Tetris Perfect Clear Study Phase 2
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"Perfect Clear" - Clearing the playing field ("matrix") of all blocks ("tetrominos") in a game of Tetris.
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Perfect clears have been around since the birth of Tetris, but prior to most modern Tetris games, nothing "special" happened when a player cleared the playing field. The first known instance of players being rewarded for a perfect clear was in "Sega Tetris" (1988). Modern versions of Tetris also reward players for completing a perfect clear. Some Tetris versions refer to them as a "bravo" or "all clear (AC)". Alex Kerr (known as "kitaru" in the Tetris community) provided more details on this:
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"Several non-modern games since the 1988 version of Sega Tetris have rewarded players for building perfect clears. Other games that reward players for building perfect clears are Bloxeed, Tetris Plus's Classic mode (based on Sega's model and also has a big Special Bonus that multiplies Perfect Clear scores), TGM1 (1998) and TGM2 (2000) have a 4x score multiplier for perfect clear, and might be the first games with a "bravo" bonus in Versus (though he said he hasn't yet checked Bloxeed for this). It was a 2x lines sent bonus in TGM series games, except for TGM3 since they were probably assumed to be too "luck based" with Memory 4 and no patterns to play off of (by "patterns", we mean like Sega's famous Power On pattern, which was studied for maximizing Perfect Clears to counterstop the game as fast as possible. If you reset your Sega Tetris board to factory defaults, the first game's pattern was always the same!)"
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Ever since I first discovered perfect clearing, I've been very interested in it. But prior to mid-November 2011, I never really took the time to learn how to build/complete perfect clears. I had completed them a couple dozen times, but rarely because I actually intentionally set out to do it.
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Once I decided to study perfect clears, I chose to analyze the possibilities by reviewing 10 pieces at a time, since this is already a proven and common method of effectively building perfect clears. In doing so, my study focused on building perfect clears in the first 1/5th of the playing field; the bottom 4x10 section of the matrix consisting of rows 1 thru 4.
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Note: A Tetris playfield can also be "perfect cleared" with 5 pieces (2x10). And there are even ways of perfect clearing a single row, or 3 rows (but these situations occur when a larger section of the playfield has been filled/built up first, such as clearing three rows with some remainder pieces in the fourth row, then a final piece that clears the single row that's left (or vice versa). However, as I stated before, this study only focuses on 4x10 clearing.
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What you're about to review, if you are interested enough to invest the time, is my second in-depth study of perfect clears. Since I'm hoping to dig even deeper with this study, and will hopefully have help from others in the community, I like to think of this study as "Phase 2". This phase uses a legitimate guideline game as its reference, analyzing the first 3000+ tetrominos generated and sequenced by the game's randomizer. I decided to use Nullpomino Practice mode with the Standard-Friends rule (https://code.google.com/p/nullpomino/) because it's a modern guideline game (http://harddrop.com/wiki/Tetris_Guideline) with heavy support from the Tetris community, it's a commonly known game played by millions, and its piece randomizer is "perfect clear friendly". I also like the fact that I can set a fixed gravity in Practice mode. I'm hoping to look at other games and piece randomizers in future studies.
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NOTE 1: When playing Nullpomino using the settings outlined above, the game starts by introducing the player with one piece, and displays the upcoming pieces on the right side of the screen. So a player will be able to analyze his/her options by considering the current piece, the "next" piece, and four upcoming pieces ("previews"). This means that a player can consider 6 total pieces while the current piece is falling in the matrix. As soon as a player "holds" a piece, this increases the consideration to 7 total pieces. As previously stated, since this study focuses on 10 pieces at a time, combined with the consideration of hold pieces and preview pieces, the total pieces considered when attempting any perfect clear from a clean matrix is 12 (1 hold piece, 10 pieces from the current sequence, and the first piece from the next sequence); even though the total allowed in an actual game is limited to 7.
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NOTE 2: Since the official guideline games do not allow 180 degree rotations, any solutions involving them will not be considered or used in this study.
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With eventually enough data collected, I'm hoping to discover patterns that players can be aware of which will hopefully help give an increased chance of successfully building perfect clears on a much more consistent basis.
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Other thoughts: In the process of studying perfect clears, I originally came up with a few questions and/or theories that I had hoped could eventually be proven (I've listed them below). Since working on Phase 2 of this project, I've realized that it's likely impossible for someone to build endless perfect clears in a "live" game (because there's not enough preview pieces in order to successfully and consistently strategize the building of back-to-back perfect clears). I have however realized new things though. I'll respond to my own original questions below:
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1. Is there a "building pattern" (or more than one building pattern) that must be or can be maintained in order to keep successfully building perfect clears? (In the same way that the "playing forever" technique (http://harddrop.com/wiki/Playing_forever) must be maintained in order to successfully complete it over and over again).
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Answer (in my opinion): I wouldn't say that there's a "building pattern that must be maintained in order to successfully build endless back-to-back perfect clears", but I would simply say that it's clearly possible to build back-to-back perfect clears (and possibly "forever"). One thing I've noticed though is that it's NOT possible to build them endlessly without, on at least rare occasions, carrying over at least one piece from one sequence of ten pieces to the next sequence of ten pieces.
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2. Whether a specific building pattern exists or not, is it possibly as simple as "keep building perfect clears, one after another, and you'll be able to keep building them infinitely"?
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Answer: As stated above in answer 1, it is definitely possible to build them for a long time (the furthest I've tested so far is 300 back-to-back perfect clears), and may be possible to build them infinitely.
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3. If the answer to 1 or 2 is "true", if a player makes a mistake while building a perfect clear, if he/she can get the matrix back to a clean state, would he/she be able to immediately start building perfect clears again, starting with the first piece entering into the clean matrix (as long as they don't make a mistake again -or- until they make a mistake again)?
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Answer: Based on my experience thus far, I would say "yes".
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Things to be aware of in this documentation:
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I used a Google Sheets workbook to track the information and results from Phase 2 (Phase 1 was tracked in an Excel workbook).
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When I worked on Phase 1, I tracked the solutions in what I would call a "Parallel Timeline" (there were "original" sequences, and "actual" sequences). I tracked the solutions differently in Phase 2 because I realized it was no longer necessary to track them in the same way that I did in Phase 1 (with the main reason being that Phase I was attempting to prove if endless perfect clears were possible, whereas Phase 2's goal was to simply build 300 back-to-back perfect clears, since I was already confident that it was possible to build endless back-to-back perfect clears). Phase 2 clearly proved that the possibilities are nearly infinite.
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Now that I'm convinced that it's possible to build endless back-to-back perfect clears, my new goal is to eventually document every possible solution. In doing so, I'd like to also show that there are some solutions that are technically the same, and because they are, they both count as a single solution. Example: "Solution 1" has three groups of pieces that fit together to build a perfect clear, and "Solution 2" has the same three groups of pieces, but they're placed in different columns (Solution 1 has group 1 occupying columns 1-3, group 2 occupying columns 4-8, and group 3 occupying columns 9-10 / Solution 2 has group 1 occupying columns 8-10, group 2 occupying columns 1-5, and group 3 occupying columns 6-7). The Rubik's Cube could be used as another comparison. If you take a solved cube and you rotate one face clockwise, the state of the cube would technically be the same state of the cube if you rotated any one of the other five faces once clockwise (6 different states where only one face has been rotated once clockwise, but they're technically all the same state since they really only differ by orientation).
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Preface
Phase II Piece Sequence (Pt 1)
Phase II Piece Sequence (Pt 2)
Finishing Piece Statistics
Alternate Solutions
Credits