fewer and less useful than skimming solutions Smile.png

By shape templates I mean this:


These are shapes you can fill with the appropriate piece in those situations. The parts that matter will be the parts above the piece shape and to the left-right of it. For example, these will NOT work:



These are the important bits:



If one of the minos marked in red were filled, those kicks would work (the piece could be placed there). This is assuming NO 180 and standard SRS kicks, which seems the most reasonable assumption.

I've thought about this with regards to AIs that can do spins, and it seems to me that you should be able to determine if a placement is reachable by rotating the piece backwards and out through the reverse of the kick table... but at the same time, I feel like you could also just test the right spots around it directly to see if yes or no.

Edit: nevermind, I see that your solutions do account for skimming Smile.png

Worth noting from your examples is that none of them are actually stackable. If you examine the T piece, you can see that it is always either |- or -|, and that's a placement that must be done before the pieces that go on top of it - yet with the T almost last in the bag, even with hold, no such luck. Any chance you can program it or search the results to find a T in 180 orientation at the top of the 10x4 area? That is, like "T", point down, sitting on top...

Also also, I see that some of your solutions split pieces by two rows (say, a Z with the top part on the top row and the bottom part on the bottom row). These are pretty unlikely, especially the more pieces that are split, and some are impossible. You could reduce your result set by ensuring that there is a valid ordering for which every piece can be placed, and make it more useful by sorting first by the number of pieces that are 'split' and second by the magnitude of the split. No-split or one-split solutions are going to be the most likely to work. Two-split solutions may simply be harder to find to the human, but I imagine also that they are more restrictive to execute.

Here's an example of an impossible solution:



It is impossible because in order to clear the 2nd-from-bottom line, the vertical S piece (green) has to be stacked, but that piece is split above that position. The splits are dependent on each other in an impossible-to-execute fashion. You could reduce false positives here by requiring that every piece that is part of a line that splits another piece is whole.

P.S. do you have Skype or use IRC?

One other thing... more on-topic to the thread, if you consider the recent-ish discussion about 'parity', you will note that it (may?) only be possible to perfect clear with one T by stacking it vertically like this or skimming an L or J piece appropriately. Since there's only a J and T available they hay have to go together, both vertically, so that each row gets 2 minos contributed. In that case, there's no way to get any other piece into the hole left by them due to their shapes, so if these premises can be proven we could potentially prove this sequence impossible...

Posted by: Kitaru Jun 24 2013, 03:43 AM

QUOTE(Kitaru @ Apr 21 2013, 07:48 AM) *
Or, I suppose, if you were to implement the rules of Tetris in reverse, you could produce a list of possible orderings from a drawn tiling by iterating over all possible ways to remove piece from the playfield?
^This was my proposition for verifying if a solution can be built and with what orderings.

I have other projects competing for my time at the moment so I'm not sure if I can help code right now, but I might like to be included in Skype/Mumble/Teamspeak/etc. conversations if those end up happening. This has been on my to-do list for much too long.

Posted by: Ethereal_Intellect Jun 24 2013, 01:40 PM

Yeah, skimming was kind of the main feature. If you don't do skimming, the sequence you posted is unsolvable, 0 solutions. Also, without skimming the entire code ends in 10 seconds, not 3-4 hours Smile.png .

I'd like to avoid missing solutions as much as I can. Right now I'm concentrated on finding out if playing forever using perfect clears is even mathematically possible, and possible for a computer, and reducing solutions would make it even harder. For example without skimming, even this sequence is unsolvable. Without twists some solutions would be invalidated, like the one I'll post next.

About the split solutions, since this sequence requires skimming, all solutions will have at least 1 split piece. That's not really as scary as you make it out to be though. It just means the piece has to be placed after the pieces that make up the line that broke it. As for double line splits, they are hard, but still possible for the right sequence.

QUOTE(insatiate @ Jun 24 2013, 02:34 AM) *

Worth noting from your examples is that none of them are actually stackable. If you examine the T piece, you can see that it is always either |- or -|, and that's a placement that must be done before the pieces that go on top of it - yet with the T almost last in the bag, even with hold, no such luck. Any chance you can program it or search the results to find a T in 180 orientation at the top of the 10x4 area? That is, like "T", point down, sitting on top...

