Perfect Clear Study - Phase 1

[myndzi]

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.

[Ravendarksky]

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

[Paul676]

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".

[Xdarkshadow8]

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

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.... >.<)....

[Panda]

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?

[zaphod77]

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.

[Shuey]

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".

[caffeine]

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

He's referring to the one myndzi posted (#Q=

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

[Shuey]

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 ): I believe that another playing forever pattern DOES exist, that has not yet been discovered.

[UJS3]

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?

[Shuey]

I came up with a similar solution to caff's, but still no cigar .  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...

[fumen]110@7eKxMWeAFLDmClcJSAVjiSAVG88A4N88A52jFDa9CM?C0/AAATaB3bBMhBTjBXiBTeBRcB9iBmfBAAA[/fumen]

[Kitaru]

I think these near-solutions are still important, even if they don't directly solve the problem initially proposed. Consider also special considerations for the final bag in Playing Forever -- 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.

[myndzi]

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

I think these near-solutions are still important, even if they don't directly solve the problem initially proposed. Consider also special considerations for the final bag in Playing Forever -- 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.

[Shuey]

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)...

[Kitaru]

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?