Also, are you sure that none of them are stackable? Here's the very first solution (top left)-
IO hold(S) Z drop(S) Z hold(S) OIT drop (S) J
iosz zsoitj

Pardon the very basic fumen, it's the first time I've used it.
http://harddrop.com/wiki/List_of_twists seems to say they are possible, though I don't know much more about twists than what I've read. I'd call myself an intermediate player, and twists are expert territory, I only learned they existed after I joined this website.
This is what I meant when I said we can't ignore twists. This would be impossible without twists.
Also, I went over the solutions visually, there doesn't seem to be one with a T orientation, though I may have missed it.

QUOTE(insatiate @ Jun 24 2013, 02:34 AM) *
You could reduce false positives here by requiring that every piece that is part of a line that splits another piece is whole.

It should technically already be like this, at least for the first split. The impossible example you posted isn't impossible because a split piece is a part of a line that splits another piece, but because there's no gravity to hold up the third line from the bottom as it's built (Specifically the blue piece). Like I said, no gravity for now. The line deletion order would be third from bottom, second from bottom, remaining 2 lines.

My Skype is ethereal_intellect by the way. I don't use it too much though, but I'll try to get on when I'm free. It still delivers messages sent when I'm offline when I log in right?
You can also reach me at ethereal_intellect at hotmail.com - it's connected to my phone and I'll get the message within minutes.

Posted by: UJS3 Jun 24 2013, 03:00 PM

That's a valid solution for IOSZ ZSOITJ, nice! Here's a quizzed fumen:


Now for a solution without hold Wink.png

Posted by: caffeine Jun 24 2013, 04:22 PM

Just a heads up, the sequence no one has solved yet is #Q=[O](I)OSZZSOITJ, not #Q=[](I)OSZZSOITJ (there should be an O-piece in the hold queue to start with).

Posted by: Ethereal_Intellect Jun 24 2013, 05:26 PM

Ok, so which bag in the bag 7 system can create this? We are talking about
[O](I)OSZZSOITJ
OIOSZZSOITJ
Or converted to numbers using this https://sites.google.com/site/polynominos/tetrominos
1=I
2=J
3=L
4=T
5=Z
6=O
7=S

OIOSZZSOITJ
61675 576142
Let's consider the 2 to be the beginning of the set for the next perfect clear.
61675 57614
Ordered
1145 566677
Ordered in a bag system
14567 1567 6
That's a 5+4+1 bag.

As Xael posted, the possible bags are

QUOTE(XaeL @ Jun 8 2012, 05:39 AM) *

To prove that you can play forever using perfect clears, you must:
prove that you can complete all (7-3), (4-6), (1-7-2), (5-5), (2-7-1),(6-4),(3-7) arrangements of bags
By solving each of these 6 unrelated subproblems we can prove whether or not we can play forever using PC.

A 5+4+1 is not a part of these bags. That means it was created by carrying over something from the last bag, and that the [O] is because of a bad solution of the last Perfect clear. To quote Shuey
QUOTE(Shuey @ Apr 21 2013, 01:32 PM) *

I don't know why I never thought of this before, but I just looked at the original collective again and started wondering, "should we run through it again and try to limit ourselves to ONLY using each set of 10 consecutive pieces, without allowing ourselves to use a piece from the next set of 10 in each current set we're working on?". If we could run through the original 28 sets again like this, and still "solve" each set, it would not only provide more patterns/possibilities, but it would also lend itself to proving the theory even more (especially since nobody has yet come up with a way to use programming to prove it)...

So one way to solve the unsolvable sequence would be to use the O properly in the last perfect clear.

As for the other way, that's a bit harder. There are 11 possibilities of where we can use the hold function to remove one of the 11 pieces to place it in the next perfect clear 10 piece set.
Original:
OIOSZZSOITJ
61675 576142
Versions: - (Using r instead of the removed piece to keep the numbers aligned)

r1675 576142
6r675 576142
61r75 576142
616r5 576142
6167r 576142
61675 r76142
61675 5r6142
61675 57r142
61675 576r42
61675 5761r2 Unsolvable - 0 solutions
61675 57614r Unsolvable - 0 solutions

The problem here is that with everything from the r forward we are blocking ourselves from using Hold ever again, since hold is now transporting the piece we want out of the set. And without hold, well, since we are ending with a TJ
QUOTE(insatiate @ Jun 24 2013, 02:34 AM) *
If you examine the T piece, you can see that it is always either |- or -|, and that's a placement that must be done before the pieces that go on top of it - yet with the T almost last in the bag, even with hold, no such luck.

Yeah, with no hold, we would need to find a solution with the J above the T, or the T in vertical position. This is a lot harder than it sounds, and is something that I would need to program, and not find by hand, and that might take a while. I still stand by using the O better in the last perfect clear as a cleaner solution.

Posted by: Blitz Jun 24 2013, 05:43 PM

QUOTE(Ethereal_Intellect @ Jun 24 2013, 05:26 PM) *


1=I
2=J
3=L
4=T
5=Z
6=O
7=S

OIOSZZSOITJ
61675 576142
Let's consider the 2 to be the beginning of the next bag


May I point out J is not the beginning of the next bag? You got two Z pieces in a row in the middle of that sequence. Two of the same piece in a row indicates the first Z piece is the last piece from bag 1 and the last Z piece is the first piece in bag 2.

Also, you can't solve that sequence in a normal game with or without the O piece on the hold. The only solution includes impossible kicks.


Posted by: Ethereal_Intellect Jun 24 2013, 05:49 PM

^Thanks for catching that. That was a mistake in terminology, what I meant to say is "Let's consider the 2 to be the beginning of the set for the next perfect clear."

Still, it's a good trick to see the bags as they are, thanks. I might use that sometime.
OIOSZZSOITJ
One possible way would be
O
IOSZ
ZSOITJ
Cool.

QUOTE(Blitz @ Jun 24 2013, 05:43 PM) *
Also, you can't solve that sequence in a normal game with or without the O piece on the hold. The only solutions includes impossible kicks.

Could you elaborate? We did solve it without the O piece, as IOSZ ZSOITJ as UJS3 posted. The problem is there because O is the first piece, which makes the pieces an impossible sequence in normal 7 bag play without carrying it over from a previous perfect clear (Three O pieces in 10 without a full 7 piece bag).

Posted by: caffeine Jun 24 2013, 06:33 PM

It might now be interesting to try to find a sequence where the only solution is one that leaves IOSZ and has O in the hold chamber.

Posted by: Blitz Jun 24 2013, 07:23 PM

Heres one that leaves IOSZ and has O in hold.

Posted by: UJS3 Jun 24 2013, 07:33 PM

QUOTE(caffeine @ Jun 24 2013, 04:22 PM) *

Just a heads up, the sequence no one has solved yet is #Q=[O](I)OSZZSOITJ, not #Q=[](I)OSZZSOITJ (there should be an O-piece in the hold queue to start with).


Ah, you're right. It's still a counterexample to perfectclear's earlier proposition though (any sequence with a T for the ninth piece, no T for the last piece, and only O, I, S, Z otherwise, doesn't allow a PC).

Posted by: Ethereal_Intellect Jun 24 2013, 08:16 PM

QUOTE(Blitz @ Jun 24 2013, 07:23 PM) *

Heres one that leaves IOSZ and has O in hold.


And here's a solution for the same sequence that doesn't leave O in hold

JJILOTSTLJIOSZ
JJI hold(Z) L drop(Z) O hold(T) S drop(T) TL --- JIOSZ

This is still a perfect clear, and leaves the bags intact, leaving JIOSZ for the next clear.
This is what I meant when I said that the last perfect clear could be done better to avoid the #Q=[O](I)OSZZSOITJ sequence from even appearing in the first place. However, for now, I can't prove it will always work. I'd need to finish the program/checker/builder first, and that can take weeks or longer.

Posted by: caffeine Jun 24 2013, 08:39 PM

I should've mentioned that it'd probably be best to start with a "fresh" bag with nothing in hold. Otherwise, you could use the same argument (the starting hold piece before the kill sequence's O-piece in hold could've been different had the PC two cycles ago been played differently).

Edit: The above will only show that there exists at least one sequence that isn't possible to play forever with PCs. It doesn't allow us to say that any starting sequence cannot be played out forever. However, one way to do that would be to find a sequence that satisfies the following conditions:

Such a kill-sequence, if it could be found, would show that a player cannot sustain continuous PCs forever no matter what pieces given from the start, even if he has infinite piece previews to plan ahead (assuming that #Q=[O](I)OSZZSOITJ cannot be solved). This is because inevitably he will run into such a sequence, and there's no way to solve it even if he plays earlier PCs in such a way that leaves him a different piece in the hold chamber.

Posted by: insatiate Jun 25 2013, 01:21 AM

QUOTE(caffeine @ Jun 24 2013, 04:22 PM) *

Just a heads up, the sequence no one has solved yet is #Q=[O](I)OSZZSOITJ, not #Q=[](I)OSZZSOITJ (there should be an O-piece in the hold queue to start with).


Any sequence buildable with hold can be represented as a sequence without hold. I left the hold off because I assume his program doesn't have support for it, and also doesn't need it. The extra O in hold essentially serves the purpose of ensuring that hold can't be used to help solve the sequence...

As for the division of the bag (seam), since the number of pieces in a bag and the number of pieces in a perfect clear are relatively prime, it should be possible to have the bag seam anywhere in the sequence to be valid. Recall that the O in hold is not part of the sequence, it is by definition out-of-sequence, so it shouldn't be counted as part of the leading bag. That aside, if you are testing every possible sequence, there's no reason to deal with hold (and it is simpler not to do so) -- to 'solve' a sequence involving hold, you can calculate directly all the potential reorderings given hold (not that many) and look each of them up in the output data.

Posted by: Ethereal_Intellect Jun 25 2013, 01:48 AM

QUOTE(caffeine @ Jun 24 2013, 08:39 PM) *

[*]Full bag + either TJL, TLJ, LJT, LTJ, JLT, or JTL.
[*]Forced to end up with O in hold no matter how you play it.[list]

Actually it doesn't even have to be an O. An I,Z or S would cause similar problems.
The question is do you have to end up with anything in hold, or can you just keep the L,J,T,J,T,L that were the 11th piece anyway.

Posted by: insatiate Jun 25 2013, 01:52 AM

Hold is one-way; once you use it you always have a piece in hold. But you don't have to swap it out, so you can still use whole bags in their 'pure' form if you so wish. The only way to truly remove a piece from the sequence would be to never hold until that piece.

Posted by: Ethereal_Intellect Jun 26 2013, 03:29 AM

QUOTE(Ethereal_Intellect @ Jun 25 2013, 01:48 AM) *

The question is do you have to end up with anything in hold, or can you just keep the L,J,T,J,T,L that were the 11th piece anyway.

Turns out the answer for this is sadly yes, sometimes you will be forced to use hold. I programmed the code to find unsolvable sequences for all the possible bag sets, and it does find a few. These are quite possibly not the only ones, but they are unsolvable without using the first piece of the next sequence of 10.

1=I
2=J
3=L
4=T
5=Z
6=O
7=S

(7-3) - Nothing found

(4-6) - 8 Unsolvable sets found
123567 1256 // translated as IJLZOS IJ ZO
123567 1257 // translated as IJLZOS IJ ZS
123567 1267 // translated as IJLZOS IJ OS
123567 1356 // translated as IJLZOS IL ZS
123567 1357 // translated as IJLZOS IL ZS
123567 1367 // translated as IJLZOS IL OS
123567 2567 // translated as IJLZOS JZ OS
123567 3567 // translated as IJLZOS LZ OS

(1-7-2) - Nothing found

(5-5) - As we can see these get reduced back to the 8 sets we had in (4-6)
12356 12567 - 123567 1256
12356 13567 - 123567 1356
12357 12567 - 123567 1257
12357 13567 - 123567 1357
12367 12567 - 123567 1267
12367 13567 - 123567 1367
12567 23567 - 123567 2567
13567 23567 - 123567 3567

(2-7-1) - Nothing found

(6-4) - Same as (4-6)

(3-7) - Nothing found

Since all the even 10 piece bag combinations ((4-6),(5-5),(2-7-1)) have these impossible sets within them, that means that we can also get a (1-1-7-1) situation when holding from (5-5) into a (2-7-1).

I haven't found any unsolvable sequences for (1-1-7-1) for now, which is in accordance with http://harddrop.com/forums/index.php?showtopic=1985&st=10&p=20773&#entry20773. So I guess the next step would be to find a way to see if all the 7+1+1+1 sequences are possible. Still, I thought these 8 were interesting enough to share.

Also, can anyone explain how I can watch http://harddrop.com/forums/index.php?showtopic=1186&st=470&p=39042&#entry39042? Also, how did he do this? Did he solve them in real time while playing, did he use a pre-set sequence that he knew in advance, and was it a guideline sequence? How many previews did he use?

Posted by: insatiate Jun 26 2013, 04:42 AM

Download Nullpomino
Download replay to nullpomino/replay
Run Nullpomino, select 'play replay', scroll to file and play.

It helps to name the replay something descriptive.

He did them manually, though used a lot of nullpomino lolkicks (180 kicks) that aren't generally valid. He came up with various partial setups to help, and I think used a very large number of previews(?).

I've done 10 in a row with normal SRS, and it's fairly difficult but not impossible (you can try your hand at it on king of stackers -- there's a perfect clear single player mode now)

As for bringing pieces in with hold, 1-1-7-1 is an extreme edge case but it is an interesting one. You'd have to also include 1-7-1-1 to the list. Proving one of these sequences to be unsolvable still falls victim to the 'just don't put yourself in that position' philosophy, however. For what we're talking about here, instead of looking for "any" solvable sequences, it seems useful to look for all of them. That is, the 1-1-7-1 case will only matter if it doesn't work for every piece as the hold piece (J-1-7-1, O-1-7-1, etc.) If an exhaustive search shows that they all work, you can pretty safely ignore this case.

Posted by: UJS3 Jun 26 2013, 09:11 AM

Also change the replay file extension to .rep for nullpo to recognize it.

QUOTE(Ethereal_Intellect @ Jun 26 2013, 03:29 AM) *

8 Unsolvable sets found

So these cannot be solved without hold, right? Does that take twists into account?

Posted by: Ethereal_Intellect Jun 26 2013, 01:53 PM

QUOTE(UJS3 @ Jun 26 2013, 09:11 AM) *

Also change the replay file extension to .rep for nullpo to recognize it.
So these cannot be solved without hold, right? Does that take twists into account?

These cannot be solved without using the first piece of the next 10. If you only had these 10 you can't find a solution, even with hold, even with twists, even with skimming, even by reordering them as much as you want to, even by teleporting them in place.

You must use hold on one of the pieces and carry it out of these 10 into the next 10.

Posted by: Blitz Jul 15 2013, 05:01 PM

I think I have identifyed a parity related problem that occurs in any sequence where the following applies.
1 J piece is used in the matrix
1 L piece is used in the matrix
1 T piece is used in the matrix
7 or 8 pieces that are not L J or T.

I believe a pc cannot be done with this sequence because no matter how you play them you will either encounter parity issues or encounter the need for a second L or J piece. Not going deeper into this. I'm right untill someone can prove me wrong by posting a pc fumen where they use a sequence ccontaining 1 L piece 1 T piece 1 J piece and any other pieces.
NOTE: ONLY USE ONE L J and T. Do not use 0, do not use 2.

Posted by: Ethereal_Intellect Jul 15 2013, 07:49 PM

^Here's one.

And just in case that quadruple I is bothering you, here's another

Posted by: insatiate Jul 15 2013, 11:28 PM

QUOTE
I'm right untill someone can prove me wrong


http://en.wikipedia.org/wiki/Philosophic_burden_of_proof

I just realized I only talked to caffeine about this and didn't post anything. I was studying the properties of various pieces as they affect the odd/even parity on a row-by-row basis. I imagine this is what you are approaching. In short, count the number of minos a piece in a given rotation adds to each row. All rows have to end up even. Certain pieces cannot make certain rows even if they are odd. This lends itself to a number of interesting observations, none of which I remember right now, but I see caffeine lurking the thread so maybe he'll want to go into detail Smile.png

Posted by: myndzi Jul 19 2013, 10:58 PM

Just something I was doing out of boredom..




I certainly didn't cover them all, but I got many of the ones I've found useful.

Posted by: zaphod77 Oct 21 2013, 05:43 AM

Okay, now try a 10-11 piece sequence that has

a) bag 1.
b) pieces 8-11 have no duplicates, and no I L or T

Can one of these be made into a PC?

hmm. suppose it can, if you spin in the second z when it arrives in the second bag and hold the J.

The vertical S placement is what causes the parity after lineclear to change, to accommodate the T piece.

Posted by: Aaron Oct 21 2013, 05:48 AM


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